Master Equations for Correlated Quantum Channels
NASA Astrophysics Data System (ADS)
Giovannetti, V.; Palma, G. M.
2012-01-01
We derive the general form of a master equation describing the reduced time evolution of a sequence of subsystems “propagating” in an environment which can be described as a sequence of subenvironments. The interaction between subsystems and subenvironments is described in terms of a collision model, with the irreversible dynamics of the subenvironments between collisions explicitly taken into account. In the weak coupling regime, we show that the collisional model produces a correlated Markovian evolution for the joint density matrix of the multipartite system. The associated Lindblad superoperator contains pairwise terms describing cross correlation between the different subsystems. Such a model can describe a broad range of physical situations, ranging from quantum channels with memory to photon propagation in concatenated quantum optical systems.
Master Equation for a Quantum Particle in a Gas
Hornberger, Klaus
2006-08-11
The equation for the quantum motion of a Brownian particle in a gaseous environment is derived by means of S-matrix theory. This quantum version of the linear Boltzmann equation accounts nonperturbatively for the quantum effects of the scattering dynamics and describes decoherence and dissipation in a unified framework. As a completely positive master equation it incorporates both the known equation for an infinitely massive Brownian particle and the classical linear Boltzmann equation as limiting cases.
The Complexity of Relating Quantum Channels to Master Equations
NASA Astrophysics Data System (ADS)
Cubitt, Toby S.; Eisert, Jens; Wolf, Michael M.
2012-03-01
Completely positive, trace preserving (CPT) maps and Lindblad master equations are both widely used to describe the dynamics of open quantum systems. The connection between these two descriptions is a classic topic in mathematical physics. One direction was solved by the now famous result due to Lindblad, Kossakowski, Gorini and Sudarshan, who gave a complete characterisation of the master equations that generate completely positive semi-groups. However, the other direction has remained open: given a CPT map, is there a Lindblad master equation that generates it (and if so, can we find its form)? This is sometimes known as the Markovianity problem. Physically, it is asking how one can deduce underlying physical processes from experimental observations. We give a complexity theoretic answer to this problem: it is NP-hard. We also give an explicit algorithm that reduces the problem to integer semi-definite programming, a well-known NP problem. Together, these results imply that resolving the question of which CPT maps can be generated by master equations is tantamount to solving P = NP: any efficiently computable criterion for Markovianity would imply P = NP; whereas a proof that P = NP would imply that our algorithm already gives an efficiently computable criterion. Thus, unless P does equal NP, there cannot exist any simple criterion for determining when a CPT map has a master equation description. However, we also show that if the system dimension is fixed (relevant for current quantum process tomography experiments), then our algorithm scales efficiently in the required precision, allowing an underlying Lindblad master equation to be determined efficiently from even a single snapshot in this case. Our work also leads to similar complexity-theoretic answers to a related long-standing open problem in probability theory.
Quantum Markovian master equation for scattering from surfaces
Li, Haifeng; Shao, Jiushu; Azuri, Asaf; Pollak, Eli Alicki, Robert
2014-01-07
We propose a semi-phenomenological Markovian Master equation for describing the quantum dynamics of atom-surface scattering. It embodies the Lindblad-like structure and can describe both damping and pumping of energy between the system and the bath. It preserves positivity and correctly accounts for the vanishing of the interaction of the particle with the surface when the particle is distant from the surface. As a numerical test, we apply it to a model of an Ar atom scattered from a LiF surface, allowing for interaction only in the vertical direction. At low temperatures, we find that the quantum mechanical average energy loss is smaller than the classical energy loss. The numerical results obtained from the space dependent friction master equation are compared with numerical simulations for a discretized bath, using the multi-configurational time dependent Hartree methodology. The agreement between the two simulations is quantitative.
Fission rate and transient time with a quantum master equation
Sargsyan, V. V.; Palchikov, Yu. V.; Antonenko, N. V.; Kanokov, Z.; Adamian, G. G.
2007-12-15
The induced nuclear fission is considered a transport process over the fission barrier underlying dissipative forces. Using a quantum master equation for the reduced density matrix, the influence of microscopical diffusion coefficients on the total fission time and transient time is studied. The influence of transient effects on the probability of the first-chance fission is estimated. For different temperatures and friction coefficients, the quasistationary fission rate is compared with the analytical Kramers formula.
Post-Markovian quantum master equations from classical environment fluctuations
NASA Astrophysics Data System (ADS)
Budini, Adrián A.
2014-01-01
In this paper we demonstrate that two commonly used phenomenological post-Markovian quantum master equations can be derived without using any perturbative approximation. A system coupled to an environment characterized by self-classical configurational fluctuations, the latter obeying a Markovian dynamics, defines the underlying physical model. Both Shabani-Lidar equation [A. Shabani and D. A. Lidar, Phys. Rev. A 71, 020101(R) (2005), 10.1103/PhysRevA.71.020101] and its associated approximated integrodifferential kernel master equation are obtained by tracing out two different bipartite Markovian Lindblad dynamics where the environment fluctuations are taken into account by an ancilla system. Furthermore, conditions under which the non-Markovian system dynamics can be unraveled in terms of an ensemble of measurement trajectories are found. In addition, a non-Markovian quantum jump approach is formulated. Contrary to recent analysis [L. Mazzola, E. M. Laine, H. P. Breuer, S. Maniscalco, and J. Piilo, Phys. Rev. A 81, 062120 (2010), 10.1103/PhysRevA.81.062120], we also demonstrate that these master equations, even with exponential memory functions, may lead to non-Markovian effects such as an environment-to-system backflow of information if the Hamiltonian system does not commutate with the dissipative dynamics.
Decoherence and quantum-classical master equation dynamics
NASA Astrophysics Data System (ADS)
Grunwald, Robbie; Kapral, Raymond
2007-03-01
The conditions under which quantum-classical Liouville dynamics may be reduced to a master equation are investigated. Systems that can be partitioned into a quantum-classical subsystem interacting with a classical bath are considered. Starting with an exact non-Markovian equation for the diagonal elements of the density matrix, an evolution equation for the subsystem density matrix is derived. One contribution to this equation contains the bath average of a memory kernel that accounts for all coherences in the system. It is shown to be a rapidly decaying function, motivating a Markovian approximation on this term in the evolution equation. The resulting subsystem density matrix equation is still non-Markovian due to the fact that bath degrees of freedom have been projected out of the dynamics. Provided the computation of nonequilibrium average values or correlation functions is considered, the non-Markovian character of this equation can be removed by lifting the equation into the full phase space of the system. This leads to a trajectory description of the dynamics where each fictitious trajectory accounts for decoherence due to the bath degrees of freedom. The results are illustrated by computations of the rate constant of a model nonadiabatic chemical reaction.
Nonadiabatic quantum Liouville and master equations in the adiabatic basis
Jang, Seogjoo
2012-12-14
A compact form of nonadiabatic molecular Hamiltonian in the basis of adiabatic electronic states and nuclear position states is presented. The Hamiltonian, which includes both the first and the second derivative couplings, is Hermitian and thus leads to a standard expression for the quantum Liouville equation for the density operator. With the application of a projection operator technique, a quantum master equation for the diagonal components of the density operator is derived. Under the assumption that nuclear states are much more short ranged compared to electronic states and assuming no singularity, a semi-adiabatic approximation is invoked, which results in expressions for the nonadiabatic molecular Hamiltonian and the quantum Liouville equation that are much more amenable to advanced quantum dynamics calculation. The semi-adiabatic approximation is also applied to a resonance energy transfer system consisting of a donor and an acceptor interacting via Coulomb terms, and explicit detailed expressions for exciton-bath Hamiltonian including all the non-adiabatic terms are derived.
Dynamics of open quantum spin systems: An assessment of the quantum master equation approach.
Zhao, P; De Raedt, H; Miyashita, S; Jin, F; Michielsen, K
2016-08-01
Data of the numerical solution of the time-dependent Schrödinger equation of a system containing one spin-1/2 particle interacting with a bath of up to 32 spin-1/2 particles is used to construct a Markovian quantum master equation describing the dynamics of the system spin. The procedure of obtaining this quantum master equation, which takes the form of a Bloch equation with time-independent coefficients, accounts for all non-Markovian effects inasmuch the general structure of the quantum master equation allows. Our simulation results show that, with a few rather exotic exceptions, the Bloch-type equation with time-independent coefficients provides a simple and accurate description of the dynamics of a spin-1/2 particle in contact with a thermal bath. A calculation of the coefficients that appear in the Redfield master equation in the Markovian limit shows that this perturbatively derived equation quantitatively differs from the numerically estimated Markovian master equation, the results of which agree very well with the solution of the time-dependent Schrödinger equation. PMID:27627265
Magnetic adatoms as memory bits: A quantum master equation analysis
NASA Astrophysics Data System (ADS)
Karlewski, Christian; Marthaler, Michael; Märkl, Tobias; Balashov, Timofey; Wulfhekel, Wulf; Schön, Gerd
2015-06-01
Due to underlying symmetries, the ground states of magnetic adatoms may be highly stable, which opens perspectives for application as single-atom memory. A specific example is a single holmium atom (with J =8 ) on a platinum (111) surface for which exceptionally long lifetimes were observed in recent scanning tunneling microscopy studies. For control and read-out, the atom must be coupled to electronic contacts. Hence the spin dynamics of the system is governed by a quantum master equation. Our analysis shows that, in general, it cannot be reduced to a classical master equation in the basis of the unperturbed crystal-field Hamiltonian. Rather, depending on parameters and control fields, "environment-induced superselection" principles choose the appropriate set of basis states, which in turn determines the specific relaxation channels and lifetimes. Our simulations suggest that in ideal situations the lifetimes should be even longer than observed in the experiment. We, therefore, investigate the influence of various perturbations. We also study the initialization process of the state of the Ho atom by applied voltage pulses and conclude that fast, high fidelity preparation, on a 100 -ns time scale, should be possible.
Number-resolved master equation approach to quantum measurement and quantum transport
NASA Astrophysics Data System (ADS)
Li, Xin-Qi
2016-08-01
In addition to the well-known Landauer-Büttiker scattering theory and the nonequilibrium Green's function technique for mesoscopic transports, an alternative (and very useful) scheme is quantum master equation approach. In this article, we review the particle-number ( n)-resolved master equation ( n-ME) approach and its systematic applications in quantum measurement and quantum transport problems. The n-ME contains rich dynamical information, allowing efficient study of topics such as shot noise and full counting statistics analysis. Moreover, we also review a newly developed master equation approach (and its n-resolved version) under self-consistent Born approximation. The application potential of this new approach is critically examined via its ability to recover the exact results for noninteracting systems under arbitrary voltage and in presence of strong quantum interference, and the challenging non-equilibrium Kondo effect.
Convolutionless Non-Markovian master equations and quantum trajectories: Brownian motion
Strunz, Walter T.; Yu Ting
2004-05-01
Stochastic Schroedinger equations for quantum trajectories offer an alternative and sometimes superior approach to the study of open quantum system dynamics. Here we show that recently established convolutionless non-Markovian stochastic Schroedinger equations may serve as a powerful tool for the derivation of convolutionless master equations for non-Markovian open quantum systems. The most interesting example is quantum Brownian motion (QBM) of a harmonic oscillator coupled to a heat bath of oscillators, one of the most employed exactly soluble models of open system dynamics. We show explicitly how to establish the direct connection between the exact convolutionless master equation of QBM and the corresponding convolutionless exact stochastic Schroedinger equation.
Exact non-Markovian master equations for multiple qubit systems: Quantum-trajectory approach
NASA Astrophysics Data System (ADS)
Chen, Yusui; You, J. Q.; Yu, Ting
2014-11-01
A wide class of exact master equations for a multiple qubit system can be explicitly constructed by using the corresponding exact non-Markovian quantum-state diffusion equations. These exact master equations arise naturally from the quantum decoherence dynamics of qubit system as a quantum memory coupled to a collective colored noisy source. The exact master equations are also important in optimal quantum control, quantum dissipation, and quantum thermodynamics. In this paper, we show that the exact non-Markovian master equation for a dissipative N -qubit system can be derived explicitly from the statistical average of the corresponding non-Markovian quantum trajectories. We illustrated our general formulation by an explicit construction of a three-qubit system coupled to a non-Markovian bosonic environment. This multiple qubit master equation offers an accurate time evolution of quantum systems in various domains, and paves the way to investigate the memory effect of an open system in a non-Markovian regime without any approximation.
Non-equilibrium effects upon the non-Markovian Caldeira-Leggett quantum master equation
Bolivar, A.O.
2011-05-15
Highlights: > Classical Brownian motion described by a non-Markovian Fokker-Planck equation. > Quantization process. > Quantum Brownian motion described by a non-Markovian Caldeira-Leggett equation. > A non-equilibrium quantum thermal force is predicted. - Abstract: We obtain a non-Markovian quantum master equation directly from the quantization of a non-Markovian Fokker-Planck equation describing the Brownian motion of a particle immersed in a generic environment (e.g. a non-thermal fluid). As far as the especial case of a heat bath comprising of quantum harmonic oscillators is concerned, we derive a non-Markovian Caldeira-Leggett master equation on the basis of which we work out the concept of non-equilibrium quantum thermal force exerted by the harmonic heat bath upon the Brownian motion of a free particle. The classical limit (or dequantization process) of this sort of non-equilibrium quantum effect is scrutinized, as well.
Calculating work in weakly driven quantum master equations: Backward and forward equations
NASA Astrophysics Data System (ADS)
Liu, Fei
2016-01-01
I present a technical report indicating that the two methods used for calculating characteristic functions for the work distribution in weakly driven quantum master equations are equivalent. One involves applying the notion of quantum jump trajectory [Phys. Rev. E 89, 042122 (2014), 10.1103/PhysRevE.89.042122], while the other is based on two energy measurements on the combined system and reservoir [Silaev et al., Phys. Rev. E 90, 022103 (2014), 10.1103/PhysRevE.90.022103]. These represent backward and forward methods, respectively, which adopt a very similar approach to that of the Kolmogorov backward and forward equations used in classical stochastic theory. The microscopic basis for the former method is also clarified. In addition, a previously unnoticed equality related to the heat is also revealed.
Nonequilibrium quantum dynamics in the condensed phase via the generalized quantum master equation
NASA Astrophysics Data System (ADS)
Zhang, Ming-Liang; Ka, Being J.; Geva, Eitan
2006-07-01
The Nakajima-Zwanzig generalized quantum master equation provides a general, and formally exact, prescription for simulating the reduced dynamics of a quantum system coupled to a quantum bath. In this equation, the memory kernel accounts for the influence of the bath on the system's dynamics, and the inhomogeneous term accounts for initial system-bath correlations. In this paper, we propose a new approach for calculating the memory kernel and inhomogeneous term for arbitrary initial state and system-bath coupling. The memory kernel and inhomogeneous term are obtained by numerically solving a single inhomogeneous Volterra equation of the second kind for each. The new approach can accommodate a very wide range of projection operators, and requires projection-free two-time correlation functions as input. An application to the case of a two-state system with diagonal coupling to an arbitrary bath is described in detail. Finally, the utility and self-consistency of the formalism are demonstrated by an explicit calculation on a spin-boson model.
Closed description of arbitrariness in resolving quantum master equation
NASA Astrophysics Data System (ADS)
Batalin, Igor A.; Lavrov, Peter M.
2016-07-01
In the most general case of the Delta exact operator valued generators constructed of an arbitrary Fermion operator, we present a closed solution for the transformed master action in terms of the original master action in the closed form of the corresponding path integral. We show in detail how that path integral reduces to the known result in the case of being the Delta exact generators constructed of an arbitrary Fermion function.
Fleming, C.H.; Roura, Albert; Hu, B.L.
2011-05-15
Research Highlights: > We study the model of a quantum oscillator linearly coupled to a bath of oscillators. > We derive the master equation and solutions for general spectra and temperatures. > We generalize to cases with an external force and arbitrary number of oscillators. > Other derivations have incorrect diffusion and force response for nonlocal damping. > We give exact results for ohmic, sub-ohmic and supra-ohmic environments. - Abstract: We revisit the model of a quantum Brownian oscillator linearly coupled to an environment of quantum oscillators at finite temperature. By introducing a compact and particularly well-suited formulation, we give a rather quick and direct derivation of the master equation and its solutions for general spectral functions and arbitrary temperatures. The flexibility of our approach allows for an immediate generalization to cases with an external force and with an arbitrary number of Brownian oscillators. More importantly, we point out an important mathematical subtlety concerning boundary-value problems for integro-differential equations which led to incorrect master equation coefficients and impacts on the description of nonlocal dissipation effects in all earlier derivations. Furthermore, we provide explicit, exact analytical results for the master equation coefficients and its solutions in a wide variety of cases, including ohmic, sub-ohmic and supra-ohmic environments with a finite cut-off.
Roura, Albert; Fleming, C H; Hu, B L
2008-01-01
We revisit the model of a system made up of a Brownian quantum oscillator linearly coupled to an environment made up of many quantum oscillators at finite temperature. We show that the HPZ master equation for the reduced density matrix derived earlier [B.L. Hu, J.P. Paz, Y. Zhang, Phys. Rev. D 45, 2843 (1992)] has incorrectly specified coefficients for the case of nonlocal dissipation. We rederive the QBM master equation, correctly specifying all coefficients, and determine the position uncertainty to be free of excessive cutoff sensitivity. Our coefficients and solutions are reduced entirely to contour integration for analytic spectra at arbitrary temperature, coupling strength, and cut-off. As an illustration we calculate the master equation coefficients and solve the master equation for ohmic coupling (with finite cutoff) and example supra-ohmic and sub-ohmic spectral densities. We determine the effect of an external force on the quantum oscillator and also show that our representation of the master equation and solutions naturally extends to a system of multiple oscillators bilinearly coupled to themselves and the bath in arbitrary fashion. This produces a formula for investigating the standard quantum limit which is central to addressing many theoretical issues in macroscopic quantum phenomena and experimental concerns related to low temperature precision measurements. We find that in a dissipative environment, all initial states settle down to a Gaussian density matrix whose covariance is determined by the thermal reservoir and whose mean is determined by the external force. We specify the thermal covariance for the spectral densities we explore.
Biorthonormal eigenbasis of a Markovian master equation for the quantum Brownian motion
Tay, B. A.; Petrosky, T.
2008-11-15
The solution to a quantum Markovian master equation of a harmonic oscillator weakly coupled to a thermal reservoir is investigated as a non-Hermitian eigenvalue problem in space coordinates. In terms of a pair of quantum action-angle variables, the equation becomes separable and a complete set of biorthogonal eigenfunctions can be constructed. Properties of quantum states, such as the change in the quantum coherence length, damping in the motion, and disappearance of the spatial interference pattern, can then be described as the decay of the nonequilibrium modes in the eigenbasis expansion. It is found that the process of gaining quantum coherence from the environment takes a longer time than the opposite process of losing quantum coherence to the environment. An estimate of the time scales of these processes is obtained.
Continuous Time Open Quantum Random Walks and Non-Markovian Lindblad Master Equations
NASA Astrophysics Data System (ADS)
Pellegrini, Clément
2014-02-01
A new type of quantum random walks, called Open Quantum Random Walks, has been developed and studied in Attal et al. (Open quantum random walks, preprint) and (Central limit theorems for open quantum random walks, preprint). In this article we present a natural continuous time extension of these Open Quantum Random Walks. This continuous time version is obtained by taking a continuous time limit of the discrete time Open Quantum Random Walks. This approximation procedure is based on some adaptation of Repeated Quantum Interactions Theory (Attal and Pautrat in Annales Henri Poincaré Physique Théorique 7:59-104, 2006) coupled with the use of correlated projectors (Breuer in Phys Rev A 75:022103, 2007). The limit evolutions obtained this way give rise to a particular type of quantum master equations. These equations appeared originally in the non-Markovian generalization of the Lindblad theory (Breuer in Phys Rev A 75:022103, 2007). We also investigate the continuous time limits of the quantum trajectories associated with Open Quantum Random Walks. We show that the limit evolutions in this context are described by jump stochastic differential equations. Finally we present a physical example which can be described in terms of Open Quantum Random Walks and their associated continuous time limits.
Capture process in nuclear reactions with a quantum master equation
Sargsyan, V. V.; Kanokov, Z.; Adamian, G. G.; Antonenko, N. V.; Scheid, W.
2009-09-15
Projectile-nucleus capture by a target nucleus at bombarding energies in the vicinity of the Coulomb barrier is treated with the reduced-density-matrix formalism. The effects of dissipation and fluctuations on the capture process are taken self-consistently into account within the quantum model suggested. The excitation functions for the capture in the reactions {sup 16}O, {sup 19}F, {sup 26}Mg, {sup 28}Si, {sup 32,34,36,38}S, {sup 40,48}Ca, {sup 50}Ti, {sup 52}Cr+{sup 208}Pb with spherical nuclei are calculated and compared with the experimental data. At bombarding energies about (15-25) MeV above the Coulomb barrier the maximum of capture cross section is revealed for the {sup 58}Ni+{sup 208}Pb reaction.
Jin, Jinshuang; Li, Jun; Liu, Yu; Li, Xin-Qi; Yan, YiJing
2014-06-28
Beyond the second-order Born approximation, we propose an improved master equation approach to quantum transport under self-consistent Born approximation. The basic idea is to replace the free Green's function in the tunneling self-energy diagram by an effective reduced propagator under the Born approximation. This simple modification has remarkable consequences. It not only recovers the exact results for quantum transport through noninteracting systems under arbitrary voltages, but also predicts the challenging nonequilibrium Kondo effect. Compared to the nonequilibrium Green's function technique that formulates the calculation of specific correlation functions, the master equation approach contains richer dynamical information to allow more efficient studies for such as the shot noise and full counting statistics.
Tscherbul, Timur V. Brumer, Paul
2015-03-14
We present an efficient theoretical method for calculating the time evolution of the density matrix of a multilevel quantum system weakly interacting with incoherent light. The method combines the Bloch-Redfield theory with a partial secular approximation for one-photon coherences, resulting in a master equation that explicitly exposes the reliance on transition rates and the angles between transition dipole moments in the energy basis. The partial secular Bloch-Redfield master equation allows an unambiguous distinction between the regimes of quantum coherent vs. incoherent energy transfer under incoherent light illumination. The fully incoherent regime is characterized by orthogonal transition dipole moments in the energy basis, leading to a dynamical evolution governed by a coherence-free Pauli-type master equation. The coherent regime requires non-orthogonal transition dipole moments in the energy basis and leads to the generation of noise-induced quantum coherences and population-to-coherence couplings. As a first application, we consider the dynamics of excited state coherences arising under incoherent light excitation from a single ground state and observe population-to-coherence transfer and the formation of non-equilibrium quasisteady states in the regime of small excited state splitting. Analytical expressions derived earlier for the V-type system [T. V. Tscherbul and P. Brumer, Phys. Rev. Lett. 113, 113601 (2014)] are found to provide a nearly quantitative description of multilevel excited-state populations and coherences in both the small- and large-molecule limits.
Tscherbul, Timur V; Brumer, Paul
2015-03-14
We present an efficient theoretical method for calculating the time evolution of the density matrix of a multilevel quantum system weakly interacting with incoherent light. The method combines the Bloch-Redfield theory with a partial secular approximation for one-photon coherences, resulting in a master equation that explicitly exposes the reliance on transition rates and the angles between transition dipole moments in the energy basis. The partial secular Bloch-Redfield master equation allows an unambiguous distinction between the regimes of quantum coherent vs. incoherent energy transfer under incoherent light illumination. The fully incoherent regime is characterized by orthogonal transition dipole moments in the energy basis, leading to a dynamical evolution governed by a coherence-free Pauli-type master equation. The coherent regime requires non-orthogonal transition dipole moments in the energy basis and leads to the generation of noise-induced quantum coherences and population-to-coherence couplings. As a first application, we consider the dynamics of excited state coherences arising under incoherent light excitation from a single ground state and observe population-to-coherence transfer and the formation of non-equilibrium quasisteady states in the regime of small excited state splitting. Analytical expressions derived earlier for the V-type system [T. V. Tscherbul and P. Brumer, Phys. Rev. Lett. 113, 113601 (2014)] are found to provide a nearly quantitative description of multilevel excited-state populations and coherences in both the small- and large-molecule limits. PMID:25770526
NASA Astrophysics Data System (ADS)
Tscherbul, Timur V.; Brumer, Paul
2015-03-01
We present an efficient theoretical method for calculating the time evolution of the density matrix of a multilevel quantum system weakly interacting with incoherent light. The method combines the Bloch-Redfield theory with a partial secular approximation for one-photon coherences, resulting in a master equation that explicitly exposes the reliance on transition rates and the angles between transition dipole moments in the energy basis. The partial secular Bloch-Redfield master equation allows an unambiguous distinction between the regimes of quantum coherent vs. incoherent energy transfer under incoherent light illumination. The fully incoherent regime is characterized by orthogonal transition dipole moments in the energy basis, leading to a dynamical evolution governed by a coherence-free Pauli-type master equation. The coherent regime requires non-orthogonal transition dipole moments in the energy basis and leads to the generation of noise-induced quantum coherences and population-to-coherence couplings. As a first application, we consider the dynamics of excited state coherences arising under incoherent light excitation from a single ground state and observe population-to-coherence transfer and the formation of non-equilibrium quasisteady states in the regime of small excited state splitting. Analytical expressions derived earlier for the V-type system [T. V. Tscherbul and P. Brumer, Phys. Rev. Lett. 113, 113601 (2014)] are found to provide a nearly quantitative description of multilevel excited-state populations and coherences in both the small- and large-molecule limits.
Hermitian non-Markovian stochastic master equations for quantum dissipative dynamics
NASA Astrophysics Data System (ADS)
Yan, Yun-An; Zhou, Yun
2015-08-01
It remains a challenge for theory to simulate nonperturbative and non-Markovian quantum dissipative dynamics at low temperatures. In this study we suggest a Hermitian non-Markovian stochastic master equation suitable for dissipative dynamics at arbitrary temperatures. The memory effect of the bath is embedded within two real correlated Gaussian noises. This scheme is numerically verified by the hierarchical equation of motion and symmetry preserving for a symmetric two-level system. An exemplary application is carried out for the dynamics over a broad range of temperatures to investigate the temperature dependence of the Rabi frequency shift and the non-Markovianity.
On the accuracy of the Padé-resummed master equation approach to dissipative quantum dynamics
NASA Astrophysics Data System (ADS)
Chen, Hsing-Ta; Berkelbach, Timothy C.; Reichman, David R.
2016-04-01
Well-defined criteria are proposed for assessing the accuracy of quantum master equations whose memory functions are approximated by Padé resummation of the first two moments in the electronic coupling. These criteria partition the parameter space into distinct levels of expected accuracy, ranging from quantitatively accurate regimes to regions of parameter space where the approach is not expected to be applicable. Extensive comparison of Padé-resummed master equations with numerically exact results in the context of the spin-boson model demonstrates that the proposed criteria correctly demarcate the regions of parameter space where the Padé approximation is reliable. The applicability analysis we present is not confined to the specifics of the Hamiltonian under consideration and should provide guidelines for other classes of resummation techniques.
On the accuracy of the Padé-resummed master equation approach to dissipative quantum dynamics.
Chen, Hsing-Ta; Berkelbach, Timothy C; Reichman, David R
2016-04-21
Well-defined criteria are proposed for assessing the accuracy of quantum master equations whose memory functions are approximated by Padé resummation of the first two moments in the electronic coupling. These criteria partition the parameter space into distinct levels of expected accuracy, ranging from quantitatively accurate regimes to regions of parameter space where the approach is not expected to be applicable. Extensive comparison of Padé-resummed master equations with numerically exact results in the context of the spin-boson model demonstrates that the proposed criteria correctly demarcate the regions of parameter space where the Padé approximation is reliable. The applicability analysis we present is not confined to the specifics of the Hamiltonian under consideration and should provide guidelines for other classes of resummation techniques. PMID:27389208
Density-matrix operatorial solution of the non-Markovian master equation for quantum Brownian motion
Intravaia, F.; Maniscalco, S.; Messina, A.
2003-04-01
An original method to exactly solve the non-Markovian master equation describing the interaction of a single harmonic oscillator with a quantum environment in the weak-coupling limit is reported. By using a superoperatorial approach, we succeed in deriving the operatorial solution for the density matrix of the system. Our method is independent of the physical properties of the environment. We show the usefulness of our solution deriving explicit expressions for the dissipative time evolution of some observables of physical interest for the system, such as, for example, its mean energy.
Application of quantum master equation for long-term prognosis of asset-prices
NASA Astrophysics Data System (ADS)
Khrennikova, Polina
2016-05-01
This study combines the disciplines of behavioral finance and an extension of econophysics, namely the concepts and mathematical structure of quantum physics. We apply the formalism of quantum theory to model the dynamics of some correlated financial assets, where the proposed model can be potentially applied for developing a long-term prognosis of asset price formation. At the informational level, the asset price states interact with each other by the means of a "financial bath". The latter is composed of agents' expectations about the future developments of asset prices on the finance market, as well as financially important information from mass-media, society, and politicians. One of the essential behavioral factors leading to the quantum-like dynamics of asset prices is the irrationality of agents' expectations operating on the finance market. These expectations lead to a deeper type of uncertainty concerning the future price dynamics of the assets, than given by a classical probability theory, e.g., in the framework of the classical financial mathematics, which is based on the theory of stochastic processes. The quantum dimension of the uncertainty in price dynamics is expressed in the form of the price-states superposition and entanglement between the prices of the different financial assets. In our model, the resolution of this deep quantum uncertainty is mathematically captured with the aid of the quantum master equation (its quantum Markov approximation). We illustrate our model of preparation of a future asset price prognosis by a numerical simulation, involving two correlated assets. Their returns interact more intensively, than understood by a classical statistical correlation. The model predictions can be extended to more complex models to obtain price configuration for multiple assets and portfolios.
Chang, Hung-Tzu; Cheng, Yuan-Chung; Zhang, Pan-Pan
2013-12-14
The small polaron quantum master equation (SPQME) proposed by Jang et al. [J. Chem. Phys. 129, 101104 (2008)] is a promising approach to describe coherent excitation energy transfer dynamics in complex molecular systems. To determine the applicable regime of the SPQME approach, we perform a comprehensive investigation of its accuracy by comparing its simulated population dynamics with numerically exact quasi-adiabatic path integral calculations. We demonstrate that the SPQME method yields accurate dynamics in a wide parameter range. Furthermore, our results show that the accuracy of polaron theory depends strongly upon the degree of exciton delocalization and timescale of polaron formation. Finally, we propose a simple criterion to assess the applicability of the SPQME theory that ensures the reliability of practical simulations of energy transfer dynamics with SPQME in light-harvesting systems.
A semiclassical generalized quantum master equation for an arbitrary system-bath coupling
NASA Astrophysics Data System (ADS)
Shi, Qiang; Geva, Eitan
2004-06-01
The Nakajima-Zwanzig generalized quantum master equation (GQME) provides a general, and formally exact, prescription for simulating the reduced dynamics of a quantum system coupled to a, possibly anharmonic, quantum bath. In this equation, a memory kernel superoperator accounts for the influence of the bath on the dynamics of the system. In a previous paper [Q. Shi and E. Geva, J. Chem. Phys. 119, 12045 (2003)] we proposed a new approach to calculating the memory kernel, in the case of arbitrary system-bath coupling. Within this approach, the memory kernel is obtained by solving a set of two integral equations, which requires a new type of two-time system-dependent bath correlation functions as input. In the present paper, we consider the application of the linearized semiclassical (LSC) approximation for calculating those correlation functions, and subsequently the memory kernel. The new approach is tested on a benchmark spin-boson model. Application of the LSC approximation for calculating the relatively short-lived memory kernel, followed by a numerically exact solution of the GQME, is found to provide an accurate description of the relaxation dynamics. The success of the proposed LSC-GQME methodology is contrasted with the failure of both the direct application of the LSC approximation and the weak coupling treatment to provide an accurate description of the dynamics, for the same model, except at very short times. The feasibility of the new methodology to anharmonic systems is also demonstrated in the case of a two level system coupled to a chain of Lennard-Jones atoms.
Generalized quantum master equations in and out of equilibrium: When can one win?
NASA Astrophysics Data System (ADS)
Kelly, Aaron; Montoya-Castillo, Andrés; Wang, Lu; Markland, Thomas E.
2016-05-01
Generalized quantum master equations (GQMEs) are an important tool in modeling chemical and physical processes. For a large number of problems, it has been shown that exact and approximate quantum dynamics methods can be made dramatically more efficient, and in the latter case more accurate, by proceeding via the GQME formalism. However, there are many situations where utilizing the GQME approach with an approximate method has been observed to return the same dynamics as using that method directly. Here, for systems both in and out of equilibrium, we provide a more detailed understanding of the conditions under which using an approximate method can yield benefits when combined with the GQME formalism. In particular, we demonstrate the necessary manipulations, which are satisfied by exact quantum dynamics, that are required to recast the memory kernel in a form that can be analytically shown to yield the same result as a direct application of the dynamics regardless of the approximation used. By considering the connections between these forms of the kernel, we derive the conditions that approximate methods must satisfy if they are to offer different results when used in conjunction with the GQME formalism. These analytical results thus provide new insights as to when proceeding via the GQME approach can be used to improve the accuracy of simulations.
Generalized quantum master equations in and out of equilibrium: When can one win?
Kelly, Aaron; Montoya-Castillo, Andrés; Wang, Lu; Markland, Thomas E
2016-05-14
Generalized quantum master equations (GQMEs) are an important tool in modeling chemical and physical processes. For a large number of problems, it has been shown that exact and approximate quantum dynamics methods can be made dramatically more efficient, and in the latter case more accurate, by proceeding via the GQME formalism. However, there are many situations where utilizing the GQME approach with an approximate method has been observed to return the same dynamics as using that method directly. Here, for systems both in and out of equilibrium, we provide a more detailed understanding of the conditions under which using an approximate method can yield benefits when combined with the GQME formalism. In particular, we demonstrate the necessary manipulations, which are satisfied by exact quantum dynamics, that are required to recast the memory kernel in a form that can be analytically shown to yield the same result as a direct application of the dynamics regardless of the approximation used. By considering the connections between these forms of the kernel, we derive the conditions that approximate methods must satisfy if they are to offer different results when used in conjunction with the GQME formalism. These analytical results thus provide new insights as to when proceeding via the GQME approach can be used to improve the accuracy of simulations. PMID:27179469
Kritsotakis, M; Kominis, I K
2014-10-01
Radical-ion-pair reactions, central in photosynthesis and the avian magnetic compass mechanism, have been recently shown to be a paradigm system for applying quantum information science in a biochemical setting. The fundamental quantum master equation describing radical-ion-pair reactions is still under debate. Here we use quantum retrodiction to formally refine the theory put forward in the paper by Kominis [I. K. Kominis, Phys. Rev. E 83, 056118 (2011)]. We also provide a rigorous analysis of the measure of singlet-triplet coherence required for deriving the radical-pair master equation. A Monte Carlo simulation with single-molecule quantum trajectories supports the self-consistency of our approach. PMID:25375535
NASA Astrophysics Data System (ADS)
Kritsotakis, M.; Kominis, I. K.
2014-10-01
Radical-ion-pair reactions, central in photosynthesis and the avian magnetic compass mechanism, have been recently shown to be a paradigm system for applying quantum information science in a biochemical setting. The fundamental quantum master equation describing radical-ion-pair reactions is still under debate. Here we use quantum retrodiction to formally refine the theory put forward in the paper by Kominis [I. K. Kominis, Phys. Rev. E 83, 056118 (2011), 10.1103/PhysRevE.83.056118]. We also provide a rigorous analysis of the measure of singlet-triplet coherence required for deriving the radical-pair master equation. A Monte Carlo simulation with single-molecule quantum trajectories supports the self-consistency of our approach.
Kelly, Aaron; Markland, Thomas E.; Brackbill, Nora
2015-03-07
In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.
NASA Astrophysics Data System (ADS)
Purkayastha, Archak; Dhar, Abhishek; Kulkarni, Manas
2016-06-01
We present the Born-Markov approximated Redfield quantum master equation (RQME) description for an open system of noninteracting particles (bosons or fermions) on an arbitrary lattice of N sites in any dimension and weakly connected to multiple reservoirs at different temperatures and chemical potentials. The RQME can be reduced to the Lindblad equation, of various forms, by making further approximations. By studying the N =2 case, we show that RQME gives results which agree with exact analytical results for steady-state properties and with exact numerics for time-dependent properties over a wide range of parameters. In comparison, the Lindblad equations have a limited domain of validity in nonequilibrium. We conclude that it is indeed justified to use microscopically derived full RQME to go beyond the limitations of Lindblad equations in out-of-equilibrium systems. We also derive closed-form analytical results for out-of-equilibrium time dynamics of two-point correlation functions. These results explicitly show the approach to steady state and thermalization. These results are experimentally relevant for cold atoms, cavity QED, and far-from-equilibrium quantum dot experiments.
Busch, Anna; González-García, Núria; Lendvay, György; Olzmann, Matthias
2015-07-16
The thermal decomposition of cyanonitrene, NCN, was studied behind reflected shock waves in the temperature range 1790-2960 K at pressures near 1 and 4 bar. Highly diluted mixtures of NCN3 in argon were shock-heated to produce NCN, and concentration-time profiles of C atoms as reaction product were monitored with atomic resonance absorption spectroscopy at 156.1 nm. Calibration was performed with methane pyrolysis experiments. Rate coefficients for the reaction (3)NCN + M → (3)C + N2 + M (R1) were determined from the initial slopes of the C atom concentration-time profiles. Reaction R1 was found to be in the low-pressure regime at the conditions of the experiments. The temperature dependence of the bimolecular rate coefficient can be expressed with the following Arrhenius equation: k1(bim) = (4.2 ± 2.1) × 10(14) exp[-242.3 kJ mol(-1)/(RT)] cm(3) mol(-1) s(-1). The rate coefficients were analyzed by using a master equation with specific rate coefficients from RRKM theory. The necessary molecular data and energies were calculated with quantum chemical methods up to the CCSD(T)/CBS//CCSD/cc-pVTZ level of theory. From the topography of the potential energy surface, it follows that reaction R1 proceeds via isomerization of NCN to CNN and subsequent C-N bond fission along a collinear reaction coordinate without a tight transition state. The calculations reproduce the magnitude and temperature dependence of the rate coefficient and confirm that reaction R1 is in the low-pressure regime under our experimental conditions. PMID:25853321
NASA Astrophysics Data System (ADS)
Polyakov, Evgeny A.
2016-02-01
The time-dependent fermionic Hartree-Fock equations can be stochastically extended in such a way as to become the exact representation of quantum dynamics. This fact was first observed in the work of Juillet and Chomaz [Phys. Rev. Lett. 88, 142503 (2002), 10.1103/PhysRevLett.88.142503]. During the past decade, this observation has led to the emergence of a whole family of stochastic wave-function methods for fermions. The common feature of all these methods is that they are based on the expansion of the density operator over the dyadic product of the two fermionic Slater determinant states. In this work, we develop a unified and rigorous foundation for this family of methods. We find a general form of stochastic equations and describe the sufficient conditions under which these methods converge towards exact quantum dynamics. To achieve these goals, we employ the representation of quantum dynamics in generalized phase space. In particular, we consider the quasiprobability distributions which emerge in these stochastic methods and their master equations. It is shown that the convergence towards exact quantum dynamics is controlled by the problem of boundary terms. We provide an example of stochastic Hartree-Fock method which is well-defined and free from this problem.
Using non-Markovian measures to evaluate quantum master equations for photosynthesis
NASA Astrophysics Data System (ADS)
Chen, Hong-Bin; Lambert, Neill; Cheng, Yuan-Chung; Chen, Yueh-Nan; Nori, Franco
2015-08-01
When dealing with system-reservoir interactions in an open quantum system, such as a photosynthetic light-harvesting complex, approximations are usually made to obtain the dynamics of the system. One question immediately arises: how good are these approximations, and in what ways can we evaluate them? Here, we propose to use entanglement and a measure of non-Markovianity as benchmarks for the deviation of approximate methods from exact results. We apply two frequently-used perturbative but non-Markovian approximations to a photosynthetic dimer model and compare their results with that of the numerically-exact hierarchy equation of motion (HEOM). This enables us to explore both entanglement and non-Markovianity measures as means to reveal how the approximations either overestimate or underestimate memory effects and quantum coherence. In addition, we show that both the approximate and exact results suggest that non-Markonivity can, counter-intuitively, increase with temperature, and with the coupling to the environment.
Stochastically averaged master equation for a quantum-dynamic system interacting with a thermal bath
NASA Astrophysics Data System (ADS)
Petrov, E. G.; Teslenko, V. I.; Goychuk, I. A.
1994-05-01
The methods of nonequilibrium density-matrix and coarse-temporal conception are used to obtain the kinetic equation for the parameters γnm(t)=Sp[ρ^(t)||n>
Soares-Pinto, D. O.; Moussa, M. H. Y.; Azevedo, E. R. de; Bonagamba, T. J.; Maziero, J.; Serra, R. M.; Celeri, L. C.
2011-06-15
We present a derivation of the Redfield formalism for treating the dissipative dynamics of a time-dependent quantum system coupled to a classical environment. We compare such a formalism with the master equation approach where the environments are treated quantum mechanically. Focusing on a time-dependent spin-1/2 system we demonstrate the equivalence between both approaches by showing that they lead to the same Bloch equations and, as a consequence, to the same characteristic times T{sub 1} and T{sub 2} (associated with the longitudinal and transverse relaxations, respectively). These characteristic times are shown to be related to the operator-sum representation and the equivalent phenomenological-operator approach. Finally, we present a protocol to circumvent the decoherence processes due to the loss of energy (and thus, associated with T{sub 1}). To this end, we simply associate the time dependence of the quantum system to an easily achieved modulated frequency. A possible implementation of the protocol is also proposed in the context of nuclear magnetic resonance.
NASA Astrophysics Data System (ADS)
Luo, JunYan; Jin, Jinshuang; Wang, Shi-Kuan; Hu, Jing; Huang, Yixiao; He, Xiao-Ling
2016-03-01
We present a generic unraveling scheme for a detailed-balance-preserved quantum master equation applicable for stochastic point processes in mesoscopic transport. It enables us to investigate continuous measurement of a qubit on the level of single quantum trajectories, where essential correlations between the inherent dynamics of the qubit and detector current fluctuations are revealed. Based on this unraveling scheme, feedback control of the charge qubit is implemented to achieve a desired pure state in the presence of the detailed-balance condition. With sufficient feedback strength, coherent oscillations of the measured qubit can be maintained for arbitrary qubit-detector coupling. Competition between the loss and restoration of coherence entailed, respectively, by measurement back action and feedback control is reflected in the noise power spectrum of the detector's output. It is demonstrated unambiguously that the signal-to-noise ratio is significantly enhanced with increasing feedback strength and could even exceed the well-known Korotkov-Averin bound in quantum measurement. The proposed unraveling and feedback scheme offers a transparent and straightforward approach to effectively sustaining ideal coherent oscillations of a charge qubit in the field of quantum computation.
Using non-Markovian measures to evaluate quantum master equations for photosynthesis
Chen, Hong-Bin; Lambert, Neill; Cheng, Yuan-Chung; Chen, Yueh-Nan; Nori, Franco
2015-01-01
When dealing with system-reservoir interactions in an open quantum system, such as a photosynthetic light-harvesting complex, approximations are usually made to obtain the dynamics of the system. One question immediately arises: how good are these approximations, and in what ways can we evaluate them? Here, we propose to use entanglement and a measure of non-Markovianity as benchmarks for the deviation of approximate methods from exact results. We apply two frequently-used perturbative but non-Markovian approximations to a photosynthetic dimer model and compare their results with that of the numerically-exact hierarchy equation of motion (HEOM). This enables us to explore both entanglement and non-Markovianity measures as means to reveal how the approximations either overestimate or underestimate memory effects and quantum coherence. In addition, we show that both the approximate and exact results suggest that non-Markonivity can, counter-intuitively, increase with temperature, and with the coupling to the environment. PMID:26238479
Markovian master equation for nonlinear systems
NASA Astrophysics Data System (ADS)
de los Santos-Sánchez, O.; Récamier, J.; Jáuregui, R.
2015-06-01
Within the f-deformed oscillator formalism, we derive a Markovian master equation for the description of the damped dynamics of nonlinear systems that interact with their environment. The applicability of this treatment to the particular case of a Morse-like oscillator interacting with a thermal field is illustrated, and the decay of quantum coherence in such a system is analyzed in terms of the evolution on phase space of its nonlinear coherent states via the Wigner function.
NASA Astrophysics Data System (ADS)
Shi, Qiang; Geva, Eitan
2003-12-01
The Nakajima-Zwanzig generalized quantum master equation provides a general, and formally exact, prescription for simulating the reduced dynamics of a quantum system coupled to a quantum bath. In this equation, the memory kernel accounts for the influence of the bath on the system's dynamics. The standard approach is based on using a perturbative treatment of the system-bath coupling for calculating this kernel, and is therefore restricted to systems weakly coupled to the bath. In this paper, we propose a new approach for calculating the memory kernel for an arbitrary system-bath coupling. The memory kernel is obtained by solving a set of two coupled integral equations that relate it to a new type of two-time system-dependent bath correlation functions. The feasibility of the method is demonstrated in the case of an asymetrical two-level system linearly coupled to a harmonic bath.
NASA Astrophysics Data System (ADS)
Härtle, R.; Cohen, G.; Reichman, D. R.; Millis, A. J.
2015-08-01
We give a detailed comparison of the hierarchical quantum master equation (HQME) method to a continuous-time quantum Monte Carlo (CT-QMC) approach, assessing the usability of these numerically exact schemes as impurity solvers in practical nonequilibrium calculations. We review the main characteristics of the methods and discuss the scaling of the associated numerical effort. We substantiate our discussion with explicit numerical results for the nonequilibrium transport properties of a single-site Anderson impurity. The numerical effort of the HQME scheme scales linearly with the simulation time but increases (at worst exponentially) with decreasing temperature. In contrast, CT-QMC is less restricted by temperature at short times, but in general the cost of going to longer times is also exponential. After establishing the numerical exactness of the HQME scheme, we use it to elucidate the influence of different ways to induce transport through the impurity on the initial dynamics, discuss the phenomenon of coherent current oscillations, known as current ringing, and explain the nonmonotonic temperature dependence of the steady-state magnetization as a result of competing broadening effects. We also elucidate the pronounced nonlinear magnetization dynamics, which appears on intermediate time scales in the presence of an asymmetric coupling to the electrodes.
NASA Astrophysics Data System (ADS)
Manson, Ross; Roy-Choudhury, Kaushik; Hughes, Stephen
2016-04-01
We introduce an intuitive and semianalytical polaron master equation approach to model pulse-driven population inversion and emitted single photons from a quantum dot exciton. The master equation theory allows one to identify important phonon-induced scattering rates analytically and fully includes the role of the time-dependent pump field. As an application of the theory, we first study a quantum dot driven by a time-varying laser pulse on and off resonance, showing the population inversion caused by acoustic phonon emission in direct agreement with recent experiments of Quilter et al. [Phys. Rev. Lett. 114, 137401 (2015), 10.1103/PhysRevLett.114.137401]. We then model quantum dots in weakly coupled cavities and show the difference in population response between exciton-driven and cavity-driven systems. Finally, we assess the nonresonant phonon-assisted loading scheme with a quantum dot resonantly coupled to a cavity as a deterministic single-photon source. We also compare and contrast the important single photon figures of merit with direct Rabi oscillation of the population using a resonant π pulse, and show that the resonant scheme is much more efficient.
Master equation based steady-state cluster perturbation theory
NASA Astrophysics Data System (ADS)
Nuss, Martin; Dorn, Gerhard; Dorda, Antonius; von der Linden, Wolfgang; Arrigoni, Enrico
2015-09-01
A simple and efficient approximation scheme to study electronic transport characteristics of strongly correlated nanodevices, molecular junctions, or heterostructures out of equilibrium is provided by steady-state cluster perturbation theory. In this work, we improve the starting point of this perturbative, nonequilibrium Green's function based method. Specifically, we employ an improved unperturbed (so-called reference) state ρ̂S, constructed as the steady state of a quantum master equation within the Born-Markov approximation. This resulting hybrid method inherits beneficial aspects of both the quantum master equation as well as the nonequilibrium Green's function technique. We benchmark this scheme on two experimentally relevant systems in the single-electron transistor regime: an electron-electron interaction based quantum diode and a triple quantum dot ring junction, which both feature negative differential conductance. The results of this method improve significantly with respect to the plain quantum master equation treatment at modest additional computational cost.
Staying positive: going beyond Lindblad with perturbative master equations
NASA Astrophysics Data System (ADS)
Whitney, Robert S.
2008-05-01
The perturbative master equation (Bloch-Redfield) is used extensively to study dissipative quantum mechanics—particularly for qubits—despite the 25-year-old criticism that it violates positivity (generating negative probabilities). We take an arbitrary system coupled to an environment containing many degrees-of-freedom and cast its perturbative master equation (derived from a perturbative treatment of Nakajima-Zwanzig or Schoeller-Schön equations) in the form of a Lindblad master equation. We find that the equation's parameters are time dependent. This time dependence is rarely accounted for and invalidates Lindblad's dynamical semigroup analysis. We analyse one such Bloch-Redfield master equation (for a two-level system coupled to an environment with a short but non-vanishing memory time), which apparently violates positivity. We analytically show that, once the time dependence of the parameters is accounted for, positivity is preserved.
Sun, Ke-Wei; Fujihashi, Yuta; Ishizaki, Akihito; Zhao, Yang
2016-05-28
A master equation approach based on an optimized polaron transformation is adopted for dynamics simulation with simultaneous diagonal and off-diagonal spin-boson coupling. Two types of bath spectral density functions are considered, the Ohmic and the sub-Ohmic. The off-diagonal coupling leads asymptotically to a thermal equilibrium with a nonzero population difference Pz(t → ∞) ≠ 0, which implies localization of the system, and it also plays a role in restraining coherent dynamics for the sub-Ohmic case. Since the new method can extend to the stronger coupling regime, we can investigate the coherent-incoherent transition in the sub-Ohmic environment. Relevant phase diagrams are obtained for different temperatures. It is found that the sub-Ohmic environment allows coherent dynamics at a higher temperature than the Ohmic environment. PMID:27250278
NASA Astrophysics Data System (ADS)
Sun, Ke-Wei; Fujihashi, Yuta; Ishizaki, Akihito; Zhao, Yang
2016-05-01
A master equation approach based on an optimized polaron transformation is adopted for dynamics simulation with simultaneous diagonal and off-diagonal spin-boson coupling. Two types of bath spectral density functions are considered, the Ohmic and the sub-Ohmic. The off-diagonal coupling leads asymptotically to a thermal equilibrium with a nonzero population difference Pz(t → ∞) ≠ 0, which implies localization of the system, and it also plays a role in restraining coherent dynamics for the sub-Ohmic case. Since the new method can extend to the stronger coupling regime, we can investigate the coherent-incoherent transition in the sub-Ohmic environment. Relevant phase diagrams are obtained for different temperatures. It is found that the sub-Ohmic environment allows coherent dynamics at a higher temperature than the Ohmic environment.
A closure scheme for chemical master equations
Smadbeck, Patrick; Kaznessis, Yiannis N.
2013-01-01
Probability reigns in biology, with random molecular events dictating the fate of individual organisms, and propelling populations of species through evolution. In principle, the master probability equation provides the most complete model of probabilistic behavior in biomolecular networks. In practice, master equations describing complex reaction networks have remained unsolved for over 70 years. This practical challenge is a reason why master equations, for all their potential, have not inspired biological discovery. Herein, we present a closure scheme that solves the master probability equation of networks of chemical or biochemical reactions. We cast the master equation in terms of ordinary differential equations that describe the time evolution of probability distribution moments. We postulate that a finite number of moments capture all of the necessary information, and compute the probability distribution and higher-order moments by maximizing the information entropy of the system. An accurate order closure is selected, and the dynamic evolution of molecular populations is simulated. Comparison with kinetic Monte Carlo simulations, which merely sample the probability distribution, demonstrates this closure scheme is accurate for several small reaction networks. The importance of this result notwithstanding, a most striking finding is that the steady state of stochastic reaction networks can now be readily computed in a single-step calculation, without the need to simulate the evolution of the probability distribution in time. PMID:23940327
Approximate probability distributions of the master equation
NASA Astrophysics Data System (ADS)
Thomas, Philipp; Grima, Ramon
2015-07-01
Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation using orthogonal polynomials. The solution is given in two alternative formulations: a series with continuous and a series with discrete support, both of which can be systematically truncated. While both approximations satisfy the system size expansion of the master equation, the continuous distribution approximations become increasingly negative and tend to oscillations with increasing truncation order. In contrast, the discrete approximations rapidly converge to the underlying non-Gaussian distributions. The theory is shown to lead to particularly simple analytical expressions for the probability distributions of molecule numbers in metabolic reactions and gene expression systems.
Hybrid method for the chemical master equation
Hellander, Andreas Loetstedt, Per
2007-11-10
The chemical master equation is solved by a hybrid method coupling a macroscopic, deterministic description with a mesoscopic, stochastic model. The molecular species are divided into one subset where the expected values of the number of molecules are computed and one subset with species with a stochastic variation in the number of molecules. The macroscopic equations resemble the reaction rate equations and the probability distribution for the stochastic variables satisfy a master equation. The probability distribution is obtained by the Stochastic Simulation Algorithm due to Gillespie. The equations are coupled via a summation over the mesoscale variables. This summation is approximated by Quasi-Monte Carlo methods. The error in the approximations is analyzed. The hybrid method is applied to three chemical systems from molecular cell biology.
Master equation as a radial constraint
NASA Astrophysics Data System (ADS)
Hussain, Uzair; Booth, Ivan; Kunduri, Hari K.
2016-06-01
We revisit the problem of perturbations of Schwarzschild-AdS4 black holes by using a combination of the Martel-Poisson formalism for perturbations of four-dimensional spherically symmetric spacetimes [K. Martel and E. Poisson, Phys. Rev. D 71, 104003 (2005).] and the Kodama-Ishibashi formalism [H. Kodama and A. Ishibashi, Prog. Theor. Phys. 110, 701 (2003).]. We clarify the relationship between both formalisms and express the Brown-York-Balasubramanian-Krauss boundary stress-energy tensor, T¯μ ν, on a finite-r surface purely in terms of the even and odd master functions. Then, on these surfaces we find that the spacelike components of the conservation equation D¯μT¯μ ν=0 are equivalent to the wave equations for the master functions. The renormalized stress-energy tensor at the boundary r/L lim r →∞ T¯μ ν is calculated directly in terms of the master functions.
Kishi, Ryohei; Fujii, Hiroaki; Minami, Takuya; Shigeta, Yasuteru; Nakano, Masayoshi
2015-01-22
In this study, we apply the ab initio molecular orbital - configuration interaction based quantum master equation (MOQME) approach to the calculation and analysis of the dynamic first hyperpolarizabilities (β) of asymmetric π-conjugated molecules. In this approach, we construct the excited state models by the ab initio configuration interaction singles method. Then, time evolutions of system reduced density matrix ρ(t) and system polarization p(t) are calculated by the QME approach. Dynamic β in the second harmonic generation is calculated based on the nonperturbative definition of nonlinear optical susceptibility, using the frequency domain system polarization p(ω). Spatial contributions of electrons to β are analyzed based on the dynamic hyperpolarizability density map, which visualizes the second-order response of charge density oscillating with a frequency of 2ω. We apply the present method to the calculation of the dynamic β of a series of donor/acceptor substituted polyene oligomers, and then discuss the applicability of the MOQME method to the calculation and analysis of dynamic NLO properties of molecular systems.
NASA Astrophysics Data System (ADS)
Fan, Hong-Yi; Hu, Li-Yun
2009-04-01
By introducing a fictitious mode to be a counterpart mode of the system mode under review we introduce the entangled state representation langleη|, which can arrange master equations of density operators ρ(t) in quantum statistics as state-vector evolution equations due to the elegant properties of langleη|. In this way many master equations (respectively describing damping oscillator, laser, phase sensitive, and phase diffusion processes with different initial density operators) can be concisely solved. Specially, for a damping process characteristic of the decay constant κ we find that the matrix element of ρ(t) at time t in langleη| representation is proportional to that of the initial ρ0 in the decayed entangled state langleηe-κt| representation, accompanying with a Gaussian damping factor. Thus we have a new insight about the nature of the dissipative process. We also set up the so-called thermo-entangled state representation of density operators, ρ = ∫(d2η/π)langleη|ρrangleD(η), which is different from all the previous known representations.
NASA Astrophysics Data System (ADS)
Kumar, Praveen; Jang, Seogjoo
2013-04-01
The emission lineshape of the B850 band in the light harvesting complex 2 of purple bacteria is calculated by extending the approach of 2nd order time-nonlocal quantum master equation [S. Jang and R. J. Silbey, J. Chem. Phys. 118, 9312 (2003), 10.1063/1.1569239]. The initial condition for the emission process corresponds to the stationary excited state density where exciton states are entangled with the bath modes in equilibrium. This exciton-bath coupling, which is not diagonal in either site excitation or exciton basis, results in a new inhomogeneous term that is absent in the expression for the absorption lineshape. Careful treatment of all the 2nd order terms are made, and explicit expressions are derived for both full 2nd order lineshape expression and the one based on secular approximation that neglects off-diagonal components in the exciton basis. Numerical results are presented for a few representative cases of disorder and temperature. Comparison of emission line shape with the absorption line shape is also made. It is shown that the inhomogeneous term coming from the entanglement of the system and bath degrees of freedom makes significant contributions to the lineshape. It is also found that the perturbative nature of the theory can result in negative portion of lineshape in some situations, which can be removed significantly by inclusion of the inhomogeneous term and completely by using the secular approximation. Comparison of the emission and absorption lineshapes at different temperatures demonstrates the role of thermal population of different exciton states and exciton-phonon couplings.
Rotational master equation for cold laser-driven molecules
Adelswaerd, A.; Wallentowitz, S.; Vogel, W.
2003-06-01
The equations of motion for the molecular rotation are derived for vibrationally cold dimers that are polarized by off-resonant laser light. It is shown that, by eliminating electronic and vibrational degrees of freedom, a quantum master equation for the reduced rotational density operator can be obtained. The coherent rotational dynamics is caused by stimulated Raman transitions, whereas spontaneous Raman transitions lead to decoherence in the motion of the quantized angular momentum. As an example the molecular dynamics for the optical Kerr effect is chosen, revealing decoherence and heating of the molecular rotation.
Exact master equation for a noncommutative Brownian particle
Costa Dias, Nuno Nuno Prata, Joao
2009-01-15
We derive the Hu-Paz-Zhang master equation for a Brownian particle linearly coupled to a bath of harmonic oscillators on the plane with spatial noncommutativity. The results obtained are exact to all orders in the noncommutative parameter. As a by-product we derive some miscellaneous results such as the equilibrium Wigner distribution for the reservoir of noncommutative oscillators, the weak coupling limit of the master equation and a set of sufficient conditions for strict purity decrease of the Brownian particle. Finally, we consider a high-temperature Ohmic model and obtain an estimate for the time scale of the transition from noncommutative to ordinary quantum mechanics. This scale is considerably smaller than the decoherence scale.
A master equation for a two-sided optical cavity
Barlow, Thomas M.; Bennett, Robert; Beige, Almut
2015-01-01
Quantum optical systems, like trapped ions, are routinely described by master equations. The purpose of this paper is to introduce a master equation for two-sided optical cavities with spontaneous photon emission. To do so, we use the same notion of photons as in linear optics scattering theory and consider a continuum of travelling-wave cavity photon modes. Our model predicts the same stationary state photon emission rates for the different sides of a laser-driven optical cavity as classical theories. Moreover, it predicts the same time evolution of the total cavity photon number as the standard standing-wave description in experiments with resonant and near-resonant laser driving. The proposed resonator Hamiltonian can be used, for example, to analyse coherent cavity-fiber networks [E. Kyoseva et al., New J. Phys. 14, 023023 (2012)].
Graph theory and the Virasoro master equation
Obers, N.A.J.
1991-01-01
A brief history of affine Lie algebra, the Virasoro algebra and its culmination in the Virasoro master equation is given. By studying ansaetze of the master equation, the author obtains exact solutions and gains insight in the structure of large slices of affine-Virasoro space. He finds an isomorphism between the constructions in the ansatz SO(n){sub diag}, which is a set of unitary, generically irrational affine-Virasoro constructions on SO(n), and the unlabeled graphs of order n. On the one hand, the conformal constructions, are classified by the graphs, while, conversely, a group-theoretic and conformal field-theoretic identification is obtained for every graph of graph theory. He also defines a class of magic Lie group bases in which the Virasoro master equation admits a simple metric ansatz {l brace}g{sub metric}{r brace}, whose structure is visible in the high-level expansion. When a magic basis is real on compact g, the corresponding g{sub metric} is a large system of unitary, generically irrational conformal field theories. Examples in this class include the graph-theory ansatz SO(n){sub diag} in the Cartesian basis of SO(n), and the ansatz SU(n){sub metric} in the Pauli-like basis of SU(n). Finally, he defines the sine-area graphs' of SU(n), which label the conformal field theories of SU(n){sub metric}, and he notes that, in similar fashion, each magic basis of g defines a generalized graph theory on g which labels the conformal field theories of g{sub metric}.
Graph theory and the Virasoro master equation
Obers, N.A.J.
1991-04-01
A brief history of affine Lie algebra, the Virasoro algebra and its culmination in the Virasoro master equations is given. By studying ansaetze of the master equation, we obtain exact solutions and gain insight in the structure of large slices of affine-Virasoro space. We find an isomorphism between the constructions in the ansatz SO(n){sub diag}, which is a set of unitary, generically irrational affine-Virasoro constructions on SO(n), and the unlabelled graphs, while, conversely, a group-theoretic and conformal field-theoretic identification is obtained for every graph of graph theory. We also define a class of magic'' Lie group bases in which the Virasoro master equation admits a simple metric ansatz (gmetric), whose structure is visible in the high-level expansion. When a magic basis is real on compact g, the corresponding g{sub metric} is a large system of unitary, generically irrational conformal field theories. Examples in this class include the graph-theory ansatz SO(n){sub diag} in the Cartesian basis of SO(n), and the ansatz SU(n){sub metric} in the Pauli-like basis of SU(n). Finally, we define the sine-area graphs'' of SU(n), which label the conformal field theories of SU(n){sub metric}, and we note that, in similar fashion, each magic basis of g defines a generalized graph theory on g which labels the conformal field theories of g{sub metric}. 24 figs., 4 tabs.
Epidemics in networks: a master equation approach
NASA Astrophysics Data System (ADS)
Cotacallapa, M.; Hase, M. O.
2016-02-01
A problem closely related to epidemiology, where a subgraph of ‘infected’ links is defined inside a larger network, is investigated. This subgraph is generated from the underlying network by a random variable, which decides whether a link is able to propagate a disease/information. The relaxation timescale of this random variable is examined in both annealed and quenched limits, and the effectiveness of propagation of disease/information is analyzed. The dynamics of the model is governed by a master equation and two types of underlying network are considered: one is scale-free and the other has exponential degree distribution. We have shown that the relaxation timescale of the contagion variable has a major influence on the topology of the subgraph of infected links, which determines the efficiency of spreading of disease/information over the network.
Solution of Chemical Master Equations for Nonlinear Stochastic Reaction Networks
Smadbeck, Patrick; Kaznessis, Yiannis N.
2014-01-01
Stochasticity in the dynamics of small reacting systems requires discrete-probabilistic models of reaction kinetics instead of traditional continuous-deterministic ones. The master probability equation is a complete model of randomly evolving molecular populations. Because of its ambitious character, the master equation remained unsolved for all but the simplest of molecular interaction networks. With the first solution of chemical master equations, a wide range of experimental observations of small-system interactions may be mathematically conceptualized. PMID:25215268
Thermodynamics of the polaron master equation at finite bias
Krause, Thilo Brandes, Tobias; Schaller, Gernot; Esposito, Massimiliano
2015-04-07
We study coherent transport through a double quantum dot. Its two electronic leads induce electronic matter and energy transport and a phonon reservoir contributes further energy exchanges. By treating the system-lead couplings perturbatively, whereas the coupling to vibrations is treated non-perturbatively in a polaron-transformed frame, we derive a thermodynamic consistent low-dimensional master equation. When the number of phonon modes is finite, a Markovian description is only possible when these couple symmetrically to both quantum dots. For a continuum of phonon modes however, also asymmetric couplings can be described with a Markovian master equation. We compute the electronic current and dephasing rate. The electronic current enables transport spectroscopy of the phonon frequency and displays signatures of Franck-Condon blockade. For infinite external bias but finite tunneling bandwidths, we find oscillations in the current as a function of the internal bias due to the electron-phonon coupling. Furthermore, we derive the full fluctuation theorem and show its identity to the entropy production in the system.
Class of exact memory-kernel master equations
NASA Astrophysics Data System (ADS)
Lorenzo, Salvatore; Ciccarello, Francesco; Palma, G. Massimo
2016-05-01
A well-known situation in which a non-Markovian dynamics of an open quantum system S arises is when this is coherently coupled to an auxiliary system M in contact with a Markovian bath. In such cases, while the joint dynamics of S -M is Markovian and obeys a standard (bipartite) Lindblad-type master equation (ME), this is in general not true for the reduced dynamics of S . Furthermore, there are several instances (e.g., the dissipative Jaynes-Cummings model) in which a closed ME for the S 's state cannot even be worked out. Here, we find a class of bipartite Lindblad-type MEs such that the reduced ME of S can be derived exactly and in a closed form for any initial product state of S -M . We provide a detailed microscopic derivation of our result in terms of a mapping between two collision models.
Master Equation Approach to Current-Voltage Characteristics of Solar Cells
NASA Astrophysics Data System (ADS)
Oh, Sangchul; Zhang, Yiteng; Alharbi, Fahhad; Kais, Sabre
2015-03-01
The current-voltage characteristics of solar cells is obtained using quantum master equations for electrons, holes, and excitons, in which generation, recombination, and transport processes are taken into account. As a first example, we simulate a photocell with a molecular aggregate donor to investigate whether a delocalized quantum state could enhance the efficiency. As a second example, we calculate the current-voltage characteristics of conventional p-n junction solar cells and perovskite solar cells using the master equation. The connection between the drift-diffusion model and the master equation method is established. The short-circuit current and the open-circuit voltage are calculated numerically as a function of the intensity of the sunlight and material properties such as energy gaps, diffusion constants, etc.
Generalized master equation via aging continuous-time random walks.
Allegrini, Paolo; Aquino, Gerardo; Grigolini, Paolo; Palatella, Luigi; Rosa, Angelo
2003-11-01
We discuss the problem of the equivalence between continuous-time random walk (CTRW) and generalized master equation (GME). The walker, making instantaneous jumps from one site of the lattice to another, resides in each site for extended times. The sojourn times have a distribution density psi(t) that is assumed to be an inverse power law with the power index micro. We assume that the Onsager principle is fulfilled, and we use this assumption to establish a complete equivalence between GME and the Montroll-Weiss CTRW. We prove that this equivalence is confined to the case where psi(t) is an exponential. We argue that is so because the Montroll-Weiss CTRW, as recently proved by Barkai [E. Barkai, Phys. Rev. Lett. 90, 104101 (2003)], is nonstationary, thereby implying aging, while the Onsager principle is valid only in the case of fully aged systems. The case of a Poisson distribution of sojourn times is the only one with no aging associated to it, and consequently with no need to establish special initial conditions to fulfill the Onsager principle. We consider the case of a dichotomous fluctuation, and we prove that the Onsager principle is fulfilled for any form of regression to equilibrium provided that the stationary condition holds true. We set the stationary condition on both the CTRW and the GME, thereby creating a condition of total equivalence, regardless of the nature of the waiting-time distribution. As a consequence of this procedure we create a GME that is a bona fide master equation, in spite of being non-Markov. We note that the memory kernel of the GME affords information on the interaction between system of interest and its bath. The Poisson case yields a bath with infinitely fast fluctuations. We argue that departing from the Poisson form has the effect of creating a condition of infinite memory and that these results might be useful to shed light on the problem of how to unravel non-Markov quantum master equations. PMID:14682862
Number-conserving master equation theory for a dilute Bose-Einstein condensate
Schelle, Alexej; Wellens, Thomas; Buchleitner, Andreas; Delande, Dominique
2011-01-15
We describe the transition of N weakly interacting atoms into a Bose-Einstein condensate within a number-conserving quantum master equation theory. Based on the separation of time scales for condensate formation and noncondensate thermalization, we derive a master equation for the condensate subsystem in the presence of the noncondensate environment under the inclusion of all two-body interaction processes. We numerically monitor the condensate particle number distribution during condensate formation, and derive a condition under which the unique equilibrium steady state of a dilute, weakly interacting Bose-Einstein condensate is given by a Gibbs-Boltzmann thermal state of N noninteracting atoms.
The Approach to Equilibrium: Detailed Balance and the Master Equation
ERIC Educational Resources Information Center
Alexander, Millard H.; Hall, Gregory E.; Dagdigian, Paul J.
2011-01-01
The approach to the equilibrium (Boltzmann) distribution of populations of internal states of a molecule is governed by inelastic collisions in the gas phase and with surfaces. The set of differential equations governing the time evolution of the internal state populations is commonly called the master equation. An analytic solution to the master…
Master equation for dissipative interacting qubits in a common environment
NASA Astrophysics Data System (ADS)
Santos, J. P.; Semião, F. L.
2014-02-01
In this paper, we derive a microscopic master equation for a pair of XY-coupled two-level systems interacting with the same memoryless reservoir. In particular, we apply this master equation to the case of a pair of two-level atoms in free space where we can clearly contrast the predictions made with the microscopic master equation obtained here and the phenomenological approaches where the atom-atom coupling is included just a posteriori, i.e., not taking into account in the derivation of the open system equation of motion. We show, for instance, that the phenomenological approach fails completely in the assessment of the role played by the symmetric and antisymmetric decay channels. As a consequence, the predictions related to collective effects such as superradiance, for instance, are misleading in the phenomenological approach. We also obtain the fluorescence spectrum using the microscopic model developed here.
Variational master equation approach to dynamics of magnetic moments
NASA Astrophysics Data System (ADS)
Bogolubov, N. N.; Soldatov, A. V.
2016-07-01
Non-equilibrium properties of a model system comprised of a subsystem of magnetic moments strongly coupled to a selected Bose field mode and weakly coupled to a heat bath made of a plurality of Bose field modes was studied on the basis of non-equilibrium master equation approach combined with the approximating Hamiltonian method. A variational master equation derived within this approach is tractable numerically and can be readily used to derive a set of ordinary differential equations for various relevant physical variables belonging to the subsystem of magnetic moments. Upon further analysis of the thus obtained variational master equation, an influence of the macroscopic filling of the selected Bose field mode at low enough temperatures on the relaxation dynamics of magnetic moments was revealed.
Multiphoton-scattering theory and generalized master equations
NASA Astrophysics Data System (ADS)
Shi, Tao; Chang, Darrick E.; Cirac, J. Ignacio
2015-11-01
We develop a scattering theory to investigate the multiphoton transmission in a one-dimensional waveguide in the presence of quantum emitters. It is based on a path integral formalism, uses displacement transformations, and does not require the Markov approximation. We obtain the full time evolution of the global system, including the emitters and the photonic field. Our theory allows us to compute the transition amplitude between arbitrary initial and final states, as well as the S matrix of the asymptotic in and out states. For the case of few incident photons in the waveguide, we also rederive a generalized master equation in the Markov limit. We compare the predictions of the developed scattering theory and that with the Markov approximation. We illustrate our methods with five examples of few-photon scattering: (i) by a two-level emitter, (ii) in the Jaynes-Cummings model; (iii) by an array of two-level emitters; (iv) by a two-level emitter in the half-end waveguide; and (v) by an array of atoms coupled to Rydberg levels. In the first two, we show the application of the scattering theory in the photon scattering by a single emitter, and examine the correctness of our theory with the well-known results. In the third example, we analyze the condition of the Markov approximation for the photon scattering in the array of emitters. In the fourth one, we show how a quantum emitter can generate entanglement of outgoing photons. Finally, we highlight the interplay between the phenomenon of electromagnetic-induced transparency and the Rydberg interaction, and show how this results in a rich variety of possibilities in the quantum statistics of the scattering photons.
The pentabox Master Integrals with the Simplified Differential Equations approach
NASA Astrophysics Data System (ADS)
Papadopoulos, Costas G.; Tommasini, Damiano; Wever, Christopher
2016-04-01
We present the calculation of massless two-loop Master Integrals relevant to five-point amplitudes with one off-shell external leg and derive the complete set of planar Master Integrals with five on-mass-shell legs, that contribute to many 2 → 3 amplitudes of interest at the LHC, as for instance three jet production, γ , V, H + 2 jets etc., based on the Simplified Differential Equations approach.
Operator Approach to the Master Equation for the One-Step Process
NASA Astrophysics Data System (ADS)
Hnatič, M.; Eferina, E. G.; Korolkova, A. V.; Kulyabov, D. S.; Sevastyanov, L. A.
2016-02-01
Background. Presentation of the probability as an intrinsic property of the nature leads researchers to switch from deterministic to stochastic description of the phenomena. The kinetics of the interaction has recently attracted attention because it often occurs in the physical, chemical, technical, biological, environmental, economic, and sociological systems. However, there are no general methods for the direct study of this equation. The expansion of the equation in a formal Taylor series (the so called Kramers-Moyal's expansion) is used in the procedure of stochastization of one-step processes. Purpose. However, this does not eliminate the need for the study of the master equation. Method. It is proposed to use quantum field perturbation theory for the statistical systems (the so-called Doi method). Results: This work is a methodological material that describes the principles of master equation solution based on quantum field perturbation theory methods. The characteristic property of the work is that it is intelligible for non-specialists in quantum field theory. Conclusions: We show the full equivalence of the operator and combinatorial methods of obtaining and study of the one-step process master equation.
Non-Markovian master equation for a damped oscillator with time-varying parameters
Chang, K. W.; Law, C. K.
2010-05-15
We derive an exact non-Markovian master equation that generalizes the previous work [Hu, Paz and Zhang, Phys. Rev. D 45, 2843 (1992)] to damped harmonic oscillators with time-varying parameters. This is achieved by exploiting the linearity of the system and operator solution in Heisenberg picture. Our equation governs the non-Markovian quantum dynamics when the system is modulated by external devices. As an application, we apply our equation to parity kick decoupling problems. The time-dependent dissipative coefficients in the master equation are shown to be modified drastically when the system is driven by {pi} pulses. For coherence protection to be effective, our numerical results indicate that kicking period should be shorter than memory time of the bath. The effects of using soft pulses in an ohmic bath are also discussed.
Chemical Master Equation Closure for Computer-Aided Synthetic Biology
Smadbeck, Patrick; Kaznessis, Yiannis N.
2016-01-01
SUMMARY With inexpensive DNA synthesis technologies, we can now construct biological systems by quickly piecing together DNA sequences. Synthetic biology is the promising discipline that focuses on the construction of these new biological systems. Synthetic biology is an engineering discipline, and as such, it can benefit from mathematical modeling. This chapter focuses on mathematical models of biological systems. These models take the form of chemical reaction networks. The importance of stochasticity is discussed and methods to simulate stochastic reaction networks are reviewed. A closure scheme solution is also presented for the master equation of chemical reaction networks. The master equation is a complete model of randomly evolving molecular populations. Because of its ambitious character, the master equation remained unsolved for all but the simplest of molecular interaction networks for over seventy years. With the first complete solution of chemical master equations, a wide range of experimental observations of biomolecular interactions may be mathematically conceptualized. We anticipate that models based on the closure scheme described herein may assist in rationally designing synthetic biological systems. PMID:25487098
NASA Astrophysics Data System (ADS)
Xiang-Guo, Meng; Ji-Suo, Wang; Hong-Yi, Fan; Cheng-Wei, Xia
2016-04-01
We solve the fermionic master equation for a thermal bath to obtain its explicit Kraus operator solutions via the fermionic state approach. The normalization condition of the Kraus operators is proved. The matrix representation for these solutions is obtained, which is incongruous with the result in the book completed by Nielsen and Chuang [Quantum Computation and Quantum Information, Cambridge University Press, 2000]. As especial cases, we also present the Kraus operator solutions to master equations for describing the amplitude-decay model and the diffusion process at finite temperature. Project supported by the National Natural Science Foundation of China (Grant No. 11347026), the Natural Science Foundation of Shandong Province, China (Grant Nos. ZR2013AM012 and ZR2012AM004), and the Research Fund for the Doctoral Program and Scientific Research Project of Liaocheng University, Shandong Province, China.
Monitoring derivation of the quantum linear Boltzmann equation
Hornberger, Klaus; Vacchini, Bassano
2008-02-15
We show how the effective equation of motion for a distinguished quantum particle in an ideal gas environment can be obtained by means of the monitoring approach introduced by Hornberger [EPL 77, 50007 (2007)]. The resulting Lindblad master equation accounts for the quantum effects of the scattering dynamics in a nonperturbative fashion and it describes decoherence and dissipation in a unified framework. It incorporates various established equations as limiting cases and reduces to the classical linear Boltzmann equation once the state is diagonal in momentum.
Resummed memory kernels in generalized system-bath master equations
Mavros, Michael G.; Van Voorhis, Troy
2014-08-07
Generalized master equations provide a concise formalism for studying reduced population dynamics. Usually, these master equations require a perturbative expansion of the memory kernels governing the dynamics; in order to prevent divergences, these expansions must be resummed. Resummation techniques of perturbation series are ubiquitous in physics, but they have not been readily studied for the time-dependent memory kernels used in generalized master equations. In this paper, we present a comparison of different resummation techniques for such memory kernels up to fourth order. We study specifically the spin-boson Hamiltonian as a model system bath Hamiltonian, treating the diabatic coupling between the two states as a perturbation. A novel derivation of the fourth-order memory kernel for the spin-boson problem is presented; then, the second- and fourth-order kernels are evaluated numerically for a variety of spin-boson parameter regimes. We find that resumming the kernels through fourth order using a Padé approximant results in divergent populations in the strong electronic coupling regime due to a singularity introduced by the nature of the resummation, and thus recommend a non-divergent exponential resummation (the “Landau-Zener resummation” of previous work). The inclusion of fourth-order effects in a Landau-Zener-resummed kernel is shown to improve both the dephasing rate and the obedience of detailed balance over simpler prescriptions like the non-interacting blip approximation, showing a relatively quick convergence on the exact answer. The results suggest that including higher-order contributions to the memory kernel of a generalized master equation and performing an appropriate resummation can provide a numerically-exact solution to system-bath dynamics for a general spectral density, opening the way to a new class of methods for treating system-bath dynamics.
Resummed memory kernels in generalized system-bath master equations
NASA Astrophysics Data System (ADS)
Mavros, Michael G.; Van Voorhis, Troy
2014-08-01
Generalized master equations provide a concise formalism for studying reduced population dynamics. Usually, these master equations require a perturbative expansion of the memory kernels governing the dynamics; in order to prevent divergences, these expansions must be resummed. Resummation techniques of perturbation series are ubiquitous in physics, but they have not been readily studied for the time-dependent memory kernels used in generalized master equations. In this paper, we present a comparison of different resummation techniques for such memory kernels up to fourth order. We study specifically the spin-boson Hamiltonian as a model system bath Hamiltonian, treating the diabatic coupling between the two states as a perturbation. A novel derivation of the fourth-order memory kernel for the spin-boson problem is presented; then, the second- and fourth-order kernels are evaluated numerically for a variety of spin-boson parameter regimes. We find that resumming the kernels through fourth order using a Padé approximant results in divergent populations in the strong electronic coupling regime due to a singularity introduced by the nature of the resummation, and thus recommend a non-divergent exponential resummation (the "Landau-Zener resummation" of previous work). The inclusion of fourth-order effects in a Landau-Zener-resummed kernel is shown to improve both the dephasing rate and the obedience of detailed balance over simpler prescriptions like the non-interacting blip approximation, showing a relatively quick convergence on the exact answer. The results suggest that including higher-order contributions to the memory kernel of a generalized master equation and performing an appropriate resummation can provide a numerically-exact solution to system-bath dynamics for a general spectral density, opening the way to a new class of methods for treating system-bath dynamics.
Solving Chemical Master Equations by an Adaptive Wavelet Method
Jahnke, Tobias; Galan, Steffen
2008-09-01
Solving chemical master equations is notoriously difficult due to the tremendous number of degrees of freedom. We present a new numerical method which efficiently reduces the size of the problem in an adaptive way. The method is based on a sparse wavelet representation and an algorithm which, in each time step, detects the essential degrees of freedom required to approximate the solution up to the desired accuracy.
Resummed memory kernels in generalized system-bath master equations.
Mavros, Michael G; Van Voorhis, Troy
2014-08-01
Generalized master equations provide a concise formalism for studying reduced population dynamics. Usually, these master equations require a perturbative expansion of the memory kernels governing the dynamics; in order to prevent divergences, these expansions must be resummed. Resummation techniques of perturbation series are ubiquitous in physics, but they have not been readily studied for the time-dependent memory kernels used in generalized master equations. In this paper, we present a comparison of different resummation techniques for such memory kernels up to fourth order. We study specifically the spin-boson Hamiltonian as a model system bath Hamiltonian, treating the diabatic coupling between the two states as a perturbation. A novel derivation of the fourth-order memory kernel for the spin-boson problem is presented; then, the second- and fourth-order kernels are evaluated numerically for a variety of spin-boson parameter regimes. We find that resumming the kernels through fourth order using a Padé approximant results in divergent populations in the strong electronic coupling regime due to a singularity introduced by the nature of the resummation, and thus recommend a non-divergent exponential resummation (the "Landau-Zener resummation" of previous work). The inclusion of fourth-order effects in a Landau-Zener-resummed kernel is shown to improve both the dephasing rate and the obedience of detailed balance over simpler prescriptions like the non-interacting blip approximation, showing a relatively quick convergence on the exact answer. The results suggest that including higher-order contributions to the memory kernel of a generalized master equation and performing an appropriate resummation can provide a numerically-exact solution to system-bath dynamics for a general spectral density, opening the way to a new class of methods for treating system-bath dynamics. PMID:25106575
Reaction rates for a generalized reaction-diffusion master equation
Hellander, Stefan; Petzold, Linda
2016-01-01
It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model, and show in two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is on the order of the reaction radius of a reacting pair of molecules. PMID:26871190
Structural relaxation in atomic clusters: Master equation dynamics
NASA Astrophysics Data System (ADS)
Miller, Mark A.; Doye, Jonathan P. K.; Wales, David J.
1999-10-01
The role of the potential energy landscape in determining the relaxation dynamics of model clusters is studied using a master equation. Two types of energy landscape are examined: a single funnel, as exemplified by 13-atom Morse clusters, and the double funnel landscape of the 38-atom Lennard-Jones cluster. Interwell rate constants are calculated using Rice-Ramsperger-Kassel-Marcus theory within the harmonic approximation, but anharmonic model partition functions are also considered. Decreasing the range of the potential in the Morse clusters is shown to hinder relaxation toward the global minimum, and this effect is related to the concomitant changes in the energy landscape. The relaxation modes that emerge from the master equation are interpreted and analyzed to extract interfunnel rate constants for the Lennard-Jones cluster. Since this system is too large for a complete characterization of the energy landscape, the conditions under which the master equation can be applied to a limited database are explored. Connections are made to relaxation processes in proteins and structural glasses.
Reaction rates for a generalized reaction-diffusion master equation
NASA Astrophysics Data System (ADS)
Hellander, Stefan; Petzold, Linda
2016-01-01
It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach, in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model and show in two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is of the order of the reaction radius of a reacting pair of molecules.
A master equation for gravitational decoherence: probing the textures of spacetime
NASA Astrophysics Data System (ADS)
Anastopoulos, C.; Hu, B. L.
2013-08-01
We give a first principles derivation of a master equation for the evolution of a quantum matter field in a linearly perturbed Minkowski spacetime, based solely on quantum field theory and general relativity. We make no additional assumptions nor introduce extra ingredients, as is often done in alternative quantum theories. When the quantum matter field is projected to a one-particle state, the master equation for a non-relativistic quantum particle in a weak gravitational field predicts decoherence in the energy basis, in contrast to most existing theories of gravitational decoherence. We point out the gauge nature of time and space reparameterizations in matter-gravity couplings, and warn that ‘intrinsic’ decoherence or alternative quantum theories invoking stochastic dynamics arising from temporal or spatial fluctuations violate this fundamental symmetry of classical general relativity. Interestingly we find that the decoherence rate depends on extra parameters other than the Planck scale, an important feature of gravitational decoherence. This is similar to the dependence of the decoherence rate of a quantum Brownian particle to the temperature and spectral density of the environment it interacts with. The corresponding features when gravity acts as an environment in decohering quantum objects are what we call the ‘textures’ of spacetime. We point out the marked difference between the case when gravity is represented as a background spacetime versus the case when gravity acts like a thermodynamic bath to quantum particles. This points to the possibility of using gravitational decoherence measurements to discern whether gravity is intrinsically elemental or emergent.
Multiple re-encounter approach to radical pair reactions and the role of nonlinear master equations
Clausen, Jens; Tiersch, Markus; Briegel, Hans J.; Guerreschi, Gian Giacomo
2014-08-07
We formulate a multiple-encounter model of the radical pair mechanism that is based on a random coupling of the radical pair to a minimal model environment. These occasional pulse-like couplings correspond to the radical encounters and give rise to both dephasing and recombination. While this is in agreement with the original model of Haberkorn and its extensions that assume additional dephasing, we show how a nonlinear master equation may be constructed to describe the conditional evolution of the radical pairs prior to the detection of their recombination. We propose a nonlinear master equation for the evolution of an ensemble of independently evolving radical pairs whose nonlinearity depends on the record of the fluorescence signal. We also reformulate Haberkorn's original argument on the physicality of reaction operators using the terminology of quantum optics/open quantum systems. Our model allows one to describe multiple encounters within the exponential model and connects this with the master equation approach. We include hitherto neglected effects of the encounters, such as a separate dephasing in the triplet subspace, and predict potential new effects, such as Grover reflections of radical spins, that may be observed if the strength and time of the encounters can be experimentally controlled.
On solving the master equation in spatially periodic systems.
Kolokathis, Panagiotis D; Theodorou, Doros N
2012-07-21
We present a new method for solving the master equation for a system evolving on a spatially periodic network of states. The network contains 2(ν) images of a "unit cell" of n states, arranged along one direction with periodic boundary conditions at the ends. We analyze the structure of the symmetrized (2(ν)n) × (2(ν)n) rate constant matrix for this system and derive a recursive scheme for determining its eigenvalues and eigenvectors, and therefore analytically expressing the time-dependent probabilities of all states in the network, based on diagonalizations of n × n matrices formed by consideration of a single unit cell. We apply our new method to the problem of low-temperature, low-occupancy diffusion of xenon in the zeolite silicalite-1 using the states, interstate transitions, and transition state theory-based rate constants previously derived by June et al. [J. Phys. Chem. 95, 8866 (1991)]. The new method yields a diffusion tensor for this system which differs by less than 3% from the values derived previously via kinetic Monte Carlo (KMC) simulations and confirmed by new KMC simulations conducted in the present work. The computational requirements of the new method are compared against those of KMC, numerical solution of the master equation by the Euler method, and direct molecular dynamics. In the problem of diffusion of xenon in silicalite-1, the new method is shown to be faster than these alternative methods by factors of about 3.177 × 10(4), 4.237 × 10(3), and 1.75 × 10(7), respectively. The computational savings and ease of setting up calculations afforded by the new method of master equation solution by recursive reduction of dimensionality in diagonalizing the rate constant matrix make it attractive as a means of predicting long-time dynamical phenomena in spatially periodic systems from atomic-level information. PMID:22830688
Effective equations for the quantum pendulum from momentous quantum mechanics
Hernandez, Hector H.; Chacon-Acosta, Guillermo
2012-08-24
In this work we study the quantum pendulum within the framework of momentous quantum mechanics. This description replaces the Schroedinger equation for the quantum evolution of the system with an infinite set of classical equations for expectation values of configuration variables, and quantum dispersions. We solve numerically the effective equations up to the second order, and describe its evolution.
Evolution equation for quantum coherence
NASA Astrophysics Data System (ADS)
Hu, Ming-Liang; Fan, Heng
2016-07-01
The estimation of the decoherence process of an open quantum system is of both theoretical significance and experimental appealing. Practically, the decoherence can be easily estimated if the coherence evolution satisfies some simple relations. We introduce a framework for studying evolution equation of coherence. Based on this framework, we prove a simple factorization relation (FR) for the l1 norm of coherence, and identified the sets of quantum channels for which this FR holds. By using this FR, we further determine condition on the transformation matrix of the quantum channel which can support permanently freezing of the l1 norm of coherence. We finally reveal the universality of this FR by showing that it holds for many other related coherence and quantum correlation measures.
Evolution equation for quantum coherence
Hu, Ming-Liang; Fan, Heng
2016-01-01
The estimation of the decoherence process of an open quantum system is of both theoretical significance and experimental appealing. Practically, the decoherence can be easily estimated if the coherence evolution satisfies some simple relations. We introduce a framework for studying evolution equation of coherence. Based on this framework, we prove a simple factorization relation (FR) for the l1 norm of coherence, and identified the sets of quantum channels for which this FR holds. By using this FR, we further determine condition on the transformation matrix of the quantum channel which can support permanently freezing of the l1 norm of coherence. We finally reveal the universality of this FR by showing that it holds for many other related coherence and quantum correlation measures. PMID:27382933
Evolution equation for quantum coherence.
Hu, Ming-Liang; Fan, Heng
2016-01-01
The estimation of the decoherence process of an open quantum system is of both theoretical significance and experimental appealing. Practically, the decoherence can be easily estimated if the coherence evolution satisfies some simple relations. We introduce a framework for studying evolution equation of coherence. Based on this framework, we prove a simple factorization relation (FR) for the l1 norm of coherence, and identified the sets of quantum channels for which this FR holds. By using this FR, we further determine condition on the transformation matrix of the quantum channel which can support permanently freezing of the l1 norm of coherence. We finally reveal the universality of this FR by showing that it holds for many other related coherence and quantum correlation measures. PMID:27382933
Generalized entropy production phenomena: a master-equation approach.
Casas, G A; Nobre, F D; Curado, E M F
2014-01-01
The time rate of generalized entropic forms, defined in terms of discrete probabilities following a master equation, is investigated. Both contributions, namely entropy production and flux, are obtained, extending works carried previously for the Boltzmann-Gibbs entropy to a wide class of entropic forms. Particularly, it is shown that the entropy-production contribution is always non-negative for such entropies. Some illustrative examples for known generalized entropic forms in the literature are also worked out. Since generalized entropies have been lately associated with several complex systems in nature, the present analysis should be applicable to irreversible processes in these systems. PMID:24580179
Random transition-rate matrices for the master equation.
Timm, Carsten
2009-08-01
Random-matrix theory is applied to transition-rate matrices in the Pauli master equation. We study the distribution and correlations of eigenvalues, which govern the dynamics of complex stochastic systems. Both the cases of identical and of independent rates of forward and backward transitions are considered. The first case leads to symmetric transition-rate matrices, whereas the second corresponds to general asymmetric matrices. The resulting matrix ensembles are different from the standard ensembles and show different eigenvalue distributions. For example, the fraction of real eigenvalues scales anomalously with matrix dimension in the asymmetric case. PMID:19792110
Generalized master equations for exciton dynamics in molecular systems
NASA Astrophysics Data System (ADS)
Schreiber, Michael; May, V.
1995-02-01
The paper demonstrates the applicability of a special type of density matrix theory for the derivation of generalized Master equations. The density matrix theory has been formulated for the description of the dissipative electron transfer dynamics in molecular complexes. The theoretical approach is based on a representation of the density matrix in appropriately taken diabatic electron-vibrational states. Dissipative effects are taken into account by a coupling of these states to further vibrational modes of the molecular complex as well as to environmental degrees of freedom. The approach is applied to a two-center system as well as to a molecular chain. Memory kernels are derived in second order with respect to the inter-center coupling. The kernels are discussed under the assumption of a quick intra-center relaxation for a part of the vibrational modes as well as for all vibrational modes. Standard expressions for the transition rates between different sites are extended to include finite life times of the vibrational levels. Results which have been obtained in the study of the so-called spin boson model can be simply reproduced. The application of the derived generalized Master equations to the investigation of the motion of Frenkel excitons in molecular chains is also presented.
Friedmann equation with quantum potential
Siong, Ch'ng Han; Radiman, Shahidan; Nikouravan, Bijan
2013-11-27
Friedmann equations are used to describe the evolution of the universe. Solving Friedmann equations for the scale factor indicates that the universe starts from an initial singularity where all the physical laws break down. However, the Friedmann equations are well describing the late-time or large scale universe. Hence now, many physicists try to find an alternative theory to avoid this initial singularity. In this paper, we generate a version of first Friedmann equation which is added with an additional term. This additional term contains the quantum potential energy which is believed to play an important role at small scale. However, it will gradually become negligible when the universe evolves to large scale.
Simulation of quantum dynamics based on the quantum stochastic differential equation.
Li, Ming
2013-01-01
The quantum stochastic differential equation derived from the Lindblad form quantum master equation is investigated. The general formulation in terms of environment operators representing the quantum state diffusion is given. The numerical simulation algorithm of stochastic process of direct photodetection of a driven two-level system for the predictions of the dynamical behavior is proposed. The effectiveness and superiority of the algorithm are verified by the performance analysis of the accuracy and the computational cost in comparison with the classical Runge-Kutta algorithm. PMID:23781156
Nonlinear generalized master equations and accounting for initial correlations
NASA Astrophysics Data System (ADS)
Los, V. F.
2009-08-01
We develop a new method based on using a time-dependent operator (generally not a projection operator) converting a distribution function (statistical operator) of a total system into the relevant form that allows deriving new exact nonlinear generalized master equations (GMEs). The derived inhomogeneous nonlinear GME is a generalization of the linear Nakajima-Zwanzig GME and can be viewed as an alternative to the BBGKY chain. It is suitable for obtaining both nonlinear and linear evolution equations. As in the conventional linear GME, there is an inhomogeneous term comprising all multiparticle initial correlations. To include the initial correlations into consideration, we convert the obtained inhomogeneous nonlinear GME into the homogenous form by the previously suggested method. We use no conventional approximation like the random phase approximation (RPA) or the Bogoliubov principle of weakening of initial correlations. The obtained exact homogeneous nonlinear GME describes all evolution stages of the (sub)system of interest and treats initial correlations on an equal footing with collisions via the modified memory kernel. As an application, we obtain a new homogeneous nonlinear equation retaining initial correlations for a one-particle distribution function of the spatially inhomogeneous nonideal gas of classical particles. In contrast to existing approaches, this equation holds for all time scales and takes the influence of pair collisions and initial correlations on the dissipative and nondissipative characteristics of the system into account consistently with the adopted approximation (linear in the gas density). We show that on the kinetic time scale, the time-reversible terms resulting from the initial correlations vanish (if the particle dynamics are endowed with the mixing property) and this equation can be converted into the Vlasov-Landau and Boltzmann equations without any additional commonly used approximations. The entire process of transition can
Non-Markovian master equation for a system of Fermions interacting with an electromagnetic field
Stefanescu, Eliade Scheid, Werner; Sandulescu, Aurel
2008-05-15
For a system of charged Fermions interacting with an electromagnetic field, we derive a non-Markovian master equation in the second-order approximation of the weak dissipative coupling. A complex dissipative environment including Fermions, Bosons and the free electromagnetic field is taken into account. Besides the well-known Markovian term of Lindblad's form, that describes the decay of the system by correlated transitions of the system and environment particles, this equation includes new Markovian and non-Markovian terms proceeding from the fluctuations of the self-consistent field of the environment. These terms describe fluctuations of the energy levels, transitions among these levels stimulated by the fluctuations of the self-consistent field of the environment, and the influence of the time-evolution of the environment on the system dynamics. We derive a complementary master equation describing the environment dynamics correlated with the dynamics of the system. As an application, we obtain non-Markovian Maxwell-Bloch equations and calculate the absorption spectrum of a field propagation mode transversing an array of two-level quantum dots.
Master equation calculations of cluster formation in supersonic jets
NASA Astrophysics Data System (ADS)
Wolf, K.; Kuge, H.-H.; Kleinermanns, K.
1991-12-01
The kinetics of cluster formation in supersonic jets is examined by numerical integration of the master equation system. Some general characteristics of cluster kinetics could be formulated. Excellent agreement between experimental curves of p-cresol (H2O)0, 1, 2, 3 formation as function of H2O pressure and the corresponding calculated curves were obtained assuming successive cluster formation. From the kinetic curves, an unambiguous assignment of cluster size was possible which agreed with mass-resolved REMPI measurements. The fit of the rate coefficients shows the formation of p-cresol (H2O)1 to be faster than p-cresol (H2O)2 and p-cresol (H2O)3.
Delay chemical master equation: direct and closed-form solutions
Leier, Andre; Marquez-Lago, Tatiana T.
2015-01-01
The stochastic simulation algorithm (SSA) describes the time evolution of a discrete nonlinear Markov process. This stochastic process has a probability density function that is the solution of a differential equation, commonly known as the chemical master equation (CME) or forward-Kolmogorov equation. In the same way that the CME gives rise to the SSA, and trajectories of the latter are exact with respect to the former, trajectories obtained from a delay SSA are exact representations of the underlying delay CME (DCME). However, in contrast to the CME, no closed-form solutions have so far been derived for any kind of DCME. In this paper, we describe for the first time direct and closed solutions of the DCME for simple reaction schemes, such as a single-delayed unimolecular reaction as well as chemical reactions for transcription and translation with delayed mRNA maturation. We also discuss the conditions that have to be met such that such solutions can be derived. PMID:26345616
Grima, Ramon
2011-11-01
The mesoscopic description of chemical kinetics, the chemical master equation, can be exactly solved in only a few simple cases. The analytical intractability stems from the discrete character of the equation, and hence considerable effort has been invested in the development of Fokker-Planck equations, second-order partial differential equation approximations to the master equation. We here consider two different types of higher-order partial differential approximations, one derived from the system-size expansion and the other from the Kramers-Moyal expansion, and derive the accuracy of their predictions for chemical reactive networks composed of arbitrary numbers of unimolecular and bimolecular reactions. In particular, we show that the partial differential equation approximation of order Q from the Kramers-Moyal expansion leads to estimates of the mean number of molecules accurate to order Ω(-(2Q-3)/2), of the variance of the fluctuations in the number of molecules accurate to order Ω(-(2Q-5)/2), and of skewness accurate to order Ω(-(Q-2)). We also show that for large Q, the accuracy in the estimates can be matched only by a partial differential equation approximation from the system-size expansion of approximate order 2Q. Hence, we conclude that partial differential approximations based on the Kramers-Moyal expansion generally lead to considerably more accurate estimates in the mean, variance, and skewness than approximations of the same order derived from the system-size expansion. PMID:22181475
The Master Equation for Two-Level Accelerated Systems at Finite Temperature
NASA Astrophysics Data System (ADS)
Tomazelli, J. L.; Cunha, R. O.
2016-07-01
In this work, we study the behaviour of two weakly coupled quantum systems, described by a separable density operator; one of them is a single oscillator, representing a microscopic system, while the other is a set of oscillators which perform the role of a reservoir in thermal equilibrium. From the Liouville-Von Neumann equation for the reduced density operator, we devise the master equation that governs the evolution of the microscopic system, incorporating the effects of temperature via Thermofield Dynamics formalism by suitably redefining the vacuum of the macroscopic system. As applications, we initially investigate the behaviour of a Fermi oscillator in the presence of a heat bath consisting of a set of Fermi oscillators and that of an atomic two-level system interacting with a scalar radiation field, considered as a reservoir, by constructing the corresponding master equation which governs the time evolution of both sub-systems at finite temperature. Finally, we calculate the energy variation rates for the atom and the field, as well as the atomic population levels, both in the inertial case and at constant proper acceleration, considering the two-level system as a prototype of an Unruh detector, for admissible couplings of the radiation field.
Fractional Diffusion Equation, Quantum Subdynamics and EINSTEIN'S Theory of Brownian Motion
NASA Astrophysics Data System (ADS)
Abe, Sumiyoshi
The fractional diffusion equation for describing the anomalous diffusion phenomenon is derived in the spirit of Einstein's 1905 theory of Brownian motion. It is shown how naturally fractional calculus appears in the theory. Then, Einstein's theory is examined in view of quantum theory. An isolated quantum system composed of the objective system and the environment is considered, and then subdynamics of the objective system is formulated. The resulting quantum master equation is found to be of the Lindblad type.
Jang, Seogjoo; Hoyer, Stephan; Fleming, Graham; Whaley, K Birgitta
2014-10-31
A generalized master equation (GME) governing quantum evolution of modular exciton density (MED) is derived for large scale light harvesting systems composed of weakly interacting modules of multiple chromophores. The GME-MED offers a practical framework to incorporate real time coherent quantum dynamics calculations of small length scales into dynamics over large length scales, and also provides a non-Markovian generalization and rigorous derivation of the Pauli master equation employing multichromophoric Förster resonance energy transfer rates. A test of the GME-MED for four sites of the Fenna-Matthews-Olson complex demonstrates how coherent dynamics of excitonic populations over coupled chromophores can be accurately described by transitions between subgroups (modules) of delocalized excitons. Application of the GME-MED to the exciton dynamics between a pair of light harvesting complexes in purple bacteria demonstrates its promise as a computationally efficient tool to investigate large scale exciton dynamics in complex environments. PMID:25396397
NASA Astrophysics Data System (ADS)
Jang, Seogjoo; Hoyer, Stephan; Fleming, Graham; Whaley, K. Birgitta
2014-10-01
A generalized master equation (GME) governing quantum evolution of modular exciton density (MED) is derived for large scale light harvesting systems composed of weakly interacting modules of multiple chromophores. The GME-MED offers a practical framework to incorporate real time coherent quantum dynamics calculations of small length scales into dynamics over large length scales, and also provides a non-Markovian generalization and rigorous derivation of the Pauli master equation employing multichromophoric Förster resonance energy transfer rates. A test of the GME-MED for four sites of the Fenna-Matthews-Olson complex demonstrates how coherent dynamics of excitonic populations over coupled chromophores can be accurately described by transitions between subgroups (modules) of delocalized excitons. Application of the GME-MED to the exciton dynamics between a pair of light harvesting complexes in purple bacteria demonstrates its promise as a computationally efficient tool to investigate large scale exciton dynamics in complex environments.
Evolution equation for geometric quantum correlation measures
NASA Astrophysics Data System (ADS)
Hu, Ming-Liang; Fan, Heng
2015-05-01
A simple relation is established for the evolution equation of quantum-information-processing protocols such as quantum teleportation, remote state preparation, Bell-inequality violation, and particularly the dynamics of geometric quantum correlation measures. This relation shows that when the system traverses the local quantum channel, various figures of merit of the quantum correlations for different protocols demonstrate a factorization decay behavior for dynamics. We identified the family of quantum states for different kinds of quantum channels under the action of which the relation holds. This relation simplifies the assessment of many quantum tasks.
Symmetric and antisymmetric forms of the Pauli master equation.
Klimenko, A Y
2016-01-01
When applied to matter and antimatter states, the Pauli master equation (PME) may have two forms: time-symmetric, which is conventional, and time-antisymmetric, which is suggested in the present work. The symmetric and antisymmetric forms correspond to symmetric and antisymmetric extensions of thermodynamics from matter to antimatter - this is demonstrated by proving the corresponding H-theorem. The two forms are based on the thermodynamic similarity of matter and antimatter and differ only in the directions of thermodynamic time for matter and antimatter (the same in the time-symmetric case and the opposite in the time-antisymmetric case). We demonstrate that, while the symmetric form of PME predicts an equibalance between matter and antimatter, the antisymmetric form of PME favours full conversion of antimatter into matter. At this stage, it is impossible to make an experimentally justified choice in favour of the symmetric or antisymmetric versions of thermodynamics since we have no experience of thermodynamic properties of macroscopic objects made of antimatter, but experiments of this kind may become possible in the future. PMID:27440454
Symmetric and antisymmetric forms of the Pauli master equation
Klimenko, A. Y.
2016-01-01
When applied to matter and antimatter states, the Pauli master equation (PME) may have two forms: time-symmetric, which is conventional, and time-antisymmetric, which is suggested in the present work. The symmetric and antisymmetric forms correspond to symmetric and antisymmetric extensions of thermodynamics from matter to antimatter — this is demonstrated by proving the corresponding H-theorem. The two forms are based on the thermodynamic similarity of matter and antimatter and differ only in the directions of thermodynamic time for matter and antimatter (the same in the time-symmetric case and the opposite in the time-antisymmetric case). We demonstrate that, while the symmetric form of PME predicts an equibalance between matter and antimatter, the antisymmetric form of PME favours full conversion of antimatter into matter. At this stage, it is impossible to make an experimentally justified choice in favour of the symmetric or antisymmetric versions of thermodynamics since we have no experience of thermodynamic properties of macroscopic objects made of antimatter, but experiments of this kind may become possible in the future. PMID:27440454
Derivation of exact master equation with stochastic description: Dissipative harmonic oscillator
NASA Astrophysics Data System (ADS)
Li, Haifeng; Shao, Jiushu; Wang, Shikuan
2011-11-01
A systematic procedure for deriving the master equation of a dissipative system is reported in the framework of stochastic description. For the Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and elementary derivation of the bath-induced stochastic field is presented. The dynamics of the system is thereby fully described by a stochastic differential equation, and the desired master equation would be acquired with statistical averaging. It is shown that the existence of a closed-form master equation depends on the specificity of the system as well as the feature of the dissipation characterized by the spectral density function. For a dissipative harmonic oscillator it is observed that the correlation between the stochastic field due to the bath and the system can be decoupled, and the master equation naturally results. Such an equation possesses the Lindblad form in which time-dependent coefficients are determined by a set of integral equations. It is proved that the obtained master equation is equivalent to the well-known Hu-Paz-Zhang equation based on the path-integral technique. The procedure is also used to obtain the master equation of a dissipative harmonic oscillator in time-dependent fields.
Paillotin, G; Swenberg, C E; Breton, J; Geacintov, N E
1979-01-01
A Pauli master equation is formulated and solved to describe the fluorescence quantum yield, phi, and the fluorescence temporal decay curves. F(t), obtained in picosecond laser excitation experiments of photosynthetic systems. It is assumed that the lowering of phi with increasing pulse intensity is due to bimolecular singlet exciton annihilation processes which compete with the monomolecular exciton decay processes; Poisson statistics are taken into account. Calculated curves of phi as a function of the number of photon hits per domain are compared with experimental data, and it is concluded that these domains contain at least two to four connected photosynthetic units (depending on the temperature), where each photosynthetic unit is assumed to contain approximately 300 pigment molecules. It is shown that under conditions of high excitation intensities, the fluorescence decays approximately according to the (time)1/2 law. PMID:262402
Paillotin, G; Swenberg, C E; Breton, J; Geacintov, N E
1979-03-01
A Pauli master equation is formulated and solved to describe the fluorescence quantum yield, phi, and the fluorescence temporal decay curves. F(t), obtained in picosecond laser excitation experiments of photosynthetic systems. It is assumed that the lowering of phi with increasing pulse intensity is due to bimolecular singlet exciton annihilation processes which compete with the monomolecular exciton decay processes; Poisson statistics are taken into account. Calculated curves of phi as a function of the number of photon hits per domain are compared with experimental data, and it is concluded that these domains contain at least two to four connected photosynthetic units (depending on the temperature), where each photosynthetic unit is assumed to contain approximately 300 pigment molecules. It is shown that under conditions of high excitation intensities, the fluorescence decays approximately according to the (time)1/2 law. PMID:262402
Monte Carlo simulation of the atomic master equation for spontaneous emission
NASA Astrophysics Data System (ADS)
Dum, R.; Zoller, P.; Ritsch, H.
1992-04-01
A Monte Carlo simulation of the atomic master equation for spontaneous emission in terms of atomic wave functions is developed. Realizations of the time evolution of atomic wave functions are constructed that correspond to an ensemble of atoms driven by laser light undergoing a sequence of spontaneous emissions. The atomic decay times are drawn according to the photon count distribution of the driven atom. Each quantum jump of the atomic electron projects the atomic wave function to the ground state of the atom. Our theory is based on a stochastic interpretation and generalization of Mollow's pure-state analysis of resonant light scattering, and the Srinivas-Davies theory of continuous measurements in photodetection. An extension of the theory to include mechanical light effects and a generalization to atomic systems with Zeeman substructure are given. We illustrate the method by simulating the solutions of the optical Bloch equations for two-level systems, and laser cooling of a two-level atom in an ion trap where the center-of-mass motion of the atom is described quantum mechanically.
NASA Astrophysics Data System (ADS)
Horowitz, Jordan M.
2015-07-01
The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.
Horowitz, Jordan M.
2015-07-28
The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.
Master equation solutions in the linear regime of characteristic formulation of general relativity
NASA Astrophysics Data System (ADS)
Cedeño M., C. E.; de Araujo, J. C. N.
2015-12-01
From the field equations in the linear regime of the characteristic formulation of general relativity, Bishop, for a Schwarzschild's background, and Mädler, for a Minkowski's background, were able to show that it is possible to derive a fourth order ordinary differential equation, called master equation, for the J metric variable of the Bondi-Sachs metric. Once β , another Bondi-Sachs potential, is obtained from the field equations, and J is obtained from the master equation, the other metric variables are solved integrating directly the rest of the field equations. In the past, the master equation was solved for the first multipolar terms, for both the Minkowski's and Schwarzschild's backgrounds. Also, Mädler recently reported a generalisation of the exact solutions to the linearised field equations when a Minkowski's background is considered, expressing the master equation family of solutions for the vacuum in terms of Bessel's functions of the first and the second kind. Here, we report new solutions to the master equation for any multipolar moment l , with and without matter sources in terms only of the first kind Bessel's functions for the Minkowski, and in terms of the Confluent Heun's functions (Generalised Hypergeometric) for radiative (nonradiative) case in the Schwarzschild's background. We particularize our families of solutions for the known cases for l =2 reported previously in the literature and find complete agreement, showing the robustness of our results.
Iles-Smith, Jake; Dijkstra, Arend G; Lambert, Neill; Nazir, Ahsan
2016-01-28
We explore excitonic energy transfer dynamics in a molecular dimer system coupled to both structured and unstructured oscillator environments. By extending the reaction coordinate master equation technique developed by Iles-Smith et al. [Phys. Rev. A 90, 032114 (2014)], we go beyond the commonly used Born-Markov approximations to incorporate system-environment correlations and the resultant non-Markovian dynamical effects. We obtain energy transfer dynamics for both underdamped and overdamped oscillator environments that are in perfect agreement with the numerical hierarchical equations of motion over a wide range of parameters. Furthermore, we show that the Zusman equations, which may be obtained in a semiclassical limit of the reaction coordinate model, are often incapable of describing the correct dynamical behaviour. This demonstrates the necessity of properly accounting for quantum correlations generated between the system and its environment when the Born-Markov approximations no longer hold. Finally, we apply the reaction coordinate formalism to the case of a structured environment comprising of both underdamped (i.e., sharply peaked) and overdamped (broad) components simultaneously. We find that though an enhancement of the dimer energy transfer rate can be obtained when compared to an unstructured environment, its magnitude is rather sensitive to both the dimer-peak resonance conditions and the relative strengths of the underdamped and overdamped contributions. PMID:26827205
Generalized mean-field or master equation for nonlinear cavities with transverse effects.
Dunlop, A M; Firth, W J; Heatley, D R; Wright, E M
1996-06-01
We present a general form of master equation for nonlinear-optical cavities that can be described by an ABCD matrix. It includes as special cases some previous models of spatiotemporal effects in lasers. PMID:19876153
Quantum simulation of the Dirac equation.
Gerritsma, R; Kirchmair, G; Zähringer, F; Solano, E; Blatt, R; Roos, C F
2010-01-01
The Dirac equation successfully merges quantum mechanics with special relativity. It provides a natural description of the electron spin, predicts the existence of antimatter and is able to reproduce accurately the spectrum of the hydrogen atom. The realm of the Dirac equation-relativistic quantum mechanics-is considered to be the natural transition to quantum field theory. However, the Dirac equation also predicts some peculiar effects, such as Klein's paradox and 'Zitterbewegung', an unexpected quivering motion of a free relativistic quantum particle. These and other predicted phenomena are key fundamental examples for understanding relativistic quantum effects, but are difficult to observe in real particles. In recent years, there has been increased interest in simulations of relativistic quantum effects using different physical set-ups, in which parameter tunability allows access to different physical regimes. Here we perform a proof-of-principle quantum simulation of the one-dimensional Dirac equation using a single trapped ion set to behave as a free relativistic quantum particle. We measure the particle position as a function of time and study Zitterbewegung for different initial superpositions of positive- and negative-energy spinor states, as well as the crossover from relativistic to non-relativistic dynamics. The high level of control of trapped-ion experimental parameters makes it possible to simulate textbook examples of relativistic quantum physics. PMID:20054392
Pouthier, Vincent
2010-09-29
A detailed analysis is performed to show that the second order time-convolutionless master equation fails to describe the exciton-phonon dynamics in a finite size lattice. To proceed, special attention is paid to characterizing the coherences of the exciton reduced density matrix. These specific elements measure the ability of the exciton to develop superimpositions involving the vacuum and the one-exciton states. It is shown that the coherences behave as wavefunctions whose dynamics is governed by a time-dependent effective Hamiltonian defined in terms of the so-called time-dependent relaxation operator. Due to the confinement, quantum recurrences provide to the relaxation operator an almost periodic nature, so the master equation reduces to a linear system of differential equations with almost periodic coefficients. We show that, in accordance with the Floquet theory, unstable solutions emerge due to parametric resonances involving specific frequencies of the relaxation operator and specific excitonic eigenfrequencies. These resonances give rise to an unphysical exponential growth of the coherences, indicating the breakdown of the second order master equation. PMID:21386551
Zakharov equations in quantum dusty plasmas
Sayed, F.; Vladimirov, S. V.; Ishihara, O.
2015-08-15
By generalizing the formalism of modulational interactions in quantum dusty plasmas, we derive the kinetic quantum Zakharov equations in dusty plasmas that describe nonlinear coupling of high frequency Langmuir waves to low frequency plasma density variations, for cases of non-degenerate and degenerate plasma electrons.
Lattice Boltzmann equation for relativistic quantum mechanics.
Succi, Sauro
2002-03-15
Relativistic versions of the quantum lattice Boltzmann equation are discussed. It is shown that the inclusion of nonlinear interactions requires the standard collision operator to be replaced by a pair of dynamic fields coupling to the relativistic wave function in a way which can be described by a multicomponent complex lattice Boltzmann equation. PMID:16210189
Matsugi, Akira
2015-03-12
Rate constants for thermal decomposition of 1,1,1-trifluoroethane (CH3CF3) in the high-temperature falloff region were previously reported to have an unusual pressure dependence that could not be explained by Rice-Ramsperger-Kassel-Marcus (RRKM) theory in combination with unimolecular master equation analysis. This study investigates the dynamics of the CH3CF3 dissociation and the energy transfer of CH3CF3 in collisions with Ar and Kr by classical trajectory calculations on a global potential energy surface constructed from a large number of quantum chemical calculations. The simulations showed that the ensemble-averaged CH3CF3 populations decay with single exponential profiles that have rate constants close to those predicted by RRKM theory, indicating that the microcanonical ensemble is maintained during decomposition. The trajectory calculation also indicated that a significant portion of the HF product is formed in its vibrationally excited state. Such observation motivated this study to correct some of the reported rate constants for the CH3CF3 decomposition. With the correction applied, the experimental rate constants were well reproduced by the RRKM/master equation calculation using the collisional energy transfer parameters that were also obtained from trajectory calculations. Overall, the title reaction is demonstrated to be another successful example of RRKM/master equation modeling. PMID:25664485
Gelin, Maxim F
2014-12-01
We consider a classical point particle bilinearly coupled to a harmonic bath. Assuming that the evolution of the particle is monitored on a timescale which is longer than the characteristic bath correlation time, we derive the Markovian master equation for the probability density of the particle. The relaxation operator of this master equation is evaluated analytically, without invoking the perturbation theory and the approximation of weak system-bath coupling. When the bath correlation time tends to zero, the Fokker-Planck equation is recovered. For a finite bath correlation time, the relaxation operator contains contributions of all orders in the system-bath coupling. PMID:25481131
Kidon, Lyran; Wilner, Eli Y.; Rabani, Eran
2015-12-21
The generalized quantum master equation provides a powerful tool to describe the dynamics in quantum impurity models driven away from equilibrium. Two complementary approaches, one based on Nakajima–Zwanzig–Mori time-convolution (TC) and the other on the Tokuyama–Mori time-convolutionless (TCL) formulations provide a starting point to describe the time-evolution of the reduced density matrix. A key in both approaches is to obtain the so called “memory kernel” or “generator,” going beyond second or fourth order perturbation techniques. While numerically converged techniques are available for the TC memory kernel, the canonical approach to obtain the TCL generator is based on inverting a super-operator in the full Hilbert space, which is difficult to perform and thus, nearly all applications of the TCL approach rely on a perturbative scheme of some sort. Here, the TCL generator is expressed using a reduced system propagator which can be obtained from system observables alone and requires the calculation of super-operators and their inverse in the reduced Hilbert space rather than the full one. This makes the formulation amenable to quantum impurity solvers or to diagrammatic techniques, such as the nonequilibrium Green’s function. We implement the TCL approach for the resonant level model driven away from equilibrium and compare the time scales for the decay of the generator with that of the memory kernel in the TC approach. Furthermore, the effects of temperature, source-drain bias, and gate potential on the TCL/TC generators are discussed.
Equation of Motion of a Quantum Vortex
NASA Astrophysics Data System (ADS)
Cox, Timothy; Stamp, Philip
Understanding the motion of vortices in quantum fluids is key to understanding the dynamics of such fluids. The motion of quantum vortices has long been understood in terms of the Hall-Vinen-Iordanski (HVI) equations. A fully quantum mechanical treatment of vortex motion in a two-dimensional Bose superfluid leads to a modified version of the HVI equations which include significant history dependent forces and a fluctuating noise force. The dynamics deviates from that described by the HVI equations when the frequency of motion is higher than the temperature. We describe the consequences of the memory and noise for the motion of a single superfluid vortex as well as the circumstances under which their effects should be experimentally observable.
Coarse-grained kinetic equations for quantum systems
NASA Astrophysics Data System (ADS)
Petrov, E. G.
2013-01-01
The nonequilibrium density matrix method is employed to derive a master equation for the averaged state populations of an open quantum system subjected to an external high frequency stochastic field. It is shown that if the characteristic time τstoch of the stochastic process is much lower than the characteristic time τsteady of the establishment of the system steady state populations, then on the time scale Δ t ˜ τsteady, the evolution of the system populations can be described by the coarse-grained kinetic equations with the averaged transition rates. As an example, the exact averaging is carried out for the dichotomous Markov process of the kangaroo type.
Metabasin approach for computing the master equation dynamics of systems with broken ergodicity.
Mauro, John C; Loucks, Roger J; Gupta, Prabhat K
2007-08-16
We propose a technique for computing the master equation dynamics of systems with broken ergodicity. The technique involves a partitioning of the system into components, or metabasins, where the relaxation times within a metabasin are short compared to an observation time scale. In this manner, equilibrium statistical mechanics is assumed within each metabasin, and the intermetabasin dynamics are computed using a reduced set of master equations. The number of metabasins depends upon both the temperature of the system and its derivative with respect to time. With this technique, the integration time step of the master equations is governed by the observation time scale rather than the fastest transition time between basins. We illustrate the technique using a simple model landscape with seven basins and show validation against direct Euler integration. Finally, we demonstrate the use of the technique for a realistic glass-forming system (viz., selenium) where direct Euler integration is not computationally feasible. PMID:17649986
Vibrational energy flow in the villin headpiece subdomain: Master equation simulations
Leitner, David M. E-mail: stock@physik.uni-freiburg.de; Buchenberg, Sebastian; Brettel, Paul; Stock, Gerhard E-mail: stock@physik.uni-freiburg.de
2015-02-21
We examine vibrational energy flow in dehydrated and hydrated villin headpiece subdomain HP36 by master equation simulations. Transition rates used in the simulations are obtained from communication maps calculated for HP36. In addition to energy flow along the main chain, we identify pathways for energy transport in HP36 via hydrogen bonding between residues quite far in sequence space. The results of the master equation simulations compare well with all-atom non-equilibrium simulations to about 1 ps following initial excitation of the protein, and quite well at long times, though for some residues we observe deviations between the master equation and all-atom simulations at intermediate times from about 1–10 ps. Those deviations are less noticeable for hydrated than dehydrated HP36 due to energy flow into the water.
Complete positivity of a spin-1/2 master equation with memory
Maniscalco, Sabrina
2007-06-15
We study a non-Markovian spin-1/2 master equation with exponential memory. We derive the conditions under which the dynamical map describing the reduced system dynamics is completely positive, i.e., the nonunitary evolution of the system is compatible with a description in terms of a closed total spin-reservoir system. Our results show that for a zero-T reservoir, the dynamical map of the model here considered is never completely positive. For moderate- and high-T reservoirs, on the contrary, positivity is a necessary and sufficient condition for complete positivity. We also consider the Shabani-Lidar master equation recently introduced [A. Shabani and D.A. Lidar, Phys. Rev. A 71, 020101(R) (2005)] and we demonstrate that such a master equation is always completely positive.
Wigner-Lindblad Equations for Quantum Friction.
Bondar, Denys I; Cabrera, Renan; Campos, Andre; Mukamel, Shaul; Rabitz, Herschel A
2016-05-01
Dissipative forces are ubiquitous and thus constitute an essential part of realistic physical theories. However, quantization of dissipation has remained an open challenge for nearly a century. We construct a quantum counterpart of classical friction, a velocity-dependent force acting against the direction of motion. In particular, a translationary invariant Lindblad equation is derived satisfying the appropriate dynamical relations for the coordinate and momentum (i.e., the Ehrenfest equations). Numerical simulations establish that the model approximately equilibrates. These findings significantly advance a long search for a universally valid Lindblad model of quantum friction and open opportunities for exploring novel dissipation phenomena. PMID:27078510
Non-Markovian Effects in the Lindblad Master Equation Approach to Electronic Transport
NASA Astrophysics Data System (ADS)
Ribeiro, P.; Vieira, V. R.
Non-equilibrium processes in open quantum systems can be generically described within the framework of the Lindblad master equation i.e. without a memory kernel. This statement holds even for processes where information can flow-back from the environment to the system. This rather contra-intuitive fact lead to define a process as non Markovian if, during the time evolution of two different initial states of the system, their distinguishability increases, reflecting a back-flow of information from the environment to the system. However, for non Markovian dynamics, the set of conditions to ensure the positivity of the density matrix for all times is not known, making difficult the explicit construction of non Markovian Lindblad operators. Using the Keldysh non equilibrium Green's functions, we explicitly solve a generic quadratic model of electrons coupled at t = 0 to a set of wide-band baths characterized by temperature and chemical potential. We identify the equivalent Lindblad operators describing the evolution of the density matrix and show that the resulting dynamical process is generically non Markovian. We further discuss the cases in which Markovian dynamics is recovered. We apply our approach to a simple model for electronic transport thought a one dimensional wire coupled at t = 0 to wide-band metallic leads, and to a XY spin chain attached to two contacts.
NASA Astrophysics Data System (ADS)
Sokolov, I. M.
2006-06-01
The work by Barbi, Bologna, and Grigolini [Phys. Rev. Lett. 95, 220601 (2005)] discusses a response to alternating external field of a non-Markovian two-state system, where the waiting time between the two attempted changes of state follows a power law. It introduced a new instrument for description of such situations based on a stochastic master equation with reset. In the present Brief Report we provide an alternative description of the situation within the framework of a generalized master equation. The results of our analytical approach are corroborated by direct numerical simulations of the system.
Quantum nonlinear Schrodinger equation on a lattice
Bogolyubov, N.M.; Korepin, V.E.
1986-09-01
A local Hamiltonian is constructed for the nonlinear Schrodinger equation on a lattice in both the classical and the quantum variants. This Hamiltonian is an explicit elementary function of the local Bose fields. The lattice model possesses the same structure of the action-angle variables as the continuous model.
Direct Solution of the Chemical Master Equation Using Quantized Tensor Trains
Kazeev, Vladimir; Khammash, Mustafa; Nip, Michael; Schwab, Christoph
2014-01-01
The Chemical Master Equation (CME) is a cornerstone of stochastic analysis and simulation of models of biochemical reaction networks. Yet direct solutions of the CME have remained elusive. Although several approaches overcome the infinite dimensional nature of the CME through projections or other means, a common feature of proposed approaches is their susceptibility to the curse of dimensionality, i.e. the exponential growth in memory and computational requirements in the number of problem dimensions. We present a novel approach that has the potential to “lift” this curse of dimensionality. The approach is based on the use of the recently proposed Quantized Tensor Train (QTT) formatted numerical linear algebra for the low parametric, numerical representation of tensors. The QTT decomposition admits both, algorithms for basic tensor arithmetics with complexity scaling linearly in the dimension (number of species) and sub-linearly in the mode size (maximum copy number), and a numerical tensor rounding procedure which is stable and quasi-optimal. We show how the CME can be represented in QTT format, then use the exponentially-converging -discontinuous Galerkin discretization in time to reduce the CME evolution problem to a set of QTT-structured linear equations to be solved at each time step using an algorithm based on Density Matrix Renormalization Group (DMRG) methods from quantum chemistry. Our method automatically adapts the “basis” of the solution at every time step guaranteeing that it is large enough to capture the dynamics of interest but no larger than necessary, as this would increase the computational complexity. Our approach is demonstrated by applying it to three different examples from systems biology: independent birth-death process, an example of enzymatic futile cycle, and a stochastic switch model. The numerical results on these examples demonstrate that the proposed QTT method achieves dramatic speedups and several orders of magnitude
Direct solution of the Chemical Master Equation using quantized tensor trains.
Kazeev, Vladimir; Khammash, Mustafa; Nip, Michael; Schwab, Christoph
2014-03-01
The Chemical Master Equation (CME) is a cornerstone of stochastic analysis and simulation of models of biochemical reaction networks. Yet direct solutions of the CME have remained elusive. Although several approaches overcome the infinite dimensional nature of the CME through projections or other means, a common feature of proposed approaches is their susceptibility to the curse of dimensionality, i.e. the exponential growth in memory and computational requirements in the number of problem dimensions. We present a novel approach that has the potential to "lift" this curse of dimensionality. The approach is based on the use of the recently proposed Quantized Tensor Train (QTT) formatted numerical linear algebra for the low parametric, numerical representation of tensors. The QTT decomposition admits both, algorithms for basic tensor arithmetics with complexity scaling linearly in the dimension (number of species) and sub-linearly in the mode size (maximum copy number), and a numerical tensor rounding procedure which is stable and quasi-optimal. We show how the CME can be represented in QTT format, then use the exponentially-converging hp-discontinuous Galerkin discretization in time to reduce the CME evolution problem to a set of QTT-structured linear equations to be solved at each time step using an algorithm based on Density Matrix Renormalization Group (DMRG) methods from quantum chemistry. Our method automatically adapts the "basis" of the solution at every time step guaranteeing that it is large enough to capture the dynamics of interest but no larger than necessary, as this would increase the computational complexity. Our approach is demonstrated by applying it to three different examples from systems biology: independent birth-death process, an example of enzymatic futile cycle, and a stochastic switch model. The numerical results on these examples demonstrate that the proposed QTT method achieves dramatic speedups and several orders of magnitude storage
Propagation of Chaos for the Thermostatted Kac Master Equation
NASA Astrophysics Data System (ADS)
Carlen, Eric; Mustafa, Dawan; Wennberg, Bernt
2015-03-01
The Kac model is a simplified model of an -particle system in which the collisions of a real particle system are modeled by random jumps of pairs of particle velocities. Kac proved propagation of chaos for this model, and hence provided a rigorous validation of the corresponding Boltzmann equation. Starting with the same model we consider an -particle system in which the particles are accelerated between the jumps by a constant uniform force field which conserves the total energy of the system. We show propagation of chaos for this model.
General transient solution of the one-step master equation in one dimension
NASA Astrophysics Data System (ADS)
Smith, Stephen; Shahrezaei, Vahid
2015-06-01
Exact analytical solutions of the master equation are limited to special cases and exact numerical methods are inefficient. Even the generic one-dimensional, one-step master equation has evaded exact solution, aside from the steady-state case. This type of master equation describes the dynamics of a continuous-time Markov process whose range consists of positive integers and whose transitions are allowed only between adjacent sites. The solution of any master equation can be written as the exponential of a (typically huge) matrix, which requires the calculation of the eigenvalues and eigenvectors of the matrix. Here we propose a linear algebraic method for simplifying this exponential for the general one-dimensional, one-step process. In particular, we prove that the calculation of the eigenvectors is actually not necessary for the computation of exponential, thereby we dramatically cut the time of this calculation. We apply our new methodology to examples from birth-death processes and biochemical networks. We show that the computational time is significantly reduced compared to existing methods.
Generalized mean-field or master equation for nonlinear cavities with transverse effects
Dunlop, A.M.; Firth, W.J.; Heatley, D.R.; Wright, E.
1996-06-01
We present a general form of master equation for nonlinear-optical cavities that can be described by an {ital ABCD}matrix. It includes as special cases some previous models of spatiotemporal effects in lasers. {copyright} {ital 1996 Optical Society of America.}
NASA Astrophysics Data System (ADS)
Umut Caglar, Mehmet; Pal, Ranadip
2010-10-01
The central dogma of molecular biology states that ``information cannot be transferred back from protein to either protein or nucleic acid.'' However, this assumption is not exactly correct in most of the cases. There are a lot of feedback loops and interactions between different levels of systems. These types of interactions are hard to analyze due to the lack of data in the cellular level and probabilistic nature of interactions. Probabilistic models like Stochastic Master Equation (SME) or deterministic models like differential equations (DE) can be used to analyze these types of interactions. SME models based on chemical master equation (CME) can provide detailed representation of genetic regulatory system, but their use is restricted by the large data requirements and computational costs of calculations. The differential equations models on the other hand, have low calculation costs and much more adequate to generate control procedures on the system; but they are not adequate to investigate the probabilistic nature of interactions. In this work the success of the mapping between SME and DE is analyzed, and the success of a control policy generated by DE model with respect to SME model is examined. Index Terms--- Stochastic Master Equation models, Differential Equation Models, Control Policy Design, Systems biology
Nonlinear quantum equations: Classical field theory
Rego-Monteiro, M. A.; Nobre, F. D.
2013-10-15
An exact classical field theory for nonlinear quantum equations is presented herein. It has been applied recently to a nonlinear Schrödinger equation, and it is shown herein to hold also for a nonlinear generalization of the Klein-Gordon equation. These generalizations were carried by introducing nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard, linear equations, are recovered in the limit q→ 1. The main characteristic of this field theory consists on the fact that besides the usual Ψ(x(vector sign),t), a new field Φ(x(vector sign),t) needs to be introduced in the Lagrangian, as well. The field Φ(x(vector sign),t), which is defined by means of an additional equation, becomes Ψ{sup *}(x(vector sign),t) only when q→ 1. The solutions for the fields Ψ(x(vector sign),t) and Φ(x(vector sign),t) are found herein, being expressed in terms of a q-plane wave; moreover, both field equations lead to the relation E{sup 2}=p{sup 2}c{sup 2}+m{sup 2}c{sup 4}, for all values of q. The fact that such a classical field theory works well for two very distinct nonlinear quantum equations, namely, the Schrödinger and Klein-Gordon ones, suggests that this procedure should be appropriate for a wider class nonlinear equations. It is shown that the standard global gauge invariance is broken as a consequence of the nonlinearity.
Dynamical invariants in a non-Markovian quantum-state-diffusion equation
NASA Astrophysics Data System (ADS)
Luo, Da-Wei; Pyshkin, P. V.; Lam, Chi-Hang; Yu, Ting; Lin, Hai-Qing; You, J. Q.; Wu, Lian-Ao
2015-12-01
We find dynamical invariants for open quantum systems described by the non-Markovian quantum-state-diffusion (QSD) equation. In stark contrast to closed systems where the dynamical invariant can be identical to the system density operator, these dynamical invariants no longer share the equation of motion for the density operator. Moreover, the invariants obtained with a biorthonormal basis can be used to render an exact solution to the QSD equation and the corresponding non-Markovian dynamics without using master equations or numerical simulations. Significantly we show that we can apply these dynamical invariants to reverse engineering a Hamiltonian that is capable of driving the system to the target state, providing a different way to design control strategy for open quantum systems.
Dynamics of the chemical master equation, a strip of chains of equations in d-dimensional space.
Galstyan, Vahe; Saakian, David B
2012-07-01
We investigate the multichain version of the chemical master equation, when there are transitions between different states inside the long chains, as well as transitions between (a few) different chains. In the discrete version, such a model can describe the connected diffusion processes with jumps between different types. We apply the Hamilton-Jacobi equation to solve some aspects of the model. We derive exact (in the limit of infinite number of particles) results for the dynamic of the maximum of the distribution and the variance of distribution. PMID:23005386
Master equation approach for interacting slow- and stationary-light polaritons
Kiffner, M.; Hartmann, M. J.
2010-09-15
A master equation approach for the description of dark-state polaritons in coherently driven atomic media is presented. This technique provides a description of light-matter interactions under conditions of electromagnetically induced transparency (EIT) that is well suited for the treatment of polariton losses. The master equation approach allows us to describe general polariton-polariton interactions that may be conservative, dissipative, or a mixture of both. In particular, it enables us to study dissipation-induced correlations as a means for the creation of strongly correlated polariton systems. Our technique reveals a loss mechanism for stationary-light polaritons that has not been discussed so far. We find that polariton losses in level configurations with nondegenerate ground states can be a multiple of those in level schemes with degenerate ground states.
A Master Equation Approach to Modeling Short-term Behaviors of the Stock Market
NASA Astrophysics Data System (ADS)
Zhao, Conan; Yang, Xiaoxiang; Mazilu, Irina
2015-03-01
Short term fluctuations in stock prices are highly random, due to the multitude of external factors acting on the price determination process. While long-term economic factors such as inflation and revenue growth rate affect short-term price fluctuation, it is difficult to obtain the complete set of information and uncertainties associated with a given period of time. Instead, we propose a simpler short-term model based on only prior price averages and extrema. In this paper, we take a master equation under the random walk hypothesis and fit parameters based on AAPL stock price data over the past ten years. We report results for small system sizes and for the short term average price. These results may lead to a general closed-form solution to this particular master equation.
NASA Astrophysics Data System (ADS)
Gelß, Patrick; Matera, Sebastian; Schütte, Christof
2016-06-01
In multiscale modeling of heterogeneous catalytic processes, one crucial point is the solution of a Markovian master equation describing the stochastic reaction kinetics. Usually, this is too high-dimensional to be solved with standard numerical techniques and one has to rely on sampling approaches based on the kinetic Monte Carlo method. In this study we break the curse of dimensionality for the direct solution of the Markovian master equation by exploiting the Tensor Train Format for this purpose. The performance of the approach is demonstrated on a first principles based, reduced model for the CO oxidation on the RuO2(110) surface. We investigate the complexity for increasing system size and for various reaction conditions. The advantage over the stochastic simulation approach is illustrated by a problem with increased stiffness.
Nguyen, Thanh Lam; Stanton, John F
2015-07-16
In the field of chemical kinetics, the solution of a two-dimensional master equation that depends explicitly on both total internal energy (E) and total angular momentum (J) is a challenging problem. In this work, a weak-E/fixed-J collisional model (i.e., weak-collisional internal energy relaxation/free-collisional angular momentum relaxation) is used along with the steady-state approach to solve the resulting (simplified) two-dimensional (E,J)-grained master equation. The corresponding solutions give thermal rate constants and product branching ratios as functions of both temperature and pressure. We also have developed a program that can be used to predict and analyze experimental chemical kinetics results. This expedient technique, when combined with highly accurate potential energy surfaces, is cable of providing results that may be meaningfully compared to experiments. The reaction of singlet oxygen with methane proceeding through vibrationally excited methanol is used as an illustrative example. PMID:25815602
Master equation for a kinetic model of a trading market and its analytic solution
NASA Astrophysics Data System (ADS)
Chatterjee, Arnab; Chakrabarti, Bikas K.; Stinchcombe, Robin B.
2005-08-01
We analyze an ideal-gas-like model of a trading market with quenched random saving factors for its agents and show that the steady state income (m) distribution P(m) in the model has a power law tail with Pareto index ν exactly equal to unity, confirming the earlier numerical studies on this model. The analysis starts with the development of a master equation for the time development of P(m) . Precise solutions are then obtained in some special cases.
Recent applications of the Boltzmann master equation to heavy ion precompound decay phenomena
Blann, M.; Remington, B.A.
1988-06-01
The Boltzmann master equation (BME) is described and used as a tool to interpret preequilibrium neutron emission from heavy ion collisions gated on evaporation residue or fission fragments. The same approach is used to interpret neutron spectra gated on deep inelastic and quasi-elastic heavy ion collisions. Less successful applications of BME to proton inclusive data with 40 MeV/u incident /sup 12/C ions are presented, and improvements required in the exciton injection term are discussed.
Breakdown of the reaction-diffusion master equation with nonelementary rates
NASA Astrophysics Data System (ADS)
Smith, Stephen; Grima, Ramon
2016-05-01
The chemical master equation (CME) is the exact mathematical formulation of chemical reactions occurring in a dilute and well-mixed volume. The reaction-diffusion master equation (RDME) is a stochastic description of reaction-diffusion processes on a spatial lattice, assuming well mixing only on the length scale of the lattice. It is clear that, for the sake of consistency, the solution of the RDME of a chemical system should converge to the solution of the CME of the same system in the limit of fast diffusion: Indeed, this has been tacitly assumed in most literature concerning the RDME. We show that, in the limit of fast diffusion, the RDME indeed converges to a master equation but not necessarily the CME. We introduce a class of propensity functions, such that if the RDME has propensities exclusively of this class, then the RDME converges to the CME of the same system, whereas if the RDME has propensities not in this class, then convergence is not guaranteed. These are revealed to be elementary and nonelementary propensities, respectively. We also show that independent of the type of propensity, the RDME converges to the CME in the simultaneous limit of fast diffusion and large volumes. We illustrate our results with some simple example systems and argue that the RDME cannot generally be an accurate description of systems with nonelementary rates.
Sqeezing generated by a nonlinear master equation and by amplifying-dissipative Hamiltonians
NASA Technical Reports Server (NTRS)
Dodonov, V. V.; Marchiolli, M. A.; Mizrahi, Solomon S.; Moussa, M. H. Y.
1994-01-01
In the first part of this contribution we show that the master equation derived from the generalized version of the nonlinear Doebner-Goldin equation leads to the squeezing of one of the quadratures. In the second part we consider two familiar Hamiltonians, the Bateman- Caldirola-Kanai and the optical parametric oscillator; going back to their classical Lagrangian form we introduce a stochastic force and a dissipative factor. From this new Lagrangian we obtain a modified Hamiltonian that treats adequately the simultaneous amplification and dissipation phenomena, presenting squeezing, too.
Variance estimates for transport in stochastic media by means of the master equation
Pautz, S. D.; Franke, B. C.; Prinja, A. K.
2013-07-01
The master equation has been used to examine properties of transport in stochastic media. It has been shown previously that not only may the Levermore-Pomraning (LP) model be derived from the master equation for a description of ensemble-averaged transport quantities, but also that equations describing higher-order statistical moments may be obtained. We examine in greater detail the equations governing the second moments of the distribution of the angular fluxes, from which variances may be computed. We introduce a simple closure for these equations, as well as several models for estimating the variances of derived transport quantities. We revisit previous benchmarks for transport in stochastic media in order to examine the error of these new variance models. We find, not surprisingly, that the errors in these variance estimates are at least as large as the corresponding estimates of the average, and sometimes much larger. We also identify patterns in these variance estimates that may help guide the construction of more accurate models. (authors)
Unification of the general non-linear sigma model and the Virasoro master equation
Boer, J. de; Halpern, M.B. |
1997-06-01
The Virasoro master equation describes a large set of conformal field theories known as the affine-Virasoro constructions, in the operator algebra (affinie Lie algebra) of the WZW model, while the einstein equations of the general non-linear sigma model describe another large set of conformal field theories. This talk summarizes recent work which unifies these two sets of conformal field theories, together with a presumable large class of new conformal field theories. The basic idea is to consider spin-two operators of the form L{sub ij}{partial_derivative}x{sup i}{partial_derivative}x{sup j} in the background of a general sigma model. The requirement that these operators satisfy the Virasoro algebra leads to a set of equations called the unified Einstein-Virasoro master equation, in which the spin-two spacetime field L{sub ij} cuples to the usual spacetime fields of the sigma model. The one-loop form of this unified system is presented, and some of its algebraic and geometric properties are discussed.
One parameter family of master equations for logistic growth and BCM theory
NASA Astrophysics Data System (ADS)
De Oliveira, L. R.; Castellani, C.; Turchetti, G.
2015-02-01
We propose a one parameter family of master equations, for the evolution of a population, having the logistic equation as mean field limit. The parameter α determines the relative weight of linear versus nonlinear terms in the population number n ⩽ N entering the loss term. By varying α from 0 to 1 the equilibrium distribution changes from maximum growth to almost extinction. The former is a Gaussian centered at n = N, the latter is a power law peaked at n = 1. A bimodal distribution is observed in the transition region. When N grows and tends to ∞, keeping the value of α fixed, the distribution tends to a Gaussian centered at n = N whose limit is a delta function corresponding to the stable equilibrium of the mean field equation. The choice of the master equation in this family depends on the equilibrium distribution for finite values of N. The presence of an absorbing state for n = 0 does not change this picture since the extinction mean time grows exponentially fast with N. As a consequence for α close to zero extinction is not observed, whereas when α approaches 1 the relaxation to a power law is observed before extinction occurs. We extend this approach to a well known model of synaptic plasticity, the so called BCM theory in the case of a single neuron with one or two synapses.
Birth and death master equation for the evolution of complex networks
NASA Astrophysics Data System (ADS)
Alvarez-Martínez, R.; Cocho, G.; Rodríguez, R. F.; Martínez-Mekler, G.
2014-05-01
Master equations for the evolution of complex networks with positive (birth) and negative (death) transition probabilities per unit time are analyzed. Explicit equations for the time evolution of the total number of nodes and for the relative node frequencies are given. It is shown that, in the continuous limit, the master equation reduces to a Fokker-Planck equation (FPE). The basic dynamical function for its stationary solution is the ratio between its drift and diffusion coefficients. When this ratio is approximated by partial fractions (Padé's approximants), a hierarchy of stationary solutions of the FPE is obtained analytically, which are expressed as an exponential times the product of powers of monomials and binomials. It is also shown that if the difference between birth and death transition probabilities goes asymptotically to zero, the exponential factor in the solution is absent. Fits to real complex network probability distribution functions are shown. Comparison with rank-ordered data shows that, in general, the value of this exponential factor is close to unity, evidencing crossovers among power-law scale invariant regimes which might be associated to an underlying criticality and are related to a generalization of the beta distribution. The time dependent solution is also obtained analytically in terms of hyper-geometric functions. It is also shown that the FPE has similarity solutions. The limitations of the approach here presented are also discussed.
NASA Astrophysics Data System (ADS)
Tessarotto, Massimo; Cremaschini, Claudio
2014-07-01
In this investigation, exact particular realizations are sought for the microscopic statistical description which is associated with the classical dynamical system (CDS) formed by N identical smooth hard spheres subject to elastic collisions ( S N -CDS). The problem is posed in the framework of the ab initio statistical description of S N -CDS recently developed. It is shown that the Liouville equation associated with SN-CDS admits an exact particular solution for the N-body probability density function (PDF). This is factorized in terms of the i-th particle 1-body PDF (for all i = 1, N) via suitable weighting factors, which are denoted here as particle occupation coefficients. The latter are found to depend functionally only on the 1-body PDFs which are associated with each of the remaining particles belonging to S N -CDS. Furthermore, the 1-body PDF is proved to obey a well-defined statistical equation, referred to here as Master kinetic equation. This is an exact kinetic equation which takes into account the occurrence of configuration-space correlations due to the finite size of the extended particles, while depending functionally on the same 1-body PDF only. The asymptotic approximation of the Master equation, which holds in validity of the Boltzmann-Grad limit, is shown to recover in a suitable asymptotic sense the customary Boltzmann equation. Finally, a critical analysis is presented of the original and modified versions of the Enskog kinetic equation, as well as of some of the non-linear kinetic approaches formulated in the past for dense granular gases. Their conditions of validity and main differences with respect to the present theory are pointed out.
Boundary transfer matrices and boundary quantum KZ equations
Vlaar, Bart
2015-07-15
A simple relation between inhomogeneous transfer matrices and boundary quantum Knizhnik-Zamolodchikov (KZ) equations is exhibited for quantum integrable systems with reflecting boundary conditions, analogous to an observation by Gaudin for periodic systems. Thus, the boundary quantum KZ equations receive a new motivation. We also derive the commutativity of Sklyanin’s boundary transfer matrices by merely imposing appropriate reflection equations, in particular without using the conditions of crossing symmetry and unitarity of the R-matrix.
Alarcón, Tomás
2014-05-14
In this paper, we propose two methods to carry out the quasi-steady state approximation in stochastic models of enzyme catalytic regulation, based on WKB asymptotics of the chemical master equation or of the corresponding partial differential equation for the generating function. The first of the methods we propose involves the development of multiscale generalisation of a WKB approximation of the solution of the master equation, where the separation of time scales is made explicit which allows us to apply the quasi-steady state approximation in a straightforward manner. To the lowest order, the multi-scale WKB method provides a quasi-steady state, Gaussian approximation of the probability distribution. The second method is based on the Hamilton-Jacobi representation of the stochastic process where, as predicted by large deviation theory, the solution of the partial differential equation for the corresponding characteristic function is given in terms of an effective action functional. The optimal transition paths between two states are then given by those paths that maximise the effective action. Such paths are the solutions of the Hamilton equations for the Hamiltonian associated to the effective action functional. The quasi-steady state approximation is applied to the Hamilton equations thus providing an approximation to the optimal transition paths and the transition time between two states. Using this approximation we predict that, unlike the mean-field quasi-steady approximation result, the rate of enzyme catalysis depends explicitly on the initial number of enzyme molecules. The accuracy and validity of our approximated results as well as that of our predictions regarding the behaviour of the stochastic enzyme catalytic models are verified by direct simulation of the stochastic model using Gillespie stochastic simulation algorithm. PMID:24832255
Alarcón, Tomás
2014-05-14
In this paper, we propose two methods to carry out the quasi-steady state approximation in stochastic models of enzyme catalytic regulation, based on WKB asymptotics of the chemical master equation or of the corresponding partial differential equation for the generating function. The first of the methods we propose involves the development of multiscale generalisation of a WKB approximation of the solution of the master equation, where the separation of time scales is made explicit which allows us to apply the quasi-steady state approximation in a straightforward manner. To the lowest order, the multi-scale WKB method provides a quasi-steady state, Gaussian approximation of the probability distribution. The second method is based on the Hamilton-Jacobi representation of the stochastic process where, as predicted by large deviation theory, the solution of the partial differential equation for the corresponding characteristic function is given in terms of an effective action functional. The optimal transition paths between two states are then given by those paths that maximise the effective action. Such paths are the solutions of the Hamilton equations for the Hamiltonian associated to the effective action functional. The quasi-steady state approximation is applied to the Hamilton equations thus providing an approximation to the optimal transition paths and the transition time between two states. Using this approximation we predict that, unlike the mean-field quasi-steady approximation result, the rate of enzyme catalysis depends explicitly on the initial number of enzyme molecules. The accuracy and validity of our approximated results as well as that of our predictions regarding the behaviour of the stochastic enzyme catalytic models are verified by direct simulation of the stochastic model using Gillespie stochastic simulation algorithm.
Unified Einstein-Virasoro Master Equation in the General Non-Linear Sigma Model
Boer, J. de; Halpern, M.B.
1996-06-05
The Virasoro master equation (VME) describes the general affine-Virasoro construction $T=L^abJ_aJ_b+iD^a \\dif J_a$ in the operator algebra of the WZW model, where $L^ab$ is the inverse inertia tensor and $D^a $ is the improvement vector. In this paper, we generalize this construction to find the general (one-loop) Virasoro construction in the operator algebra of the general non-linear sigma model. The result is a unified Einstein-Virasoro master equation which couples the spacetime spin-two field $L^ab$ to the background fields of the sigma model. For a particular solution $L_G^ab$, the unified system reduces to the canonical stress tensors and conventional Einstein equations of the sigma model, and the system reduces to the general affine-Virasoro construction and the VME when the sigma model is taken to be the WZW action. More generally, the unified system describes a space of conformal field theories which is presumably much larger than the sum of the general affine-Virasoro construction and the sigma model with its canonical stress tensors. We also discuss a number of algebraic and geometrical properties of the system, including its relation to an unsolved problem in the theory of $G$-structures on manifolds with torsion.
Computational study of p53 regulation via the chemical master equation
NASA Astrophysics Data System (ADS)
Vo, Huy D.; Sidje, Roger B.
2016-06-01
A stochastic model of cellular p53 regulation was established in Leenders, and Tuszynski (2013 Front. Oncol. 3 1–16) to study the interactions of p53 with MDM2 proteins, where the stochastic analysis was done using a Monte Carlo approach. We revisit that model here using an alternative scheme, which is to directly solve the chemical master equation (CME) by an adaptive Krylov-based finite state projection method that combines the stochastic simulation algorithm with other computational strategies, namely Krylov approximation techniques to the matrix exponential, divide and conquer, and aggregation. We report numerical results that demonstrate the extend of tackling the CME with this combination of tools.
Dinh, Khanh N; Sidje, Roger B
2016-01-01
The finite state projection (FSP) method has enabled us to solve the chemical master equation of some biological models that were considered out of reach not long ago. Since the original FSP method, much effort has gone into transforming it into an adaptive time-stepping algorithm as well as studying its accuracy. Some of the improvements include the multiple time interval FSP, the sliding windows, and most notably the Krylov-FSP approach. Our goal in this tutorial is to give the reader an overview of the current methods that build on the FSP. PMID:27176781
NASA Astrophysics Data System (ADS)
Dinh, Khanh N.; Sidje, Roger B.
2016-06-01
The finite state projection (FSP) method has enabled us to solve the chemical master equation of some biological models that were considered out of reach not long ago. Since the original FSP method, much effort has gone into transforming it into an adaptive time-stepping algorithm as well as studying its accuracy. Some of the improvements include the multiple time interval FSP, the sliding windows, and most notably the Krylov-FSP approach. Our goal in this tutorial is to give the reader an overview of the current methods that build on the FSP.
Emergence of wave equations from quantum geometry
NASA Astrophysics Data System (ADS)
Majid, Shahn
2012-10-01
We argue that classical geometry should be viewed as a special limit of noncommutative geometry in which aspects which are inter-constrained decouple and appear arbitrary in the classical limit. In particular, the wave equation is really a partial derivative in a unified extra-dimensional noncommutative geometry and arises out of the greater rigidity of the noncommutative world not visible in the classical limit. We provide an introduction to this 'wave operator' approach to noncommutative geometry as recently used[27] to quantize any static spacetime metric admitting a spatial conformal Killing vector field, and in particular to construct the quantum Schwarzschild black hole. We also give an introduction to our related result that every classical Riemannian manifold is a shadow of a slightly noncommutative one wherein the meaning of the classical Ricci tensor becomes very natural as the square of a generalised braiding.
Neutrino quantum kinetic equations: The collision term
Blaschke, Daniel N.; Cirigliano, Vincenzo
2016-08-25
We derive the collision term relevant for neutrino quantum kinetic equations in the early universe and compact astrophysical objects, displaying its full matrix structure in both flavor and spin degrees of freedom. We include in our analysis neutrino-neutrino processes, scattering and annihilation with electrons and positrons, and neutrino scattering off nucleons (the latter in the low-density limit). After presenting the general structure of the collision terms, we take two instructive limiting cases. The one-flavor limit highlights the structure in helicity space and allows for a straightforward interpretation of the off-diagonal entries in terms of the product of scattering amplitudes ofmore » the two helicity states. As a result, the isotropic limit is relevant for studies of the early universe: in this case the terms involving spin coherence vanish and the collision term can be expressed in terms of two-dimensional integrals, suitable for computational implementation.« less
Emergence of wave equations from quantum geometry
Majid, Shahn
2012-09-24
We argue that classical geometry should be viewed as a special limit of noncommutative geometry in which aspects which are inter-constrained decouple and appear arbitrary in the classical limit. In particular, the wave equation is really a partial derivative in a unified extra-dimensional noncommutative geometry and arises out of the greater rigidity of the noncommutative world not visible in the classical limit. We provide an introduction to this 'wave operator' approach to noncommutative geometry as recently used[27] to quantize any static spacetime metric admitting a spatial conformal Killing vector field, and in particular to construct the quantum Schwarzschild black hole. We also give an introduction to our related result that every classical Riemannian manifold is a shadow of a slightly noncommutative one wherein the meaning of the classical Ricci tensor becomes very natural as the square of a generalised braiding.
Quantum mechanics without an equation of motion
Alhaidari, A. D.
2011-06-15
We propose a formulation of quantum mechanics for a finite level system whose potential function is not realizable and/or analytic solution of the wave equation is not feasible. The system's wavefunction is written as an infinite sum in a complete set of square integrable functions. Interaction in the theory is introduced in function space by a real finite tridiagonal symmetric matrix. The expansion coefficients of the wavefunction satisfy a three-term recursion relation incorporating the parameters of the interaction. Information about the structure and dynamics of the system is contained in the scattering matrix, which is defined in the usual way. The bound state energy spectrum (system's structure) is finite. Apart from the 2M- 1 dimensionless parameters of the interaction matrix, whose rank is M, the theory has one additional scale parameter. In the development, we utilize the kinematic tools of the J-matrix method.
Quantum lattice gas algorithm for the telegraph equation
NASA Astrophysics Data System (ADS)
Coffey, Mark W.; Colburn, Gabriel G.
2009-06-01
The telegraph equation combines features of both the diffusion and wave equations and has many applications to heat propagation, transport in disordered media, and elsewhere. We describe a quantum lattice gas algorithm (QLGA) for this partial differential equation with one spatial dimension. This algorithm generalizes one previously known for the diffusion equation. We present an analysis of the algorithm and accompanying simulation results. The QLGA is suitable for simulation on combined classical-quantum computers.
Suitability of the master-equation approach for micromasers with non-Poissonian pumping
NASA Astrophysics Data System (ADS)
Davidovich, L.; Zhu, S.-Y.; Khoury, A. Z.; Su, C.
1992-08-01
Attention is given to the application to micromasers of a recently proposed generalized master equation, which takes into account the statistics of the pumping mechanism. This equation provides very good results when the photon number probability distribution is sharp and the average number of photons is large, while the number of Rabi turns in the cavity is not very large. It may lead to incorrect results in situations corresponding to multipeaked distributions with peaks of approximately equal height, or when theta sub(int) becomes of the order of Nex. For theta(int) much lower than Nex, adding up more terms in the expansion of the logarithm helps to improve the result, leading to a very good approximation, so long as the number of terms is not comparable to the average number of photons.
Master equation with quantized atomic motion including dipole-dipole interactions
NASA Astrophysics Data System (ADS)
Damanet, François; Braun, Daniel; Martin, John
2016-05-01
We derive a markovian master equation for the internal dynamics of an ensemble of two-level atoms including all effects related to the quantization of their motion. Our equation provides a unifying picture of the consequences of recoil and indistinguishability of atoms beyond the Lamb-Dicke regime on both their dissipative and conservative dynamics, and is relevant for experiments with ultracold trapped atoms. We give general expressions for the decay rates and the dipole-dipole shifts for any motional states, and we find analytical formulas for a number of relevant states (Gaussian states, Fock states and thermal states). In particular, we show that the dipole-dipole interactions and cooperative photon emission can be modulated through the external state of motion. The effects predicted should be experimentally observable with Rydberg atoms. FD would like to thank the F.R.S.-FNRS for financial support. FD is a FRIA Grant holder of the Fonds de la Recherche Scientifique-FNRS.
Balance equations in semi-relativistic quantum hydrodynamics
NASA Astrophysics Data System (ADS)
Ivanov, A. Yu.; Andreev, P. A.; Kuz'menkov, L. S.
2014-05-01
Method of the quantum hydrodynamics has been applied in quantum plasmas studies. As the first step in our consideration, derivation of classical semi-relativistic (i.e., described by the Darwin Lagrangian on microscopic level) hydrodynamical equations is given after a brief review of method development. It provides better distinguishing between classic and quantum semi-relativistic effects. Derivation of the classical equations is interesting since it is made by a natural, but not very widespread method. This derivation contains explicit averaging of the microscopic dynamics. Derivation of corresponding quantum hydrodynamic equations is presented further. Equations are obtained in the five-momentum approximation including the continuity equation, Euler and energy balance equations. It is shown that relativistic corrections lead to presence of new quantum terms in expressions for a force field, a work field etc. The semi-relativistic generalization of the quantum Bohm potential is obtained. Quantum part of the energy current, which is an analog of the quantum Bohm potential for the energy evolution equation, is derived. The Langmuir wave dispersion in semi-relativistic quantum plasmas, corresponding to the Darwin Lagrangian, is also considered to demonstrate contribution of semi-relativistic effects on basic plasma phenomenon.
NASA Astrophysics Data System (ADS)
Alfonso, Lester; Zamora, Jose; Cruz, Pedro
2015-04-01
The stochastic approach to coagulation considers the coalescence process going in a system of a finite number of particles enclosed in a finite volume. Within this approach, the full description of the system can be obtained from the solution of the multivariate master equation, which models the evolution of the probability distribution of the state vector for the number of particles of a given mass. Unfortunately, due to its complexity, only limited results were obtained for certain type of kernels and monodisperse initial conditions. In this work, a novel numerical algorithm for the solution of the multivariate master equation for stochastic coalescence that works for any type of kernels and initial conditions is introduced. The performance of the method was checked by comparing the numerically calculated particle mass spectrum with analytical solutions obtained for the constant and sum kernels, with an excellent correspondence between the analytical and numerical solutions. In order to increase the speedup of the algorithm, software parallelization techniques with OpenMP standard were used, along with an implementation in order to take advantage of new accelerator technologies. Simulations results show an important speedup of the parallelized algorithms. This study was funded by a grant from Consejo Nacional de Ciencia y Tecnologia de Mexico SEP-CONACYT CB-131879. The authors also thanks LUFAC® Computacion SA de CV for CPU time and all the support provided.
General features and master equations for structurization in complex dusty plasmas
Tsytovich, V. N.; Morfill, G. E.
2012-02-15
Dust structurization is considered to be typical for complex plasmas. Homogeneous dusty plasmas are shown to be universally unstable. The dusty plasma structurization instability is similar to the gravitational instability and can results in creation of different compact dust structures. A general approach for investigation of the nonlinear stage of structurization in dusty plasmas is proposed and master equations for the description of self-organized structures are formulated in the general form that can be used for any nonlinear model of dust screening. New effects due to the scattering of ions on the nonlinearly screened grains are calculated: nonlinear ion dust drag force and nonlinear ion diffusion. The physics of confinement of dust and plasma components in the equilibria of compact dust structures is presented and is supported by numerical calculations of master equations. The necessary conditions for the existence of equilibrium structures are found for an arbitrary nonlinearity in dust screening. Features of compact dust structures observed in recent experiments agree with the numerically calculated ones. Some proposals for future experiments in spherical chamber are given.
Dou, Wenjie; Subotnik, Joseph E
2016-01-14
A broadened classical master equation (BCME) is proposed for modeling nonadiabatic dynamics for molecules near metal surfaces over a wide range of parameter values and with arbitrary initial conditions. Compared with a standard classical master equation-which is valid in the limit of weak molecule-metal couplings-this BCME should be valid for both weak and strong molecule-metal couplings. (The BCME can be mapped to a Fokker-Planck equation that captures level broadening correctly.) Finally, our BCME can be solved with a simple surface hopping algorithm; numerical tests of equilibrium and dynamical observables look very promising. PMID:26772563
Hertz Vectors and the Electromagnetic-Quantum Equations
NASA Astrophysics Data System (ADS)
Kouzaev, Guennadi A.
In this letter, a new form of electromagnetic-quantum equations is proposed. The electric and magnetic potentials are expressed through a single Hertz vector, and the systems of quantum and Maxwell equations are transformed into more compact integro-differential ones. These new forms are given for the Schrödinger, Pauli, Dirac and Klein-Gordon equations, and a practical way to calculate them by available software tools is considered.
Quantum Fokker-Planck-Kramers equation and entropy production
NASA Astrophysics Data System (ADS)
de Oliveira, Mário J.
2016-07-01
We use a canonical quantization procedure to set up a quantum Fokker-Planck-Kramers equation that accounts for quantum dissipation in a thermal environment. The dissipation term is chosen to ensure that the thermodynamic equilibrium is described by the Gibbs state. An expression for the quantum entropy production that properly describes quantum systems in a nonequilibrium stationary state is also provided. The time-dependent solution is given for a quantum harmonic oscillator in contact with a heat bath. We also obtain the stationary solution for a system of two coupled harmonic oscillators in contact with reservoirs at distinct temperatures, from which we obtain the entropy production and the quantum thermal conductance.
Solving the quantum brachistochrone equation through differential geometry
NASA Astrophysics Data System (ADS)
You, Chenglong; Wilde, Mark; Dowling, Jonathan; Wang, Xiaoting
2016-05-01
The ability of generating a particular quantum state, or model a physical quantum device by exploring quantum state transfer, is important in many applications such as quantum chemistry, quantum information processing, quantum metrology and cooling. Due to the environmental noise, a quantum device suffers from decoherence causing information loss. Hence, completing the state-generation task in a time-optimal way can be considered as a straightforward method to reduce decoherence. For a quantum system whose Hamiltonian has a fixed type and a finite energy bandwidth, it has been found that the time-optimal quantum evolution can be characterized by the quantum brachistochrone equation. In addition, the brachistochrone curve is found to have a geometric interpretation: it is the limit of a one-parameter family of geodesics on a sub-Riemannian model. Such geodesic-brachistochrone connection provides an efficient numerical method to solve the quantum brachistochrone equation. In this work, we will demonstrate this numerical method by studying the time-optimal state-generating problem on a given quantum spin system. We also find that the Pareto weighted-sum optimization turns out to be a simple but efficient method in solving the quantum time-optimal problems. We would like to acknowledge support from NSF under Award No. CCF-1350397.
Computational study of p53 regulation via the chemical master equation.
Vo, Huy D; Sidje, Roger B
2016-01-01
A stochastic model of cellular p53 regulation was established in Leenders, and Tuszynski (2013 Front. Oncol. 3 1-16) to study the interactions of p53 with MDM2 proteins, where the stochastic analysis was done using a Monte Carlo approach. We revisit that model here using an alternative scheme, which is to directly solve the chemical master equation (CME) by an adaptive Krylov-based finite state projection method that combines the stochastic simulation algorithm with other computational strategies, namely Krylov approximation techniques to the matrix exponential, divide and conquer, and aggregation. We report numerical results that demonstrate the extend of tackling the CME with this combination of tools. PMID:27125857
Critical assessment of two-qubit post-Markovian master equations
NASA Astrophysics Data System (ADS)
Campbell, S.; Smirne, A.; Mazzola, L.; Lo Gullo, N.; Vacchini, B.; Busch, Th.; Paternostro, M.
2012-03-01
A post-Markovian master equation has been recently proposed as a tool to describe the evolution of a system coupled to a memory-keeping environment [A. Shabani and D. A. Lidar, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.71.020101 71, 020101(R) (2005)]. For a single qubit affected by appropriately chosen environmental conditions, the corresponding dynamics is always legitimate and physical. Here we extend such a situation to the case of two qubits, only one of which experiences the environmental effects. We show how, despite the innocence of such an extension, the introduction of the second qubit should be done cum grano salis to avoid consequences such as the breaking of the positivity of the associated dynamical map. This hints at the necessity of using care when adopting phenomenologically derived models for evolutions occurring outside the Markovian framework.
Reformulation and solution of the master equation for multiple-well chemical reactions.
Georgievskii, Yuri; Miller, James A; Burke, Michael P; Klippenstein, Stephen J
2013-11-21
We consider an alternative formulation of the master equation for complex-forming chemical reactions with multiple wells and bimolecular products. Within this formulation the dynamical phase space consists of only the microscopic populations of the various isomers making up the reactive complex, while the bimolecular reactants and products are treated equally as sources and sinks. This reformulation yields compact expressions for the phenomenological rate coefficients describing all chemical processes, i.e., internal isomerization reactions, bimolecular-to-bimolecular reactions, isomer-to-bimolecular reactions, and bimolecular-to-isomer reactions. The applicability of the detailed balance condition is discussed and confirmed. We also consider the situation where some of the chemical eigenvalues approach the energy relaxation time scale and show how to modify the phenomenological rate coefficients so that they retain their validity. PMID:24053787
Thermal fluctuation statistics in a molecular motor described by a multidimensional master equation
NASA Astrophysics Data System (ADS)
Challis, K. J.; Jack, M. W.
2013-12-01
We present a theoretical investigation of thermal fluctuation statistics in a molecular motor. Energy transfer in the motor is described using a multidimensional discrete master equation with nearest-neighbor hopping. In this theory, energy transfer leads to statistical correlations between thermal fluctuations in different degrees of freedom. For long times, the energy transfer is a multivariate diffusion process with constant drift and diffusion. The fluctuations and drift align in the strong-coupling limit enabling a one-dimensional description along the coupled coordinate. We derive formal expressions for the probability distribution and simulate single trajectories of the system in the near- and far-from-equilibrium limits both for strong and weak coupling. Our results show that the hopping statistics provide an opportunity to distinguish different operating regimes.
Rapidity window dependences of higher order cumulants and diffusion master equation
NASA Astrophysics Data System (ADS)
Kitazawa, Masakiyo
2015-10-01
We study the rapidity window dependences of higher order cumulants of conserved charges observed in relativistic heavy ion collisions. The time evolution and the rapidity window dependence of the non-Gaussian fluctuations are described by the diffusion master equation. Analytic formulas for the time evolution of cumulants in a rapidity window are obtained for arbitrary initial conditions. We discuss that the rapidity window dependences of the non-Gaussian cumulants have characteristic structures reflecting the non-equilibrium property of fluctuations, which can be observed in relativistic heavy ion collisions with the present detectors. It is argued that various information on the thermal and transport properties of the hot medium can be revealed experimentally by the study of the rapidity window dependences, especially by the combined use, of the higher order cumulants. Formulas of higher order cumulants for a probability distribution composed of sub-probabilities, which are useful for various studies of non-Gaussian cumulants, are also presented.
NASA Astrophysics Data System (ADS)
Ghosh, Atiyo; Leier, Andre; Marquez-Lago, Tatiana
2014-03-01
Spatial stochastic effects are prevalent in many biological systems spanning a variety of scales, from intracellular (e.g. gene expression) to ecological (plankton aggregation). The most common ways of simulating such systems involve drawing sample paths from either the Reaction Diffusion Master Equation (RDME) or the Smoluchowski Equation, using methods such as Gillespie's Simulation Algorithm, Green's Function Reaction Dynamics and Single Particle Tracking. The simulation times of such techniques scale with the number of simulated particles, leading to much computational expense when considering large systems. The Spatial Chemical Langevin Equation (SCLE) can be simulated with fixed time intervals, independent of the number of particles, and can thus provide significant computational savings. However, very little work has been done to investigate the behavior of the SCLE. In this talk we summarize our findings on comparing the SCLE to the well-studied RDME. We use both analytical and numerical procedures to show when one should expect the moments of the SCLE to be close to the RDME, and also when they should differ.
Master equation approach to charge injection and transport in organic insulators
NASA Astrophysics Data System (ADS)
Freire, José A.; Voss, Grasiela
2005-03-01
We develop a master equation model of a disordered organic insulator sandwiched between metallic electrodes by treating as rate processes both the injection and the internal transport. We show how the master equation model allows for the inclusion of crucial correlation effects in the charge transport, particularly of the Pauli exclusion principle and of space-charge effects, besides, being dependent on just the microscopic form of the transfer rate between the localized electronic states, it allows for the investigation of different microscopic scenarios in the organic, such as polaronic hopping, correlated energy levels, interaction with image charge, etc. The model allows for a separate analysis of the injection and the recombination currents. We find that the disorder, besides increasing the injection current, eliminates the possibility of observation of a Fowler-Nordheim injection current at zero temperature, and that it does not alter the Schottky barrier size of the zero-field thermionic injection current from the value based on the energy difference between the electrode Fermi level and the highest occupied molecular orbital/lowest unoccupied molecular orbital levels in the organic, but it makes the Arrhenius temperature dependence appear at larger temperatures. We investigate how the I(V ) characteristics of a device is affected by the presence of correlations in the site energy distribution and by the form of the internal hopping rate, specifically the Miller-Abrahams rate and the Marcus or small-polaron rate. We show that the disorder does not modify significantly the eβ√E field dependence of the net current due to the Schottky barrier lowering caused by the attraction between the charge and its image in the electrode.
Master equation approach to charge injection and transport in organic insulators.
Freire, José A; Voss, Grasiela
2005-03-22
We develop a master equation model of a disordered organic insulator sandwiched between metallic electrodes by treating as rate processes both the injection and the internal transport. We show how the master equation model allows for the inclusion of crucial correlation effects in the charge transport, particularly of the Pauli exclusion principle and of space-charge effects, besides, being dependent on just the microscopic form of the transfer rate between the localized electronic states, it allows for the investigation of different microscopic scenarios in the organic, such as polaronic hopping, correlated energy levels, interaction with image charge, etc. The model allows for a separate analysis of the injection and the recombination currents. We find that the disorder, besides increasing the injection current, eliminates the possibility of observation of a Fowler-Nordheim injection current at zero temperature, and that it does not alter the Schottky barrier size of the zero-field thermionic injection current from the value based on the energy difference between the electrode Fermi level and the highest occupied molecular orbital/lowest unoccupied molecular orbital levels in the organic, but it makes the Arrhenius temperature dependence appear at larger temperatures. We investigate how the I(V) characteristics of a device is affected by the presence of correlations in the site energy distribution and by the form of the internal hopping rate, specifically the Miller-Abrahams rate and the Marcus or small-polaron rate. We show that the disorder does not modify significantly the ebeta square root E field dependence of the net current due to the Schottky barrier lowering caused by the attraction between the charge and its image in the electrode. PMID:15836407
Ghaderi, Nima
2016-03-28
Expressions for a K-adiabatic master equation for a bimolecular recombination rate constant krec are derived for a bimolecular reaction forming a complex with a single well or complexes with multiple well, where K is the component of the total angular momentum along the axis of least moment of inertia of the recombination product. The K-active master equation is also considered. The exact analytic solutions, i.e., the K-adiabatic and K-active steady-state population distribution function of reactive complexes, g(EJK) and g(EJ), respectively, are derived for the K-adiabatic and K-active master equation cases using properties of inhomogeneous integral equations (Fredholm type). The solutions accommodate arbitrary intermolecular energy transfer models, e.g., the single exponential, double exponential, Gaussian, step-ladder, and near-singularity models. At the high pressure limit, the krec for both the K-adiabatic and K-active master equations reduce, respectively, to the K-adiabatic and K-active bimolecular Rice-Ramsperger-Kassel-Marcus theory (high pressure limit expressions). Ozone and its formation from O + O2 are known to exhibit an adiabatic K. The ratio of the K-adiabatic to the K-active recombination rate constants for ozone formation at the high pressure limit is calculated to be ∼0.9 at 300 K. Results on the temperature and pressure dependence of the recombination rate constants and populations of O3 will be presented elsewhere. PMID:27036434
NASA Astrophysics Data System (ADS)
Ghaderi, Nima
2016-03-01
Expressions for a K-adiabatic master equation for a bimolecular recombination rate constant krec are derived for a bimolecular reaction forming a complex with a single well or complexes with multiple well, where K is the component of the total angular momentum along the axis of least moment of inertia of the recombination product. The K-active master equation is also considered. The exact analytic solutions, i.e., the K-adiabatic and K-active steady-state population distribution function of reactive complexes, g(EJK) and g(EJ), respectively, are derived for the K-adiabatic and K-active master equation cases using properties of inhomogeneous integral equations (Fredholm type). The solutions accommodate arbitrary intermolecular energy transfer models, e.g., the single exponential, double exponential, Gaussian, step-ladder, and near-singularity models. At the high pressure limit, the krec for both the K-adiabatic and K-active master equations reduce, respectively, to the K-adiabatic and K-active bimolecular Rice-Ramsperger-Kassel-Marcus theory (high pressure limit expressions). Ozone and its formation from O + O2 are known to exhibit an adiabatic K. The ratio of the K-adiabatic to the K-active recombination rate constants for ozone formation at the high pressure limit is calculated to be ˜0.9 at 300 K. Results on the temperature and pressure dependence of the recombination rate constants and populations of O3 will be presented elsewhere.
Coffey, William T.; Kalmykov, Yuri P.; Titov, Serguey V.
2007-08-21
Quantum effects in the Brownian motion of a particle in the symmetric double well potential V(x)=ax{sup 2}/2+bx{sup 4}/4 are treated using the semiclassical master equation for the time evolution of the Wigner distribution function W(x,p,t) in phase space (x,p). The equilibrium position autocorrelation function, dynamic susceptibility, and escape rate are evaluated via matrix continued fractions in the manner customarily used for the classical Fokker-Planck equation. The escape rate so yielded has a quantum correction depending strongly on the barrier height and is compared with that given analytically by the quantum mechanical reaction rate solution of the Kramers turnover problem. The matrix continued fraction solution substantially agrees with the analytic solution. Moreover, the low-frequency part of the spectrum associated with noise assisted Kramers transitions across the potential barrier may be accurately described by a single Lorentzian with characteristic frequency given by the quantum mechanical reaction rate.
The finite state projection algorithm for the solution of the chemical master equation.
Munsky, Brian; Khammash, Mustafa
2006-01-28
This article introduces the finite state projection (FSP) method for use in the stochastic analysis of chemically reacting systems. One can describe the chemical populations of such systems with probability density vectors that evolve according to a set of linear ordinary differential equations known as the chemical master equation (CME). Unlike Monte Carlo methods such as the stochastic simulation algorithm (SSA) or tau leaping, the FSP directly solves or approximates the solution of the CME. If the CME describes a system that has a finite number of distinct population vectors, the FSP method provides an exact analytical solution. When an infinite or extremely large number of population variations is possible, the state space can be truncated, and the FSP method provides a certificate of accuracy for how closely the truncated space approximation matches the true solution. The proposed FSP algorithm systematically increases the projection space in order to meet prespecified tolerance in the total probability density error. For any system in which a sufficiently accurate FSP exists, the FSP algorithm is shown to converge in a finite number of steps. The FSP is utilized to solve two examples taken from the field of systems biology, and comparisons are made between the FSP, the SSA, and tau leaping algorithms. In both examples, the FSP outperforms the SSA in terms of accuracy as well as computational efficiency. Furthermore, due to very small molecular counts in these particular examples, the FSP also performs far more effectively than tau leaping methods. PMID:16460146
A master equation formalism for macroscopic modeling of asynchronous irregular activity states.
El Boustani, Sami; Destexhe, Alain
2009-01-01
Many efforts have been devoted to modeling asynchronous irregular (AI) activity states, which resemble the complex activity states seen in the cerebral cortex of awake animals. Most of models have considered balanced networks of excitatory and inhibitory spiking neurons in which AI states are sustained through recurrent sparse connectivity, with or without external input. In this letter we propose a mesoscopic description of such AI states. Using master equation formalism, we derive a second-order mean-field set of ordinary differential equations describing the temporal evolution of randomly connected balanced networks. This formalism takes into account finite size effects and is applicable to any neuron model as long as its transfer function can be characterized. We compare the predictions of this approach with numerical simulations for different network configurations and parameter spaces. Considering the randomly connected network as a unit, this approach could be used to build large-scale networks of such connected units, with an aim to model activity states constrained by macroscopic measurements, such as voltage-sensitive dye imaging. PMID:19210171
On the structure of the master equation for a two-level system coupled to a thermal bath
NASA Astrophysics Data System (ADS)
de Vega, Inés
2015-04-01
We derive a master equation from the exact stochastic Liouville-von-Neumann (SLN) equation (Stockburger and Grabert 2002 Phys. Rev. Lett. 88 170407). The latter depends on two correlated noises and describes exactly the dynamics of an oscillator (which can be either harmonic or present an anharmonicity) coupled to an environment at thermal equilibrium. The newly derived master equation is obtained by performing analytically the average over different noise trajectories. It is found to have a complex hierarchical structure that might be helpful to explain the convergence problems occurring when performing numerically the stochastic average of trajectories given by the SLN equation (Koch et al 2008 Phys. Rev. Lett. 100 230402, Koch 2010 PhD thesis Fakultät Mathematik und Naturwissenschaften der Technischen Universitat Dresden).
NASA Astrophysics Data System (ADS)
Silveri, M.; Zalys-Geller, E.; Hatridge, M.; Leghtas, Z.; Devoret, M. H.; Girvin, S. M.
2015-03-01
In the remote entanglement process, two distant stationary qubits are entangled with separate flying qubits and the which-path information is erased from the flying qubits by interference effects. As a result, an observer cannot tell from which of the two sources a signal came and the probabilistic measurement process generates perfect heralded entanglement between the two signal sources. Notably, the two stationary qubits are spatially separated and there is no direct interaction between them. We study two transmon qubits in superconducting cavities connected to a Josephson Parametric Converter (JPC). The qubit information is encoded in the traveling wave leaking out from each cavity. Remarkably, the quantum-limited phase-preserving amplification of two traveling waves provided by the JPC can work as a which-path information eraser. By using a stochastic master approach we demonstrate the probabilistic production of heralded entangled states and that unequal qubit-cavity pairs can be made indistinguishable by simple engineering of driving fields. Additionally, we will derive measurement rates, measurement optimization strategies and discuss the effects of finite amplification gain, cavity losses, and qubit relaxations and dephasing. Work supported by IARPA, ARO and NSF.
NASA Astrophysics Data System (ADS)
Schieve, William C.; Horwitz, Lawrence P.
2009-04-01
1. Foundations of quantum statistical mechanics; 2. Elementary examples; 3. Quantum statistical master equation; 4. Quantum kinetic equations; 5. Quantum irreversibility; 6. Entropy and dissipation: the microscopic theory; 7. Global equilibrium: thermostatics and the microcanonical ensemble; 8. Bose-Einstein ideal gas condensation; 9. Scaling, renormalization and the Ising model; 10. Relativistic covariant statistical mechanics of many particles; 11. Quantum optics and damping; 12. Entanglements; 13. Quantum measurement and irreversibility; 14. Quantum Langevin equation: quantum Brownian motion; 15. Linear response: fluctuation and dissipation theorems; 16. Time dependent quantum Green's functions; 17. Decay scattering; 18. Quantum statistical mechanics, extended; 19. Quantum transport with tunneling and reservoir ballistic transport; 20. Black hole thermodynamics; Appendix; Index.
Surface electromagnetic wave equations in a warm magnetized quantum plasma
Li, Chunhua; Yang, Weihong; Wu, Zhengwei; Chu, Paul K.
2014-07-15
Based on the single-fluid plasma model, a theoretical investigation of surface electromagnetic waves in a warm quantum magnetized inhomogeneous plasma is presented. The surface electromagnetic waves are assumed to propagate on the plane between a vacuum and a warm quantum magnetized plasma. The quantum magnetohydrodynamic model includes quantum diffraction effect (Bohm potential), and quantum statistical pressure is used to derive the new dispersion relation of surface electromagnetic waves. And the general dispersion relation is analyzed in some special cases of interest. It is shown that surface plasma oscillations can be propagated due to quantum effects, and the propagation velocity is enhanced. Furthermore, the external magnetic field has a significant effect on surface wave's dispersion equation. Our work should be of a useful tool for investigating the physical characteristic of surface waves and physical properties of the bounded quantum plasmas.
The Schroedinger equation with friction from the quantum trajectory perspective
Garashchuk, Sophya; Dixit, Vaibhav; Gu Bing; Mazzuca, James
2013-02-07
Similarity of equations of motion for the classical and quantum trajectories is used to introduce a friction term dependent on the wavefunction phase into the time-dependent Schroedinger equation. The term describes irreversible energy loss by the quantum system. The force of friction is proportional to the velocity of a quantum trajectory. The resulting Schroedinger equation is nonlinear, conserves wavefunction normalization, and evolves an arbitrary wavefunction into the ground state of the system (of appropriate symmetry if applicable). Decrease in energy is proportional to the average kinetic energy of the quantum trajectory ensemble. Dynamics in the high friction regime is suitable for simple models of reactions proceeding with energy transfer from the system to the environment. Examples of dynamics are given for single and symmetric and asymmetric double well potentials.
Magic bases, metric ansaetze and generalized graph theories in the Virasoro master equation
Halpern, M.B.; Obers, N.A. )
1991-11-15
The authors define a class of magic Lie group bases in which the Virasoro master equation admits a class of simple metric ansaetze (g{sub metric}), whose structure is visible in the high-level expansion. When a magic basis is real on compact g, the corresponding g{sub metric} is a large system of unitary, generically irrational conformal field theories. Examples in this class include the graph-theory ansatz SO(n){sub diag} in the Cartesian basis of So(n) and the ansatz SU(n){sub metric} in the Pauli-like basis of SU(n). A new phenomenon is observed in the high-level comparison of SU(n){sub metric}: Due to the trigonometric structure constants of the Pauli-like basis, irrational central charge is clearly visible at finite order of the expansion. They also define the sine-area graphs of SU(n), which label the conformal field theories of SU(n){sub metric} and note that, in a similar fashion, each magic basis of g defines a generalize graph theory on g which labels the conformal field theories of g{sub metric}.
Fox, Zachary; Neuert, Gregor; Munsky, Brian
2016-08-21
Emerging techniques now allow for precise quantification of distributions of biological molecules in single cells. These rapidly advancing experimental methods have created a need for more rigorous and efficient modeling tools. Here, we derive new bounds on the likelihood that observations of single-cell, single-molecule responses come from a discrete stochastic model, posed in the form of the chemical master equation. These strict upper and lower bounds are based on a finite state projection approach, and they converge monotonically to the exact likelihood value. These bounds allow one to discriminate rigorously between models and with a minimum level of computational effort. In practice, these bounds can be incorporated into stochastic model identification and parameter inference routines, which improve the accuracy and efficiency of endeavors to analyze and predict single-cell behavior. We demonstrate the applicability of our approach using simulated data for three example models as well as for experimental measurements of a time-varying stochastic transcriptional response in yeast. PMID:27544081
Hellander, Andreas; Lawson, Michael J; Drawert, Brian; Petzold, Linda
2015-01-01
The efficiency of exact simulation methods for the reaction-diffusion master equation (RDME) is severely limited by the large number of diffusion events if the mesh is fine or if diffusion constants are large. Furthermore, inherent properties of exact kinetic-Monte Carlo simulation methods limit the efficiency of parallel implementations. Several approximate and hybrid methods have appeared that enable more efficient simulation of the RDME. A common feature to most of them is that they rely on splitting the system into its reaction and diffusion parts and updating them sequentially over a discrete timestep. This use of operator splitting enables more efficient simulation but it comes at the price of a temporal discretization error that depends on the size of the timestep. So far, existing methods have not attempted to estimate or control this error in a systematic manner. This makes the solvers hard to use for practitioners since they must guess an appropriate timestep. It also makes the solvers potentially less efficient than if the timesteps are adapted to control the error. Here, we derive estimates of the local error and propose a strategy to adaptively select the timestep when the RDME is simulated via a first order operator splitting. While the strategy is general and applicable to a wide range of approximate and hybrid methods, we exemplify it here by extending a previously published approximate method, the Diffusive Finite-State Projection (DFSP) method, to incorporate temporal adaptivity. PMID:26865735
NASA Astrophysics Data System (ADS)
Hellander, Andreas; Lawson, Michael J.; Drawert, Brian; Petzold, Linda
2014-06-01
The efficiency of exact simulation methods for the reaction-diffusion master equation (RDME) is severely limited by the large number of diffusion events if the mesh is fine or if diffusion constants are large. Furthermore, inherent properties of exact kinetic-Monte Carlo simulation methods limit the efficiency of parallel implementations. Several approximate and hybrid methods have appeared that enable more efficient simulation of the RDME. A common feature to most of them is that they rely on splitting the system into its reaction and diffusion parts and updating them sequentially over a discrete timestep. This use of operator splitting enables more efficient simulation but it comes at the price of a temporal discretization error that depends on the size of the timestep. So far, existing methods have not attempted to estimate or control this error in a systematic manner. This makes the solvers hard to use for practitioners since they must guess an appropriate timestep. It also makes the solvers potentially less efficient than if the timesteps were adapted to control the error. Here, we derive estimates of the local error and propose a strategy to adaptively select the timestep when the RDME is simulated via a first order operator splitting. While the strategy is general and applicable to a wide range of approximate and hybrid methods, we exemplify it here by extending a previously published approximate method, the diffusive finite-state projection (DFSP) method, to incorporate temporal adaptivity.
Reduced master equation analysis of multiple-tunnel junction single-electron memory device
NASA Astrophysics Data System (ADS)
Jalil, M. B. A.; Wagner, M.
2000-07-01
We employ a master equation (ME) approach in the charge transport analysis across a uniform multiple-tunnel junction (MTJ) memory trap, using a much-reduced state list derived from circuit symmetry, and previous assumptions by Jensen and Martinis. This enables all significant single tunneling and higher-order cotunneling sequences to be accounted for, while avoiding the computational cost of the full ME method. The reduced ME method is conceptually simpler and yields greater accuracy, compared with previous approximations based on tunneling probabilities. For an MTJ trap with zero stray capacitance C0, the results obtained are found to agree very closely with the full ME results up to a temperature of T≈3T0/10, where T0=e2/kBC, whereas previous methods break down at T≈T0/10. Furthermore, unlike the earlier methods, the reduced ME approach can be applied to the realistic but less symmetric case of a trap with finite C0, and remains valid up to the trap's maximum operating temperature of T≈T0/100. Finally, our reduced ME results are in close agreement with available experimental data at T
Comparison of Boltzmann equations with quantum dynamics for scalar fields
Lindner, Manfred; Mueller, Markus Michael
2006-06-15
Boltzmann equations are often used to study the thermal evolution of particle reaction networks. Prominent examples are the computation of the baryon asymmetry of the universe and the evolution of the quark-gluon plasma after relativistic heavy ion collisions. However, Boltzmann equations are only a classical approximation of the quantum thermalization process which is described by the so-called Kadanoff-Baym equations. This raises the question how reliable Boltzmann equations are as approximations to the full Kadanoff-Baym equations. Therefore, we present in this paper a detailed comparison between the Kadanoff-Baym and Boltzmann equations in the framework of a scalar {phi}{sup 4} quantum field theory in 3+1 space-time dimensions. The obtained numerical solutions reveal significant discrepancies in the results predicted by both types of equations. Apart from quantitative discrepancies, on a qualitative level the universality respected by the Kadanoff-Baym equations is severely restricted in the case of Boltzmann equations. Furthermore, the Kadanoff-Baym equations strongly separate the time scales between kinetic and chemical equilibration. This separation of time scales is absent for the Boltzmann equation.
Pattern dynamics and spatiotemporal chaos in the quantum Zakharov equations.
Misra, A P; Shukla, P K
2009-05-01
The dynamical behavior of the nonlinear interaction of quantum Langmuir waves (QLWs) and quantum ion-acoustic waves (QIAWs) is studied in the one-dimensional quantum Zakharov equations. Numerical simulations of coupled QLWs and QIAWs reveal that many coherent solitary patterns can be excited and saturated via the modulational instability of unstable harmonic modes excited by a modulation wave number of monoenergetic QLWs. The evolution of such solitary patterns may undergo the states of spatially partial coherence (SPC), coexistence of temporal chaos and spatiotemporal chaos (STC), as well as STC. The SPC state is essentially due to ion-acoustic wave emission and due to quantum diffraction, while the STC is caused by the combined effects of SPC and quantum diffraction, as well as by collisions and fusions among patterns in stochastic motion. The energy in the system is strongly redistributed, which may switch on the onset of weak turbulence in dense quantum plasmas. PMID:19518570
Quantum Fokker-Planck-Kramers equation and entropy production.
de Oliveira, Mário J
2016-07-01
We use a canonical quantization procedure to set up a quantum Fokker-Planck-Kramers equation that accounts for quantum dissipation in a thermal environment. The dissipation term is chosen to ensure that the thermodynamic equilibrium is described by the Gibbs state. An expression for the quantum entropy production that properly describes quantum systems in a nonequilibrium stationary state is also provided. The time-dependent solution is given for a quantum harmonic oscillator in contact with a heat bath. We also obtain the stationary solution for a system of two coupled harmonic oscillators in contact with reservoirs at distinct temperatures, from which we obtain the entropy production and the quantum thermal conductance. PMID:27575097
Pattern dynamics and spatiotemporal chaos in the quantum Zakharov equations
Misra, A. P.; Shukla, P. K.
2009-05-15
The dynamical behavior of the nonlinear interaction of quantum Langmuir waves (QLWs) and quantum ion-acoustic waves (QIAWs) is studied in the one-dimensional quantum Zakharov equations. Numerical simulations of coupled QLWs and QIAWs reveal that many coherent solitary patterns can be excited and saturated via the modulational instability of unstable harmonic modes excited by a modulation wave number of monoenergetic QLWs. The evolution of such solitary patterns may undergo the states of spatially partial coherence (SPC), coexistence of temporal chaos and spatiotemporal chaos (STC), as well as STC. The SPC state is essentially due to ion-acoustic wave emission and due to quantum diffraction, while the STC is caused by the combined effects of SPC and quantum diffraction, as well as by collisions and fusions among patterns in stochastic motion. The energy in the system is strongly redistributed, which may switch on the onset of weak turbulence in dense quantum plasmas.
A wave equation interpolating between classical and quantum mechanics
NASA Astrophysics Data System (ADS)
Schleich, W. P.; Greenberger, D. M.; Kobe, D. H.; Scully, M. O.
2015-10-01
We derive a ‘master’ wave equation for a family of complex-valued waves {{Φ }}\\equiv R{exp}[{{{i}}S}({cl)}/{{\\hbar }}] whose phase dynamics is dictated by the Hamilton-Jacobi equation for the classical action {S}({cl)}. For a special choice of the dynamics of the amplitude R which eliminates all remnants of classical mechanics associated with {S}({cl)} our wave equation reduces to the Schrödinger equation. In this case the amplitude satisfies a Schrödinger equation analogous to that of a charged particle in an electromagnetic field where the roles of the scalar and the vector potentials are played by the classical energy and the momentum, respectively. In general this amplitude is complex and thereby creates in addition to the classical phase {S}({cl)}/{{\\hbar }} a quantum phase. Classical statistical mechanics, as described by a classical matter wave, follows from our wave equation when we choose the dynamics of the amplitude such that it remains real for all times. Our analysis shows that classical and quantum matter waves are distinguished by two different choices of the dynamics of their amplitudes rather than two values of Planck’s constant. We dedicate this paper to the memory of Richard Lewis Arnowitt—a pioneer of many-body theory, a path finder at the interface of gravity and quantum mechanics, and a true leader in non-relativistic and relativistic quantum field theory.
Loop equations and KDV hierarchy in 2-D quantum gravity
Fucito, F. ); Martellini, M. )
1992-04-20
In this paper a derivation of the loop equation for two-dimensional quantum gravity from the KdV equations and the string equation of the one-matrix model is given. The loop equation was found to be equivalent to an infinite set of linear constraints on the square root of the partition function satisfying the virasoro algebra. Starting form the equations expressing these constraints. The authors are able to rederive the equations of the KdV hierarchy using the vertex operator construction of the A{sup (I)}{sub I} infinite dimensional twisted Kac-Moody algebra. From these considerations it follows that the solutions of the string equation of the one-matrix model are given by a subset of the solutions of the KdV hierarchy.
NASA Astrophysics Data System (ADS)
Meng, Xiang-Guo; Wang, Ji-Suo; Gao, Hua-Chao
2016-08-01
Exploiting the thermo entangled state approach, we successfully solve the master equation for describing the single-mode cavity driven by an oscillating external field in the heat reservoir and then get the analytical time-evolution rule for the density operator in the infinitive Kraus operator-sum representation. It is worth noting that the Kraus operator M l, m is proved to be a trace-preserving quantum operation. As an application, the time-evolution for an initial coherent state ρ | β> = | β>< β| in such an environment is investigated, which shows that the initial coherent state decays to a new mixed state as a result of thermal noise, however the coherence can still be reserved for amplitude damping.
NASA Astrophysics Data System (ADS)
Boyd, Iain D.; Josyula, Eswar
2016-01-01
The direct simulation Monte Carlo (DSMC) method is the primary numerical technique for analysis of rarefied gas flows. While recent progress in computational chemistry is beginning to provide vibrationally resolved transition and reaction cross sections that can be employed in DSMC calculations, the particle nature of the standard DSMC method makes it difficult to use this information in a statistically significant way. The current study introduces a new technique that makes it possible to resolve all of the vibrational energy levels by using a master equation approach along with temperature-dependent transition rates. The new method is compared to the standard DSMC technique for several heat bath and shock wave conditions and demonstrates the ability to resolve the full vibrational manifold at the expected overall rates of relaxation. The ability of the new master equation approach to the DSMC method for resolving, in particular, the high-energy states addresses a well-known, longstanding deficiency of the standard DSMC method.
Variational Equation for Quantum Number Projection at Finite Temperature
NASA Astrophysics Data System (ADS)
Tanabe, Kosai; Nakada, Hitoshi
2008-04-01
To describe phase transitions in a finite system at finite temperature, we develop a formalism of the variation-after-projection (VAP) of quantum numbers based on the thermofield dynamics (TFD). We derive a new Bardeen-Cooper-Schrieffer (BCS)-type equation by variating the free energy with approximate entropy without violating Peierls inequality. The solution to the new BCS equation describes the S-shape in the specific heat curve and the superfluid-to-normal phase transition caused by the temperature effect. It simulates the exact quantum Monte Carlo results well.
Quantum Non-Markovian Langevin Equations and Transport Coefficients
Sargsyan, V.V.; Antonenko, N.V.; Kanokov, Z.; Adamian, G.G.
2005-12-01
Quantum diffusion equations featuring explicitly time-dependent transport coefficients are derived from generalized non-Markovian Langevin equations. Generalized fluctuation-dissipation relations and analytic expressions for calculating the friction and diffusion coefficients in nuclear processes are obtained. The asymptotic behavior of the transport coefficients and correlation functions for a damped harmonic oscillator that is linearly coupled in momentum to a heat bath is studied. The coupling to a heat bath in momentum is responsible for the appearance of the diffusion coefficient in coordinate. The problem of regression of correlations in quantum dissipative systems is analyzed.
Derivation of the Drude conductivity from quantum kinetic equations
NASA Astrophysics Data System (ADS)
Kitamura, Hikaru
2015-11-01
The Drude formula of ac (frequency-dependent) electric conductivity has been established as a simple and practically useful model to understand the electromagnetic response of simple free-electron-like metals. In most textbooks of solid-state physics, the Drude formula is derived from either a classical equation of motion or the semiclassical Boltzmann transport equation. On the other hand, quantum-mechanical derivation of the Drude conductivity, which requires an appropriate treatment of phonon-assisted intraband transitions with small momentum transfer, has not been well documented except for the zero- or high-frequency case. Here, a lucid derivation of the Drude conductivity that covers the entire frequency range is presented by means of quantum kinetic equations in the density-matrix formalism. The derivation is straightforward so that advanced undergraduate students or early-year graduate students will be able to gain insight into the link between the microscopic Schrödinger equation and macroscopic transport.
Quantum simulations of neutrino oscillations and the Majorana equation
NASA Astrophysics Data System (ADS)
Noh, Changsuk; Rodriguez-Lara, Blas; Angelakis, Dimitris
2013-03-01
Two recent works on quantum simulations of relativistic equations are presented. The first is on neutrino oscillations with trapped ions as a generalization of Dirac equation simulation in 1 spatial dimension. It is shown that with two or more ion qubits it is possible to mimic the flavour oscillations of neutrinos. The second part is on quantum simulations of the Majorana equation based on the earlier work by Casanova et al. (PRX 1, 021018). We show that by decoupling the equation, it is possible to simulate with a smaller number of qubits given that one can perform complete tomography, including the spatial degrees of freedom. We acknowledge the financial support by the National Research Foundation and Ministry of Education, Singapore.
Absorbing boundary conditions for relativistic quantum mechanics equations
Antoine, X.; Sater, J.; Fillion-Gourdeau, F.; Bandrauk, A.D.
2014-11-15
This paper is devoted to the derivation of absorbing boundary conditions for the Klein–Gordon and Dirac equations modeling quantum and relativistic particles subject to classical electromagnetic fields. Microlocal analysis is the main ingredient in the derivation of these boundary conditions, which are obtained in the form of pseudo-differential equations. Basic numerical schemes are derived and analyzed to illustrate the accuracy of the derived boundary conditions.
Efficient Integration of Quantum Mechanical Wave Equations by Unitary Transforms
Bauke, Heiko; Keitel, Christoph H.
2009-08-13
The integration of time dependent quantum mechanical wave equations is a fundamental problem in computational physics and computational chemistry. The energy and momentum spectrum of a wave function imposes fundamental limits on the performance of numerical algorithms for this problem. We demonstrate how unitary transforms can help to surmount these limitations.
Quantum-mechanical transport equation for atomic systems.
NASA Technical Reports Server (NTRS)
Berman, P. R.
1972-01-01
A quantum-mechanical transport equation (QMTE) is derived which should be applicable to a wide range of problems involving the interaction of radiation with atoms or molecules which are also subject to collisions with perturber atoms. The equation follows the time evolution of the macroscopic atomic density matrix elements of atoms located at classical position R and moving with classical velocity v. It is quantum mechanical in the sense that all collision kernels or rates which appear have been obtained from a quantum-mechanical theory and, as such, properly take into account the energy-level variations and velocity changes of the active (emitting or absorbing) atom produced in collisions with perturber atoms. The present formulation is better suited to problems involving high-intensity external fields, such as those encountered in laser physics.
High resolution finite volume scheme for the quantum hydrodynamic equations
NASA Astrophysics Data System (ADS)
Lin, Chin-Tien; Yeh, Jia-Yi; Chen, Jiun-Yeu
2009-03-01
The theory of quantum fluid dynamics (QFD) helps nanotechnology engineers to understand the physical effect of quantum forces. Although the governing equations of quantum fluid dynamics and classical fluid mechanics have the same form, there are two numerical simulation problems must be solved in QFD. The first is that the quantum potential term becomes singular and causes a divergence in the numerical simulation when the probability density is very small and close to zero. The second is that the unitarity in the time evolution of the quantum wave packet is significant. Accurate numerical evaluations are critical to the simulations of the flow fields that are generated by various quantum fluid systems. A finite volume scheme is developed herein to solve the quantum hydrodynamic equations of motion, which significantly improve the accuracy and stability of this method. The QFD equation is numerically implemented within the Eulerian method. A third-order modified Osher-Chakravarthy (MOC) upwind-centered finite volume scheme was constructed for conservation law to evaluate the convective terms, and a second-order central finite volume scheme was used to map the quantum potential field. An explicit Runge-Kutta method is used to perform the time integration to achieve fast convergence of the proposed scheme. In order to meet the numerical result can conform to the physical phenomenon and avoid numerical divergence happening due to extremely low probability density, the minimum value setting of probability density must exceed zero and smaller than certain value. The optimal value was found in the proposed numerical approach to maintain a converging numerical simulation when the minimum probability density is 10 -5 to 10 -12. The normalization of the wave packet remains close to unity through a long numerical simulation and the deviations from 1.0 is about 10 -4. To check the QFD finite difference numerical computations, one- and two-dimensional particle motions were
Cao, Youfang; Terebus, Anna; Liang, Jie
2016-04-01
The discrete chemical master equation (dCME) provides a general framework for studying stochasticity in mesoscopic reaction networks. Since its direct solution rapidly becomes intractable due to the increasing size of the state space, truncation of the state space is necessary for solving most dCMEs. It is therefore important to assess the consequences of state space truncations so errors can be quantified and minimized. Here we describe a novel method for state space truncation. By partitioning a reaction network into multiple molecular equivalence groups (MEGs), we truncate the state space by limiting the total molecular copy numbers in each MEG. We further describe a theoretical framework for analysis of the truncation error in the steady-state probability landscape using reflecting boundaries. By aggregating the state space based on the usage of a MEG and constructing an aggregated Markov process, we show that the truncation error of a MEG can be asymptotically bounded by the probability of states on the reflecting boundary of the MEG. Furthermore, truncating states of an arbitrary MEG will not undermine the estimated error of truncating any other MEGs. We then provide an overall error estimate for networks with multiple MEGs. To rapidly determine the appropriate size of an arbitrary MEG, we also introduce an a priori method to estimate the upper bound of its truncation error. This a priori estimate can be rapidly computed from reaction rates of the network, without the need of costly trial solutions of the dCME. As examples, we show results of applying our methods to the four stochastic networks of (1) the birth and death model, (2) the single gene expression model, (3) the genetic toggle switch model, and (4) the phage lambda bistable epigenetic switch model. We demonstrate how truncation errors and steady-state probability landscapes can be computed using different sizes of the MEG(s) and how the results validate our theories. Overall, the novel state space
Cao, Youfang; Terebus, Anna; Liang, Jie
2016-01-01
The discrete chemical master equation (dCME) provides a general framework for studying stochasticity in mesoscopic reaction networks. Since its direct solution rapidly becomes intractable due to the increasing size of the state space, truncation of the state space is necessary for solving most dCMEs. It is therefore important to assess the consequences of state space truncations so errors can be quantified and minimized. Here we describe a novel method for state space truncation. By partitioning a reaction network into multiple molecular equivalence groups (MEG), we truncate the state space by limiting the total molecular copy numbers in each MEG. We further describe a theoretical framework for analysis of the truncation error in the steady state probability landscape using reflecting boundaries. By aggregating the state space based on the usage of a MEG and constructing an aggregated Markov process, we show that the truncation error of a MEG can be asymptotically bounded by the probability of states on the reflecting boundary of the MEG. Furthermore, truncating states of an arbitrary MEG will not undermine the estimated error of truncating any other MEGs. We then provide an overall error estimate for networks with multiple MEGs. To rapidly determine the appropriate size of an arbitrary MEG, we also introduce an a priori method to estimate the upper bound of its truncation error. This a priori estimate can be rapidly computed from reaction rates of the network, without the need of costly trial solutions of the dCME. As examples, we show results of applying our methods to the four stochastic networks of 1) the birth and death model, 2) the single gene expression model, 3) the genetic toggle switch model, and 4) the phage lambda bistable epigenetic switch model. We demonstrate how truncation errors and steady state probability landscapes can be computed using different sizes of the MEG(s) and how the results validate out theories. Overall, the novel state space
ERIC Educational Resources Information Center
Field, J. H.
2011-01-01
It is shown how the time-dependent Schrodinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrodinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi…
Martirosyan, A; Saakian, David B
2011-08-01
We apply the Hamilton-Jacobi equation (HJE) formalism to solve the dynamics of the chemical master equation (CME). We found exact analytical expressions (in large system-size limit) for the probability distribution, including explicit expression for the dynamics of variance of distribution. We also give the solution for some simple cases of the model with time-dependent rates. We derived the results of the Van Kampen method from the HJE approach using a special ansatz. Using the Van Kampen method, we give a system of ordinary differential equations (ODEs) to define the variance in a two-dimensional case. We performed numerics for the CME with stationary noise. We give analytical criteria for the disappearance of bistability in the case of stationary noise in one-dimensional CMEs. PMID:21928964
Quantum hydrodynamic model by moment closure of Wigner equation
NASA Astrophysics Data System (ADS)
Cai, Zhenning; Fan, Yuwei; Li, Ruo; Lu, Tiao; Wang, Yanli
2012-10-01
In this paper, we derive the quantum hydrodynamics models based on the moment closure of the Wigner equation. The moment expansion adopted is of the Grad type first proposed by Grad ["On the kinetic theory of rarefied gases," Commun. Pure Appl. Math. 2(4), 331-407 (1949), 10.1002/cpa.3160020403]. The Grad's moment method was originally developed for the Boltzmann equation. Recently, a regularization method for the Grad's moment system of the Boltzmann equation was proposed by Cai et al. [Commun. Pure Appl. Math. "Globally hyperbolic regularization of Grad's moment system" (in press)] to achieve the global hyperbolicity so that the local well-posedness of the moment system is attained. With the moment expansion of the Wigner function, the drift term in the Wigner equation has exactly the same moment representation as in the Boltzmann equation, thus the regularization applies. The moment expansion of the nonlocal Wigner potential term in the Wigner equation turns out to be a linear source term, which can only induce very mild growth of the solution. As a result, the local well-posedness of the regularized moment system for the Wigner equation remains as for the Boltzmann equation.
Chevalier, Michael W. El-Samad, Hana
2014-12-07
Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-to-cell variability even in clonal populations. Stochastic biochemical networks have been traditionally modeled as continuous-time discrete-state Markov processes whose probability density functions evolve according to a chemical master equation (CME). In diffusion reaction systems on membranes, the Markov formalism, which assumes constant reaction propensities is not directly appropriate. This is because the instantaneous propensity for a diffusion reaction to occur depends on the creation times of the molecules involved. In this work, we develop a chemical master equation for systems of this type. While this new CME is computationally intractable, we make rational dimensional reductions to form an approximate equation, whose moments are also derived and are shown to yield efficient, accurate results. This new framework forms a more general approach than the Markov CME and expands upon the realm of possible stochastic biochemical systems that can be efficiently modeled.
Scott, M
2012-08-01
The time-covariance function captures the dynamics of biochemical fluctuations and contains important information about the underlying kinetic rate parameters. Intrinsic fluctuations in biochemical reaction networks are typically modelled using a master equation formalism. In general, the equation cannot be solved exactly and approximation methods are required. For small fluctuations close to equilibrium, a linearisation of the dynamics provides a very good description of the relaxation of the time-covariance function. As the number of molecules in the system decrease, deviations from the linear theory appear. Carrying out a systematic perturbation expansion of the master equation to capture these effects results in formidable algebra; however, symbolic mathematics packages considerably expedite the computation. The authors demonstrate that non-linear effects can reveal features of the underlying dynamics, such as reaction stoichiometry, not available in linearised theory. Furthermore, in models that exhibit noise-induced oscillations, non-linear corrections result in a shift in the base frequency along with the appearance of a secondary harmonic. PMID:23039692
Miller, James A; Klippenstein, Stephen J
2013-04-01
In this article we discuss at length the determination of phenomenological rate coefficients from the solution to a time-dependent, multiple-well master equation. Both conservative and non-conservative formulations are considered. The emphasis is placed on how to handle the situation when a CSE (chemically significant eigenvalue of the transition matrix) merges with the quasi-continuum of IEREs (internal energy relaxation eigenvalues), indicating that one or more chemical reactions begin to take place on vibrational-rotational relaxation time scales. The methodology is illustrated with four examples. PMID:23435763
A Matter of Principle: The Principles of Quantum Theory, Dirac's Equation, and Quantum Information
NASA Astrophysics Data System (ADS)
Plotnitsky, Arkady
2015-10-01
This article is concerned with the role of fundamental principles in theoretical physics, especially quantum theory. The fundamental principles of relativity will be addressed as well, in view of their role in quantum electrodynamics and quantum field theory, specifically Dirac's work, which, in particular Dirac's derivation of his relativistic equation of the electron from the principles of relativity and quantum theory, is the main focus of this article. I shall also consider Heisenberg's earlier work leading him to the discovery of quantum mechanics, which inspired Dirac's work. I argue that Heisenberg's and Dirac's work was guided by their adherence to and their confidence in the fundamental principles of quantum theory. The final section of the article discusses the recent work by D'Ariano and coworkers on the principles of quantum information theory, which extend quantum theory and its principles in a new direction. This extension enabled them to offer a new derivation of Dirac's equations from these principles alone, without using the principles of relativity.
Description of quantum noise by a Langevin equation
NASA Technical Reports Server (NTRS)
Metiu, H.; Schon, G.
1984-01-01
General features of the quantum noise problem expressed as the equations of motion for a particle coupled to a set of oscillators are investigated analytically. Account is taken of the properties of the companion oscillators by formulating quantum statistical correlation Langevin equations (QSLE). The frequency of the oscillators is then retained as a natural cut-off for the quantum noise. The QSLE is further extended to encompass the particle trajectory and is bounded by initial and final states of the oscillator. The states are expressed as the probability of existence at the moment of particle collision that takes the oscillator into a final state. Two noise sources then exist: a statistical uncertainty of the initial state and the quantum dynamical uncertainty associated with a transition from the initial to final state. Feynman's path-integral formulation is used to characterize the functional of the particle trajectory, which slows the particle. It is shown that the energy loss may be attributed to friction, which satisfies energy conservation laws.
NASA Astrophysics Data System (ADS)
Vahala, George; Yepez, Jeffrey; Vahala, Linda
2008-04-01
The ground state wave function for a Bose Einstein condensate is well described by the Gross-Pitaevskii equation. A Type-II quantum algorithm is devised that is ideally parallelized even on a classical computer. Only 2 qubits are required per spatial node. With unitary local collisions, streaming of entangled states and a spatially inhomogeneous unitary gauge rotation one recovers the Gross-Pitaevskii equation. Quantum vortex reconnection is simulated - even without any viscosity or resistivity (which are needed in classical vortex reconnection).
Quantum theory of rotational isomerism and Hill equation
Ugulava, A.; Toklikishvili, Z.; Chkhaidze, S.; Abramishvili, R.; Chotorlishvili, L.
2012-06-15
The process of rotational isomerism of linear triatomic molecules is described by the potential with two different-depth minima and one barrier between them. The corresponding quantum-mechanical equation is represented in the form that is a special case of the Hill equation. It is shown that the Hill-Schroedinger equation has a Klein's quadratic group symmetry which, in its turn, contains three invariant subgroups. The presence of these subgroups makes it possible to create a picture of energy spectrum which depends on a parameter and has many merging and branch points. The parameter-dependent energy spectrum of the Hill-Schroedinger equation, like Mathieu-characteristics, contains branch points from the left and from the right of the demarcation line. However, compared to the Mathieu-characteristics, in the Hill-Schroedinger equation spectrum the 'right' points are moved away even further for some distance that is the bigger, the bigger is the less deep well. The asymptotic wave functions of the Hill-Schroedinger equation for the energy values near the potential minimum contain two isolated sharp peaks indicating a possibility of the presence of two stable isomers. At high energy values near the potential maximum, the height of two peaks decreases, and between them there appear chaotic oscillations. This form of the wave functions corresponds to the process of isomerization.
Wieser, R
2016-10-01
The derivation of the time dependent Schrödinger equation with transversal and longitudinal relaxation, as the quantum mechanical analog of the classical Landau-Lifshitz-Bloch equation, has been described. Starting from the classical Landau-Lifshitz-Bloch equation the transition to quantum mechanics has been performed and the corresponding von-Neumann equation deduced. In a second step the time Schrödinger equation has been derived. Analytical proofs and computer simulations show the correctness and applicability of the derived Schrödinger equation. PMID:27494599
A novel quantum-mechanical interpretation of the Dirac equation
NASA Astrophysics Data System (ADS)
K-H Kiessling, M.; Tahvildar-Zadeh, A. S.
2016-04-01
A novel interpretation is given of Dirac’s ‘wave equation for the relativistic electron’ as a quantum-mechanical one-particle equation. In this interpretation the electron and the positron are merely the two different ‘topological spin’ states of a single more fundamental particle, not distinct particles in their own right. The new interpretation is backed up by the existence of such ‘bi-particle’ structures in general relativity, in particular the ring singularity present in any spacelike section of the spacetime singularity of the maximal-analytically extended, topologically non-trivial, electromagnetic Kerr-Newman (KN)spacetime in the zero-gravity limit (here, ‘zero-gravity’ means the limit G\\to 0, where G is Newton’s constant of universal gravitation). This novel interpretation resolves the dilemma that Dirac’s wave equation seems to be capable of describing both the electron and the positron in ‘external’ fields in many relevant situations, while the bi-spinorial wave function has only a single position variable in its argument, not two—as it should if it were a quantum-mechanical two-particle wave equation. A Dirac equation is formulated for such a ring-like bi-particle which interacts with a static point charge located elsewhere in the topologically non-trivial physical space associated with the moving ring particle, the motion being governed by a de Broglie-Bohm type law extracted from the Dirac equation. As an application, the pertinent general-relativistic zero-gravity hydrogen problem is studied in the usual Born-Oppenheimer approximation. Its spectral results suggest that the zero-G KN magnetic moment be identified with the so-called ‘anomalous magnetic moment of the physical electron,’ not with the Bohr magneton, so that the ring radius is only a tiny fraction of the electron’s reduced Compton wavelength.
Quantum cascade laser master-oscillator power-amplifier with 1.5 W output power at 300 K.
Menzel, Stefan; Diehl, Laurent; Pflügl, Christian; Goyal, Anish; Wang, Christine; Sanchez, Antonio; Turner, George; Capasso, Federico
2011-08-15
We report quantum cascade laser (QCL) master-oscillator power-amplifiers (MOPAs) at 300 K reaching output power of 1.5 W for tapered devices and 0.9 W for untapered devices. The devices display single-longitudinal-mode emission at λ = 7.26 µm and single-transverse-mode emission at TM(00). The maximum amplification factor is 12 dB for the tapered devices. PMID:21934985
Dissipation equation of motion approach to open quantum systems
NASA Astrophysics Data System (ADS)
Yan, YiJing; Jin, Jinshuang; Xu, Rui-Xue; Zheng, Xiao
2016-08-01
This paper presents a comprehensive account of the dissipaton-equation-of-motion (DEOM) theory for open quantum systems. This newly developed theory treats not only the quantum dissipative systems of primary interest, but also the hybrid environment dynamics that are also experimentally measurable. Despite the fact that DEOM recovers the celebrated hierarchical-equations-of-motion (HEOM) formalism, these two approaches have some fundamental differences. To show these differences, we also scrutinize the HEOM construction via its root at the influence functional path integral formalism. We conclude that many unique features of DEOM are beyond the reach of the HEOM framework. The new DEOM approach renders a statistical quasi-particle picture to account for the environment, which can be either bosonic or fermionic. The review covers the DEOM construction, the physical meanings of dynamical variables, the underlying theorems and dissipaton algebra, and recent numerical advancements for efficient DEOM evaluations of various problems. We also address the issue of high-order many-dissipaton truncations with respect to the invariance principle of quantum mechanics of Schrödinger versus Heisenberg prescriptions. DEOM serves as a universal tool for characterizing of stationary and dynamic properties of system-and-bath interferences, as highlighted with its real-time evaluation of both linear and nonlinear current noise spectra of nonequilibrium electronic transport.
Solutions of q-deformed equations with quantum conformal symmetry
Dobrev, V. K.; Kostadinov, B. S.; Petrov, S. T.
1998-12-15
We consider the construction of explicit solutions of a hierarchy of q-deformed equations which are (conditionally) quantum conformal invariant. We give two types of solutions--polynomial solutions and solutions in terms of q-deformation of the plane wave. We give a q-deformation of the plane wave as a formal power series in the noncommutative coordinates of q-Minkowski space-time and four-momenta. This q-plane wave has analogous properties to the classical one, in particular, it has the properties of q-Lorentz covariance, and it satisfies the q-d'Alembert equation on the q-Lorentz covariant momentum cone. On the other hand, this q-plane wave is not an exponent or q-exponent. Thus, it differs conceptually from the classical plane wave and may serve as a its regularization. Using this we give also solutions of the massless Dirac equation involving two conjugated q-plane waves--one for the neutrino, the other for the antineutrino. It is also interesting that the neutrino solutions are deformed only through the q-pane wave, while the prefactor is classical. Thus, we can speak of a definite left-right asymmetry of the quantum conformal deformation of the neutrino-antineutrino system.
Quantum corrections to the Mukhanov-Sasaki equations
NASA Astrophysics Data System (ADS)
Castelló Gomar, Laura; Mena Marugán, Guillermo A.; Martín-Benito, Mercedes
2016-05-01
Recently, a lot of attention has been paid to the modifications of the power spectrum of primordial fluctuations caused by quantum cosmology effects. The origin of these modifications is corrections to the Mukhanov-Sasaki equations that govern the propagation of the primeval cosmological perturbations. The specific form of these corrections depends on a series of details of the quantization approach and of the prescription followed to implement it. Generally, the complexity of the theoretical quantum formulation is simplified in practice appealing to a semiclassical or effective approximation in order to perform concrete numerical computations. In this work, we introduce technical tools and design a procedure to deal with these quantum corrections beyond the most direct approximations employed so far in the literature. In particular, by introducing an interaction picture, we extract the quantum dynamics of the homogeneous geometry in absence of scalar field potential and inhomogeneities, dynamics that has been intensively studied and that can be integrated. The rest of our analysis focuses on the interaction evolution, putting forward methods to cope with it. The ultimate aim is to develop treatments that increase our ability to discriminate between the predictions of different quantization proposals for cosmological perturbations.
Electromagnetic wave equations for relativistically degenerate quantum magnetoplasmas.
Masood, Waqas; Eliasson, Bengt; Shukla, Padma K
2010-06-01
A generalized set of nonlinear electromagnetic quantum hydrodynamic (QHD) equations is derived for a magnetized quantum plasma, including collisional, electron spin- 1/2, and relativistically degenerate electron pressure effects that are relevant for dense astrophysical systems, such as white dwarfs. For illustrative purposes, linear dispersion relations are derived for one-dimensional magnetoacoustic waves for a collisionless nonrelativistic degenerate gas in the presence of the electron spin- 1/2 contribution and for magnetoacoustic waves in a plasma containing relativistically degenerate electrons. It is found that both the spin and relativistic degeneracy at high densities tend to slow down the magnetoacoustic wave due to the Pauli paramagnetic effect and relativistic electron mass increase. The present study outlines the theoretical framework for the investigation of linear and nonlinear behaviors of electromagnetic waves in dense astrophysical systems. The results are applied to calculate the magnetoacoustic speeds for both the nonrelativistic and relativistic electron degeneracy cases typical for white dwarf stars. PMID:20866534
Pauli equation for semiconductor quantum dot photoluminescence kinetics investigation
NASA Astrophysics Data System (ADS)
Turkov, Vadim K.; Leonov, Mikhail Y.; Rukhlenko, Ivan D.; Fedorov, Anatoly V.
2012-11-01
We develop a theory of secondary emission from a single quantum dot, when the lowest-energy states of its electron-hole pairs are involved in the photoluminescence process. For the sake of definiteness, our model allows for two states contributing to the luminescence. We analyze the dependency of secondary emission intensity on the energy gap between the states, while considering that the gap is determined by the quantum dot's size. An analytical expression for the time-dependent signal of thermalized luminescence is obtained using an analytical solution to the kinetic Pauli equation. This expression yields the signal of stationary luminescence as the spectral width of the excitation pulse tends to zero.
Vortex equations governing the fractional quantum Hall effect
Medina, Luciano
2015-09-15
An existence theory is established for a coupled non-linear elliptic system, known as “vortex equations,” describing the fractional quantum Hall effect in 2-dimensional double-layered electron systems. Via variational methods, we prove the existence and uniqueness of multiple vortices over a doubly periodic domain and the full plane. In the doubly periodic situation, explicit sufficient and necessary conditions are obtained that relate the size of the domain and the vortex numbers. For the full plane case, existence is established for all finite-energy solutions and exponential decay estimates are proved. Quantization phenomena of the magnetic flux are found in both cases.
Supersymmetric quantum mechanics and Painlevé equations
Bermudez, David; Fernández C, David J.
2014-01-08
In these lecture notes we shall study first the supersymmetric quantum mechanics (SUSY QM), specially when applied to the harmonic and radial oscillators. In addition, we will define the polynomial Heisenberg algebras (PHA), and we will study the general systems ruled by them: for zero and first order we obtain the harmonic and radial oscillators, respectively; for second and third order the potential is determined by solutions to Painlevé IV (PIV) and Painlevé V (PV) equations. Taking advantage of this connection, later on we will find solutions to PIV and PV equations expressed in terms of confluent hypergeometric functions. Furthermore, we will classify them into several solution hierarchies, according to the specific special functions they are connected with.
Sidje, R B; Vo, H D
2015-11-01
The mathematical framework of the chemical master equation (CME) uses a Markov chain to model the biochemical reactions that are taking place within a biological cell. Computing the transient probability distribution of this Markov chain allows us to track the composition of molecules inside the cell over time, with important practical applications in a number of areas such as molecular biology or medicine. However the CME is typically difficult to solve, since the state space involved can be very large or even countably infinite. We present a novel way of using the stochastic simulation algorithm (SSA) to reduce the size of the finite state projection (FSP) method. Numerical experiments that demonstrate the effectiveness of the reduction are included. PMID:26319118
Optical manipulation of a multilevel nuclear spin in ZnO: Master equation and experiment
NASA Astrophysics Data System (ADS)
Buß, J. H.; Rudolph, J.; Wassner, T. A.; Eickhoff, M.; Hägele, D.
2016-04-01
We demonstrate the dynamics and optical control of a large quantum mechanical solid state spin system consisting of a donor electron spin strongly coupled to the 9/2 nuclear spin of 115In in the semiconductor ZnO. Comparison of electron spin dynamics observed by time-resolved pump-probe spectroscopy with density matrix theory reveals nuclear spin pumping via optically oriented electron spins, coherent spin-spin interaction, and quantization effects of the ten nuclear spin levels. Modulation of the optical electron spin orientation at frequencies above 1 MHz gives evidence for fast optical manipulation of the nuclear spin state.
NASA Astrophysics Data System (ADS)
Karimi, F.; Davoody, A. H.; Knezevic, I.
2016-05-01
We introduce a method for calculating the dielectric function of nanostructures with an arbitrary band dispersion and Bloch wave functions. The linear response of a dissipative electronic system to an external electromagnetic field is calculated by a self-consistent-field approach within a Markovian master-equation formalism (SCF-MMEF) coupled with full-wave electromagnetic equations. The SCF-MMEF accurately accounts for several concurrent scattering mechanisms. The method captures interband electron-hole-pair generation, as well as the interband and intraband electron scattering with phonons and impurities. We employ the SCF-MMEF to calculate the dielectric function, complex conductivity, and loss function for supported graphene. From the loss-function maximum, we obtain plasmon dispersion and propagation length for different substrate types [nonpolar diamondlike carbon (DLC) and polar SiO2 and hBN], impurity densities, carrier densities, and temperatures. Plasmons on the two polar substrates are suppressed below the highest surface phonon energy, while the spectrum is broad on the nonpolar DLC. Plasmon propagation lengths are comparable on polar and nonpolar substrates and are on the order of tens of nanometers, considerably shorter than previously reported. They improve with fewer impurities, at lower temperatures, and at higher carrier densities.
NASA Astrophysics Data System (ADS)
Caglar, Mehmet Umut; Pal, Ranadip
2011-03-01
Central dogma of molecular biology states that ``information cannot be transferred back from protein to either protein or nucleic acid''. However, this assumption is not exactly correct in most of the cases. There are a lot of feedback loops and interactions between different levels of systems. These types of interactions are hard to analyze due to the lack of cell level data and probabilistic - nonlinear nature of interactions. Several models widely used to analyze and simulate these types of nonlinear interactions. Stochastic Master Equation (SME) models give probabilistic nature of the interactions in a detailed manner, with a high calculation cost. On the other hand Probabilistic Boolean Network (PBN) models give a coarse scale picture of the stochastic processes, with a less calculation cost. Differential Equation (DE) models give the time evolution of mean values of processes in a highly cost effective way. The understanding of the relations between the predictions of these models is important to understand the reliability of the simulations of genetic regulatory networks. In this work the success of the mapping between SME, PBN and DE models is analyzed and the accuracy and affectivity of the control policies generated by using PBN and DE models is compared.
Dynamic behavior of the quantum Zakharov-Kuznetsov equations in dense quantum magnetoplasmas
Zhen, Hui-Ling; Tian, Bo Wang, Yu-Feng; Zhong, Hui; Sun, Wen-Rong
2014-01-15
Quantum Zakharov-Kuznetsov (qZK) equation is found in a dense quantum magnetoplasma. Via the spectral analysis, we investigate the Hamiltonian and periodicity of the qZK equation. Using the Hirota method, we obtain the bilinear forms and N-soliton solutions. Asymptotic analysis on the two-soliton solutions shows that the soliton interaction is elastic. Figures are plotted to reveal the propagation characteristics and interaction between the two solitons. We find that the one soliton has a single peak and its amplitude is positively related to H{sub e}, while the two solitons are parallel when H{sub e} < 2, otherwise, the one soliton has two peaks and the two solitons interact with each other. Hereby, H{sub e} is proportional to the ratio of the strength of magnetic field to the electronic Fermi temperature. External periodic force on the qZK equation yields the chaotic motions. Through some phase projections, the process from a sequence of the quasi-period doubling to chaos can be observed. The chaotic behavior is observed since the power spectra are calculated, and the quasi-period doubling states of perturbed qZK equation are given. The final chaotic state of the perturbed qZK is obtained.
Classical limit of relativistic quantum mechanical equations in the Foldy-Wouthuysen representation
NASA Astrophysics Data System (ADS)
Silenko, A. Ya.
2013-03-01
It is shown that, under the Wentzel-Kramers-Brillouin approximation conditions, using the Foldy-Wouthuysen (FW) representation allows the problem of finding a classical limit of relativistic quantum mechanical equations to be reduced to the replacement of operators in the Hamiltonian and quantum mechanical equations of motion by the respective classical quantities.
Albert, Jaroslav
2016-01-01
Modeling stochastic behavior of chemical reaction networks is an important endeavor in many aspects of chemistry and systems biology. The chemical master equation (CME) and the Gillespie algorithm (GA) are the two most fundamental approaches to such modeling; however, each of them has its own limitations: the GA may require long computing times, while the CME may demand unrealistic memory storage capacity. We propose a method that combines the CME and the GA that allows one to simulate stochastically a part of a reaction network. First, a reaction network is divided into two parts. The first part is simulated via the GA, while the solution of the CME for the second part is fed into the GA in order to update its propensities. The advantage of this method is that it avoids the need to solve the CME or stochastically simulate the entire network, which makes it highly efficient. One of its drawbacks, however, is that most of the information about the second part of the network is lost in the process. Therefore, this method is most useful when only partial information about a reaction network is needed. We tested this method against the GA on two systems of interest in biology - the gene switch and the Griffith model of a genetic oscillator—and have shown it to be highly accurate. Comparing this method to four different stochastic algorithms revealed it to be at least an order of magnitude faster than the fastest among them. PMID:26930199
Quantum defect analysis of the eigenvalue spectrum of the Newton-Schroedinger equation
Greiner, Daniel; Wunner, Guenter
2006-11-15
We point out that quantum defect theory is the appropriate framework to explain and understand the behavior of the solutions of the Newton-Schroedinger equation. We find that, beyond ordinary quantum defect theory, the nonlinearity of the equation induces novel features, in particular a strong state dependence of the quantum defects. We show how this can be compensated by a rescaling of the energy unit.
Modern integral equation techniques for quantum reactive scattering theory
Auerbach, S.M.
1993-11-01
Rigorous calculations of cross sections and rate constants for elementary gas phase chemical reactions are performed for comparison with experiment, to ensure that our picture of the chemical reaction is complete. We focus on the H/D+H{sub 2} {yields} H{sub 2}/DH + H reaction, and use the time independent integral equation technique in quantum reactive scattering theory. We examine the sensitivity of H+H{sub 2} state resolved integral cross sections {sigma}{sub v{prime}j{prime},vj}(E) for the transitions (v = 0,j = 0) to (v{prime} = 1,j{prime} = 1,3), to the difference between the Liu-Siegbahn-Truhlar-Horowitz (LSTH) and double many body expansion (DMBE) ab initio potential energy surfaces (PES). This sensitivity analysis is performed to determine the origin of a large discrepancy between experimental cross sections with sharply peaked energy dependence and theoretical ones with smooth energy dependence. We find that the LSTH and DMBE PESs give virtually identical cross sections, which lends credence to the theoretical energy dependence.
Optomechanical tests of a Schrödinger-Newton equation for gravitational quantum mechanics
NASA Astrophysics Data System (ADS)
Gan, C. C.; Savage, C. M.; Scully, S. Z.
2016-06-01
We show that optomechanical systems can test the Schrödinger-Newton equation of gravitational quantum mechanics due to Yang et al. Phys. Rev. Lett. 110, 170401 (2013). This equation is motivated by semiclassical gravity, a widely used theory of interacting gravitational and quantum fields. From the many-body Schrödinger-Newton equation follows an approximate equation for the center-of-mass dynamics of macroscopic objects. This predicts a distinctive double-peaked signature in the output optical quadrature power spectral density of certain optomechanical systems. Since the Schrödinger-Newton equation lacks free parameters, these will allow its experimental confirmation or refutation.
Cooper, Fred; Ghoshal, Gourab; Pérez-Mercader, Juan
2013-10-01
We give a first principles derivation of the stochastic partial differential equations that describe the chemical reactions of the Gray-Scott model (GS): U+2V →[λ]3V and V → [μ]P, U → [ν]Q, with a constant feed rate for U. We find that the conservation of probability ensured by the chemical master equation leads to a modification of the usual differential equations for the GS model, which now involves two composite fields and also intrinsic noise terms. One of the composites is ψ(1) = φ(v)(2), where {φ(v)}(η) =v is the concentration of the species V and the averaging is over the internal noise η(u,v,ψ(1)). The second composite field is the product of three fields χ = λφ(u)φ(v)(2) and requires a noise source to ensure probability conservation. A third composite ψ(2) = φ(u)φ(v) can also be identified from the noise-induced reactions. The Hamiltonian that governs the time evolution of the many-body wave function, associated with the master equation, has a broken U(1) symmetry related to particle number conservation. By expanding around the (broken symmetry) zero-energy solution of the Hamiltonian (by performing a Doi shift) one obtains from our path integral formulation the usual reaction diffusion equation, at the classical level. The Langevin equations that are derived from the chemical master equation have multiplicative noise sources for the density fields φ(u), φ(v),χ that induce higher-order processes such as n → n scattering for n>3. The amplitude of the noise acting on φ(v) is itself stochastic in nature. PMID:24229268
NASA Astrophysics Data System (ADS)
Grima, Ramon
2015-10-01
It is well known that the linear-noise approximation (LNA) agrees with the chemical master equation, up to second-order moments, for chemical systems composed of zero and first-order reactions. Here we show that this is also a property of the LNA for a subset of chemical systems with second-order reactions. This agreement is independent of the number of interacting molecules.
Oliveira, Luciana Renata de; Bazzani, Armando; Giampieri, Enrico; Castellani, Gastone C.
2014-08-14
We propose a non-equilibrium thermodynamical description in terms of the Chemical Master Equation (CME) to characterize the dynamics of a chemical cycle chain reaction among m different species. These systems can be closed or open for energy and molecules exchange with the environment, which determines how they relax to the stationary state. Closed systems reach an equilibrium state (characterized by the detailed balance condition (D.B.)), while open systems will reach a non-equilibrium steady state (NESS). The principal difference between D.B. and NESS is due to the presence of chemical fluxes. In the D.B. condition the fluxes are absent while for the NESS case, the chemical fluxes are necessary for the state maintaining. All the biological systems are characterized by their “far from equilibrium behavior,” hence the NESS is a good candidate for a realistic description of the dynamical and thermodynamical properties of living organisms. In this work we consider a CME written in terms of a discrete Kolmogorov forward equation, which lead us to write explicitly the non-equilibrium chemical fluxes. For systems in NESS, we show that there is a non-conservative “external vector field” whose is linearly proportional to the chemical fluxes. We also demonstrate that the modulation of these external fields does not change their stationary distributions, which ensure us to study the same system and outline the differences in the system's behavior when it switches from the D.B. regime to NESS. We were interested to see how the non-equilibrium fluxes influence the relaxation process during the reaching of the stationary distribution. By performing analytical and numerical analysis, our central result is that the presence of the non-equilibrium chemical fluxes reduces the characteristic relaxation time with respect to the D.B. condition. Within a biochemical and biological perspective, this result can be related to the “plasticity property” of biological systems
Hinkov, Borislav; Beck, Mattias; Gini, Emilio; Faist, Jérôme
2013-08-12
We present the design and realization of short-wavelength (λ = 4.53 μm) and buried-heterostructure quantum cascade lasers in a master oscillator power amplifier configuration. Watt-level, singlemode peak optical output power is demonstrated for typical non-tapered 4 μm wide and 5.25 mm long devices. Farfield measurements prove a symmetric, single transverse-mode emission in TM(00)-mode with typical divergences of 25° and 27° in and perpendicular to growth direction, respectively. We demonstrate singlemode tuning over a range of 7.9 cm(-1) for temperatures between 263K and 313K and also singlemode emission for different driving currents. The side mode suppression ratio is measured to be higher than 20 dB. PMID:23938833
The Born Rule and Time-Reversal Symmetry of Quantum Equations of Motion
NASA Astrophysics Data System (ADS)
Ilyin, Aleksey V.
2016-07-01
It was repeatedly underlined in literature that quantum mechanics cannot be considered a closed theory if the Born Rule is postulated rather than derived from the first principles. In this work the Born Rule is derived from the time-reversal symmetry of quantum equations of motion. The derivation is based on a simple functional equation that takes into account properties of probability, as well as the linearity and time-reversal symmetry of quantum equations of motion. The derivation presented in this work also allows to determine certain limits to applicability of the Born Rule.
The Born Rule and Time-Reversal Symmetry of Quantum Equations of Motion
NASA Astrophysics Data System (ADS)
Ilyin, Aleksey V.
2016-04-01
It was repeatedly underlined in literature that quantum mechanics cannot be considered a closed theory if the Born Rule is postulated rather than derived from the first principles. In this work the Born Rule is derived from the time-reversal symmetry of quantum equations of motion. The derivation is based on a simple functional equation that takes into account properties of probability, as well as the linearity and time-reversal symmetry of quantum equations of motion. The derivation presented in this work also allows to determine certain limits to applicability of the Born Rule.
NASA Astrophysics Data System (ADS)
Huestis, D. L.
2008-12-01
gases will have more than one relaxation time constant. Thus we write the chemical kinetics master equation as (1) (d/dt) Nm = Σnpq [ - kmn→pq Nm Nn + kpq→mn Np Nq ] which has the well-known time-dependent solution given by (2) Nm(t) = Σn Cmn exp(-λn t) where the λn values are the decay frequencies and the Cmn coefficients depend on how the gas was initially excited. What we have contributed is the frequency-dependent sound absorption solution to Equation (1): (3) cvint(ω) = Σnk Wn / (1 + i ω/λn) where cvint(ω) is the complex heat capacity (per molecule), ω is the circular sound frequency, 2πf, the λn are the calculated decay frequencies [as in Equation (2)] and k Wn is the real effective heat capacity for decay mode n. As pointed out by Landau and Teller [Phys. Z. Sowjet. 10, 34-43 (1936)], for a simple case when the decay modes correspond to vibrational modes, Wn is the ordinary heat capacity of the vibrational mode. In the more complicated case involving one or more reversible energy-transfer steps, e.g., water and oxygen, the vibrational modes and the decay modes do not correspond to each other, and we need to use the rate coefficients in Equation (1) to calculate both λn and Wn.
Nakagawa, Masaki; Togashi, Yuichi
2016-01-01
Cell activities primarily depend on chemical reactions, especially those mediated by enzymes, and this has led to these activities being modeled as catalytic reaction networks. Although deterministic ordinary differential equations of concentrations (rate equations) have been widely used for modeling purposes in the field of systems biology, it has been pointed out that these catalytic reaction networks may behave in a way that is qualitatively different from such deterministic representation when the number of molecules for certain chemical species in the system is small. Apart from this, representing these phenomena by simple binary (on/off) systems that omit the quantities would also not be feasible. As recent experiments have revealed the existence of rare chemical species in cells, the importance of being able to model potential small-number phenomena is being recognized. However, most preceding studies were based on numerical simulations, and theoretical frameworks to analyze these phenomena have not been sufficiently developed. Motivated by the small-number issue, this work aimed to develop an analytical framework for the chemical master equation describing the distributional behavior of catalytic reaction networks. For simplicity, we considered networks consisting of two-body catalytic reactions. We used the probability generating function method to obtain the steady-state solutions of the chemical master equation without specifying the parameters. We obtained the time evolution equations of the first- and second-order moments of concentrations, and the steady-state analytical solution of the chemical master equation under certain conditions. These results led to the rank conservation law, the connecting state to the winner-takes-all state, and analysis of 2-molecules M-species systems. A possible interpretation of the theoretical conclusion for actual biochemical pathways is also discussed. PMID:27047384
Nakagawa, Masaki; Togashi, Yuichi
2016-01-01
Cell activities primarily depend on chemical reactions, especially those mediated by enzymes, and this has led to these activities being modeled as catalytic reaction networks. Although deterministic ordinary differential equations of concentrations (rate equations) have been widely used for modeling purposes in the field of systems biology, it has been pointed out that these catalytic reaction networks may behave in a way that is qualitatively different from such deterministic representation when the number of molecules for certain chemical species in the system is small. Apart from this, representing these phenomena by simple binary (on/off) systems that omit the quantities would also not be feasible. As recent experiments have revealed the existence of rare chemical species in cells, the importance of being able to model potential small-number phenomena is being recognized. However, most preceding studies were based on numerical simulations, and theoretical frameworks to analyze these phenomena have not been sufficiently developed. Motivated by the small-number issue, this work aimed to develop an analytical framework for the chemical master equation describing the distributional behavior of catalytic reaction networks. For simplicity, we considered networks consisting of two-body catalytic reactions. We used the probability generating function method to obtain the steady-state solutions of the chemical master equation without specifying the parameters. We obtained the time evolution equations of the first- and second-order moments of concentrations, and the steady-state analytical solution of the chemical master equation under certain conditions. These results led to the rank conservation law, the connecting state to the winner-takes-all state, and analysis of 2-molecules M-species systems. A possible interpretation of the theoretical conclusion for actual biochemical pathways is also discussed. PMID:27047384
NASA Astrophysics Data System (ADS)
Reineker, P.; Kühne, R.
1980-03-01
Starting from the stochastic Liouville equation of the full Haken-Strobl model, describing the coupled coherent and incoherent motion of excitons in molecular crystals, the Nakajima-Zwanzig generalized master equation (GME) for the probability of finding an exciton at a specific lattice site is derived by an exact straightforward evaluation of its memory function. Various recently derived generalized master equations describing the excition motion are obtained as limiting cases and the Born approximation is discussed. It is shown that, even in the case of nearest-neighbor interaction in the stochastic Liouville equation, in the GME generalized time-dependent transition rates evolve between non-nearest neighbors and that their time behavior shows damped oscillations. Applying the Born approximation to the GME, the range of the generalized transition rates reduces to that of the interaction in the stochastic Liouville equation. Furthermore in this approximation the transition rates show a purely exponential decay with increasing time. Taking into account the interaction with an arbitrary number of neighbors, the mean square displacement of the exciton motion is calculated exactly from the GME. Finally the GME is solved exactly in the general case and several limiting expressions are discussed.
Quantum degeneracy corrections to plasma line emission and to Saha equation
NASA Astrophysics Data System (ADS)
Molinari, V. G.; Mostacci, D.; Rocchi, F.; Sumini, M.
2003-09-01
The effect of quantum degeneracy on the electron collisional excitation is investigated, and its effects on line emission evaluated for applications to spectroscopy of dense, cold plasmas. A correction to Saha equation for weakly-degenerate plasmas is also presented.
NASA Astrophysics Data System (ADS)
Dong, B.; Ding, G. H.; Lei, X. L.
2015-05-01
A general theoretical formulation for the effect of a strong on-site Coulomb interaction on the time-dependent electron transport through a quantum dot under the influence of arbitrary time-varying bias voltages and/or external fields is presented, based on slave bosons and the Keldysh nonequilibrium Green's function (GF) techniques. To avoid the difficulties of computing double-time GFs, we generalize the propagation scheme recently developed by Croy and Saalmann to combine the auxiliary-mode expansion with the celebrated Lacroix's decoupling approximation in dealing with the second-order correlated GFs and then establish a closed set of coupled equations of motion, called second-order quantum rate equations (SOQREs), for an exact description of transient dynamics of electron correlated tunneling. We verify that the stationary solution of our SOQREs is able to correctly describe the Kondo effect on a qualitative level. Moreover, a comparison with other methods, such as the second-order von Neumann approach and Hubbard-I approximation, is performed. As illustrations, we investigate the transient current behaviors in response to a step voltage pulse and a harmonic driving voltage, and linear admittance as well, in the cotunneling regime.
Ding, Jin-Jin; Xu, Rui-Xue; Yan, YiJing
2012-06-14
We present an optimized hierarchical equations of motion theory for quantum dissipation in multiple Brownian oscillators bath environment, followed by a mechanistic study on a model donor-bridge-acceptor system. We show that the optimal hierarchy construction, via the memory-frequency decomposition for any specified Brownian oscillators bath, is generally achievable through a universal pre-screening search. The algorithm goes by identifying the candidates for the best be just some selected Padé spectrum decomposition based schemes, together with a priori accuracy control criterions on the sole approximation, the white-noise residue ansatz, involved in the hierarchical construction. Beside the universal screening search, we also analytically identify the best for the case of Drude dissipation and that for the Brownian oscillators environment without strongly underdamped bath vibrations. For the mechanistic study, we quantify the quantum nature of bath influence and further address the issue of localization versus delocalization. Proposed are a reduced system entropy measure and a state-resolved constructive versus destructive interference measure. Their performances on quantifying the correlated system-environment coherence are exemplified in conjunction with the optimized hierarchical equations of motion evaluation of the model system dynamics, at some representing bath parameters and temperatures. Analysis also reveals the localization to delocalization transition as temperature decreases. PMID:22713032
NASA Astrophysics Data System (ADS)
Ding, Jin-Jin; Xu, Rui-Xue; Yan, YiJing
2012-06-01
We present an optimized hierarchical equations of motion theory for quantum dissipation in multiple Brownian oscillators bath environment, followed by a mechanistic study on a model donor-bridge-acceptor system. We show that the optimal hierarchy construction, via the memory-frequency decomposition for any specified Brownian oscillators bath, is generally achievable through a universal pre-screening search. The algorithm goes by identifying the candidates for the best be just some selected Padé spectrum decomposition based schemes, together with a priori accuracy control criterions on the sole approximation, the white-noise residue ansatz, involved in the hierarchical construction. Beside the universal screening search, we also analytically identify the best for the case of Drude dissipation and that for the Brownian oscillators environment without strongly underdamped bath vibrations. For the mechanistic study, we quantify the quantum nature of bath influence and further address the issue of localization versus delocalization. Proposed are a reduced system entropy measure and a state-resolved constructive versus destructive interference measure. Their performances on quantifying the correlated system-environment coherence are exemplified in conjunction with the optimized hierarchical equations of motion evaluation of the model system dynamics, at some representing bath parameters and temperatures. Analysis also reveals the localization to delocalization transition as temperature decreases.
Modern Integral Equation Techniques for Quantum Reactive Scattering Theory.
NASA Astrophysics Data System (ADS)
Auerbach, Scott Michael
Rigorous calculations of cross sections and rate constants for elementary gas phase chemical reactions are performed for comparison with experiment, to ensure that our picture of the chemical reaction is complete. We focus on the H/D + H_2 to H _2/DH + H reaction, and use the time independent integral equation technique in quantum reactive scattering theory. We examine the sensitivity of H + H_2 state resolved integral cross sections sigma_{v^' j^ ',vj}(E) for the transitions (v = 0, j = 0) to (v^' = 1,j^ ' = 1,3), to the difference between the Liu-Siegbahn-Truhlar-Horowitz (LSTH) and double many body expansion (DMBE) ab initio potential energy surfaces (PES). This sensitivity analysis is performed to determine the origin of a large discrepancy between experimental cross sections with sharply peaked energy dependence and theoretical ones with smooth energy dependence. We find that the LSTH and DMBE PESs give virtually identical cross sections, which lends credence to the theoretical energy dependence. To facilitate quantum calculations on more complex reactive systems, we develop a new method to compute the energy Green's function with absorbing boundary conditions (ABC), for use in calculating the cumulative reaction probability. The method is an iterative technique to compute the inverse of a non-Hermitian matrix which is based on Fourier transforming time dependent dynamics, and which requires very little core memory. The Hamiltonian is evaluated in a sinc-function based discrete variable representation (DVR) which we argue may often be superior to the fast Fourier transform method for reactive scattering. We apply the resulting power series Green's function to the benchmark collinear H + H_2 system over the energy range 3.37 to 1.27 eV. The convergence of the power series is stable at all energies, and is accelerated by the use of a stronger absorbing potential. The practicality of computing the ABC-DVR Green's function in a polynomial of the Hamiltonian is
Quantum statistics of overlapping modes in open resonators
Hackenbroich, Gregor; Viviescas, Carlos; Haake, Fritz
2003-12-01
We study the quantum dynamics of optical fields in weakly confining resonators with overlapping modes. Employing a recently developed quantization scheme involving a discrete set of resonator modes and continua of external modes we derive Langevin equations and a master equation for the resonator modes. Langevin dynamics and the master equation are proved to be equivalent in the Markovian limit. Our open-resonator dynamics may be used as a starting point for a quantum theory of random lasers.
NASA Astrophysics Data System (ADS)
Schuch, Dieter
2014-04-01
Theoretical physics seems to be in a kind of schizophrenic state. Many phenomena in the observable macroscopic world obey nonlinear evolution equations, whereas the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. I claim that linearity in quantum mechanics is not as essential as it apparently seems since quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown where complex Riccati equations appear in time-dependent quantum mechanics and how they can be treated and compared with similar space-dependent Riccati equations in supersymmetric quantum mechanics. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation. Finally, it will be shown that (real and complex) Riccati equations also appear in many other fields of physics, like statistical thermodynamics and cosmology.
Chou, Chia-Chun
2014-03-14
The complex quantum Hamilton-Jacobi equation-Bohmian trajectories (CQHJE-BT) method is introduced as a synthetic trajectory method for integrating the complex quantum Hamilton-Jacobi equation for the complex action function by propagating an ensemble of real-valued correlated Bohmian trajectories. Substituting the wave function expressed in exponential form in terms of the complex action into the time-dependent Schrödinger equation yields the complex quantum Hamilton-Jacobi equation. We transform this equation into the arbitrary Lagrangian-Eulerian version with the grid velocity matching the flow velocity of the probability fluid. The resulting equation describing the rate of change in the complex action transported along Bohmian trajectories is simultaneously integrated with the guidance equation for Bohmian trajectories, and the time-dependent wave function is readily synthesized. The spatial derivatives of the complex action required for the integration scheme are obtained by solving one moving least squares matrix equation. In addition, the method is applied to the photodissociation of NOCl. The photodissociation dynamics of NOCl can be accurately described by propagating a small ensemble of trajectories. This study demonstrates that the CQHJE-BT method combines the considerable advantages of both the real and the complex quantum trajectory methods previously developed for wave packet dynamics.
Chou, Chia-Chun
2014-03-14
The complex quantum Hamilton-Jacobi equation-Bohmian trajectories (CQHJE-BT) method is introduced as a synthetic trajectory method for integrating the complex quantum Hamilton-Jacobi equation for the complex action function by propagating an ensemble of real-valued correlated Bohmian trajectories. Substituting the wave function expressed in exponential form in terms of the complex action into the time-dependent Schrödinger equation yields the complex quantum Hamilton-Jacobi equation. We transform this equation into the arbitrary Lagrangian-Eulerian version with the grid velocity matching the flow velocity of the probability fluid. The resulting equation describing the rate of change in the complex action transported along Bohmian trajectories is simultaneously integrated with the guidance equation for Bohmian trajectories, and the time-dependent wave function is readily synthesized. The spatial derivatives of the complex action required for the integration scheme are obtained by solving one moving least squares matrix equation. In addition, the method is applied to the photodissociation of NOCl. The photodissociation dynamics of NOCl can be accurately described by propagating a small ensemble of trajectories. This study demonstrates that the CQHJE-BT method combines the considerable advantages of both the real and the complex quantum trajectory methods previously developed for wave packet dynamics. PMID:24628169
Solution of coupled integral equations for quantum scattering in the presence of complex potentials
Franz, Jan
2015-01-15
In this paper, we present a method to compute solutions of coupled integral equations for quantum scattering problems in the presence of a complex potential. We show how the elastic and absorption cross sections can be obtained from the numerical solution of these equations in the asymptotic region at large radial distances.
Quantum harmonic oscillator in a thermal bath
NASA Technical Reports Server (NTRS)
Zhang, Yuhong
1993-01-01
The influence functional path-integral treatment of quantum Brownian motion is briefly reviewed. A newly derived exact master equation of a quantum harmonic oscillator coupled to a general environment at arbitrary temperature is discussed. It is applied to the problem of loss of quantum coherence.
A connection between supersymmetric quantum mechanics and Painlevé V equation
NASA Astrophysics Data System (ADS)
Bermudez, D.; Fernández C, David J.
2015-06-01
In this article we introduce the relation between supersymmetric quantum mechanics (SUSY QM) and a second-order non-linear differential equation known as Painleve V (PV) equation. To that end, we will first make a swift examination on the SUSY QM treatment of the radial oscillator and we will revisit its relation with the polynomial Heisenberg algebras (PHA). After that, we will formulate a theorem that connects SUSY QM to a set of solutions of the PV equation through specific PHA.
Simulation of the Burgers equation by NMR quantum-information processing
Chen Zhiying; Cory, David G.; Yepez, Jeffrey
2006-10-15
We report on the implementation of Burgers equation as a type-II quantum computation on a NMR quantum-information processor. Since the flow field evolving under the Burgers equation develops sharp features over time, this is a better test of liquid-state NMR implementations of type-II quantum computers than the previous examples using the diffusion equation. In particular, we show that Fourier approximations used in the encoding step are not the dominant error. Small systematic errors in the collision operator accumulate and swamp all other errors. We propose, and demonstrate, that the accumulation of this error can be avoided to a large extent by replacing the single collision operator with a set of operators with random errors and similar fidelities. Experiments have been implemented on 16 two-qubit sites for eight successive time steps for the Burgers equation.
Reply to "Comment on 'Fractional quantum mechanics' and 'Fractional Schrödinger equation' ".
Laskin, Nick
2016-06-01
The fractional uncertainty relation is a mathematical formulation of Heisenberg's uncertainty principle in the framework of fractional quantum mechanics. Two mistaken statements presented in the Comment have been revealed. The origin of each mistaken statement has been clarified and corrected statements have been made. A map between standard quantum mechanics and fractional quantum mechanics has been presented to emphasize the features of fractional quantum mechanics and to avoid misinterpretations of the fractional uncertainty relation. It has been shown that the fractional probability current equation is correct in the area of its applicability. Further studies have to be done to find meaningful quantum physics problems with involvement of the fractional probability current density vector and the extra term emerging in the framework of fractional quantum mechanics. PMID:27415398
Reply to "Comment on `Fractional quantum mechanics' and `Fractional Schrödinger equation' "
NASA Astrophysics Data System (ADS)
Laskin, Nick
2016-06-01
The fractional uncertainty relation is a mathematical formulation of Heisenberg's uncertainty principle in the framework of fractional quantum mechanics. Two mistaken statements presented in the Comment have been revealed. The origin of each mistaken statement has been clarified and corrected statements have been made. A map between standard quantum mechanics and fractional quantum mechanics has been presented to emphasize the features of fractional quantum mechanics and to avoid misinterpretations of the fractional uncertainty relation. It has been shown that the fractional probability current equation is correct in the area of its applicability. Further studies have to be done to find meaningful quantum physics problems with involvement of the fractional probability current density vector and the extra term emerging in the framework of fractional quantum mechanics.
Current in open quantum systems.
Gebauer, Ralph; Car, Roberto
2004-10-15
We show that a dissipative current component is present in the dynamics generated by a Liouville-master equation, in addition to the usual component associated with Hamiltonian evolution. The dissipative component originates from coarse graining in time, implicit in a master equation, and needs to be included to preserve current continuity. We derive an explicit expression for the dissipative current in the context of the Markov approximation. Finally, we illustrate our approach with a simple numerical example, in which a quantum particle is coupled to a harmonic phonon bath and dissipation is described by the Pauli master equation. PMID:15524960
Polytropic equation of state and primordial quantum fluctuations
NASA Astrophysics Data System (ADS)
Freitas, R. C.; Gonçalves, S. V. B.
2014-12-01
We study the primordial Universe in a cosmological model where inflation is driven by a fluid with a polytropic equation of state . We calculate the dynamics of the scalar factor and build a Universe with constant density at the origin. We also find the equivalent scalar field that could create such an equation of state and calculate the corresponding slow-roll parameters. We calculate the scalar perturbations, the scalar power spectrum, and the spectral index.
Generalized guidance equation for peaked quantum solitons and effective gravity
NASA Astrophysics Data System (ADS)
Durt, Thomas
2016-04-01
Bouncing oil droplets have been shown to follow de Broglie-Bohm–like trajectories and at the same time they exhibit attractive and repulsive pseudo-gravitation. We propose a model aimed at rendering account of these phenomenological observations. It inspires, in a more speculative approach, a toy model for quantum gravity.
Integrating the quantum Hamilton-Jacobi equations by wavefront expansion and phase space analysis
NASA Astrophysics Data System (ADS)
Bittner, Eric R.; Wyatt, Robert E.
2000-11-01
In this paper we report upon our computational methodology for numerically integrating the quantum Hamilton-Jacobi equations using hydrodynamic trajectories. Our method builds upon the moving least squares method developed by Lopreore and Wyatt [Phys. Rev. Lett. 82, 5190 (1999)] in which Lagrangian fluid elements representing probability volume elements of the wave function evolve under Newtonian equations of motion which include a nonlocal quantum force. This quantum force, which depends upon the third derivative of the quantum density, ρ, can vary rapidly in x and become singular in the presence of nodal points. Here, we present a new approach for performing quantum trajectory calculations which does not involve calculating the quantum force directly, but uses the wavefront to calculate the velocity field using mv=∇S, where S/ℏ is the argument of the wave function ψ. Additional numerical stability is gained by performing local gauge transformations to remove oscillatory components of the wave function. Finally, we use a dynamical Rayleigh-Ritz approach to derive ancillary equations-of-motion for the spatial derivatives of ρ, S, and v. The methodologies described herein dramatically improve the long time stability and accuracy of the quantum trajectory approach even in the presence of nodes. The method is applied to both barrier crossing and tunneling systems. We also compare our results to semiclassical based descriptions of barrier tunneling.
Associative Yang-Baxter equation for quantum (semi-)dynamical R-matrices
NASA Astrophysics Data System (ADS)
Sechin, Ivan; Zotov, Andrei
2016-05-01
In this paper we propose versions of the associative Yang-Baxter equation and higher order R-matrix identities which can be applied to quantum dynamical R-matrices. As is known quantum non-dynamical R-matrices of Baxter-Belavin type satisfy this equation. Together with unitarity condition and skew-symmetry it provides the quantum Yang-Baxter equation and a set of identities useful for different applications in integrable systems. The dynamical R-matrices satisfy the Gervais-Neveu-Felder (or dynamical Yang-Baxter) equation. Relation between the dynamical and non-dynamical cases is described by the IRF (interaction-round-a-face)-Vertex transformation. An alternative approach to quantum (semi-)dynamical R-matrices and related quantum algebras was suggested by Arutyunov, Chekhov, and Frolov (ACF) in their study of the quantum Ruijsenaars-Schneider model. The purpose of this paper is twofold. First, we prove that the ACF elliptic R-matrix satisfies the associative Yang-Baxter equation with shifted spectral parameters. Second, we directly prove a simple relation of the IRF-Vertex type between the Baxter-Belavin and the ACF elliptic R-matrices predicted previously by Avan and Rollet. It provides the higher order R-matrix identities and an explanation of the obtained equations through those for non-dynamical R-matrices. As a by-product we also get an interpretation of the intertwining transformation as matrix extension of scalar theta function likewise R-matrix is interpreted as matrix extension of the Kronecker function. Relations to the Gervais-Neveu-Felder equation and identities for the Felder's elliptic R-matrix are also discussed.
Quantum structure emerging from the transformation design of the Dirac equation
Lin, De-Hone
2014-06-15
It is shown that a quantum structure can be created by a set of chosen constraint conditions that emerge from the transformation design of the Dirac equation in general relativity. As an explanation, the constraints that cause novel bound states with the quantization rule of a 2D Coulomb system are presented. The discussion in this paper provides a systematic way to look for constraints that generate a required quantization rule. -- Highlights: •We perform the transformation design of space and time for spin-1/2 matter waves. •A quantum rule could naturally emerge as constraints imposed on the Dirac equation itself. •New fermion states share the quantum spectrum of a 2D Coulomb system. •Transformation design uncovers a new exact solvable model. •A quantum spectrum can be created by a geometric structure.
Numerical scheme for a spatially inhomogeneous matrix-valued quantum Boltzmann equation
NASA Astrophysics Data System (ADS)
Lu, Jianfeng; Mendl, Christian B.
2015-06-01
We develop an efficient algorithm for a spatially inhomogeneous matrix-valued quantum Boltzmann equation derived from the Hubbard model. The distribution functions are 2 × 2 matrix-valued to accommodate the spin degree of freedom, and the scalar quantum Boltzmann equation is recovered as a special case when all matrices are proportional to the identity. We use Fourier discretization and fast Fourier transform to efficiently evaluate the collision kernel with spectral accuracy, and numerically investigate periodic, Dirichlet and Maxwell boundary conditions. Model simulations quantify the convergence to local and global thermal equilibrium.
Quantum lattice-gas models for the many-body schroedinger equation
Boghosian, B.M.; Taylor, W. IV
1997-08-01
A general class of discrete unitary models are described whose behavior in the continuum limit corresponds to a many-body Schroedinger equation. On a quantum computer, these models could be used to simulate quantum many-body systems with an exponential speedup over analogous simulations on classical computers. On a classical computer, these models give an explicitly unitary and local prescription for discretizing the Schroedinger equation. It is shown that models of this type can be constructed for an arbitrary number of particles moving in an arbitrary number of dimensions with an arbitrary interparticle interaction.
Numerical Analysis of Quantum Transport Equation for Bose Gas in One Dimensional Optical Lattice
NASA Astrophysics Data System (ADS)
Kuwahara, Yukiro; Nakamura, Yusuke; Yamanaka, Yoshiya
The quantum transport equation and the correction of the quasiparticle energy are derived by imposing the renormalization conditions on the improved time-dependent on-shell self-energy in nonequilibrium Thermo Field Dynamics. They are numerically analyzed for the one dimensional system of cold neutral atomic Bose gas confined by a combined harmonic and optical lattice potentials. The analysis indicates that the correction of the quaisparticle energy plays a crucial role in the thermal relaxation processes described by the quantum transport equation.
A two-qubit photonic quantum processor and its application to solving systems of linear equations
Barz, Stefanie; Kassal, Ivan; Ringbauer, Martin; Lipp, Yannick Ole; Dakić, Borivoje; Aspuru-Guzik, Alán; Walther, Philip
2014-01-01
Large-scale quantum computers will require the ability to apply long sequences of entangling gates to many qubits. In a photonic architecture, where single-qubit gates can be performed easily and precisely, the application of consecutive two-qubit entangling gates has been a significant obstacle. Here, we demonstrate a two-qubit photonic quantum processor that implements two consecutive CNOT gates on the same pair of polarisation-encoded qubits. To demonstrate the flexibility of our system, we implement various instances of the quantum algorithm for solving of systems of linear equations. PMID:25135432
Simulating the time-dependent Schr"odinger equation with a quantum lattice-gas algorithm
NASA Astrophysics Data System (ADS)
Prezkuta, Zachary; Coffey, Mark
2007-03-01
Quantum computing algorithms promise remarkable improvements in speed or memory for certain applications. Currently, the Type II (or hybrid) quantum computer is the most feasible to build. This consists of a large number of small Type I (pure) quantum computers that compute with quantum logic, but communicate with nearest neighbors in a classical way. The arrangement thus formed is suitable for computations that execute a quantum lattice gas algorithm (QLGA). We report QLGA simulations for both the linear and nonlinear time-dependent Schr"odinger equation. These evidence the stable, efficient, and at least second order convergent properties of the algorithm. The simulation capability provides a computational tool for applications in nonlinear optics, superconducting and superfluid materials, Bose-Einstein condensates, and elsewhere.
The master T-operator for vertex models with trigonometric R-matrices as a classical τ-function
NASA Astrophysics Data System (ADS)
Zabrodin, A. V.
2013-01-01
We apply the recently proposed construction of the master T-operator to integrable vertex models and the associated quantum spin chains with trigonometric R-matrices. The master T-operator is a generating function for commuting transfer matrices of integrable vertex models depending on infinitely many parameters. It also turns out to be the τ-function of an integrable hierarchy of classical soliton equations in the sense that it satisfies the same bilinear Hirota equations. We characterize the class of solutions of the Hirota equations that correspond to eigenvalues of the master T-operator and discuss its relation to the classical Ruijsenaars-Schneider system of particles.
Masters with Masters #3 features Mike Hawes, Assoc. Administrator, Office of Independent Program Cost & Evaluation, and Lynn Cline, Deputy Assoc. Administrator for Special Operations Missions, disc...
Bueyuekasik, Sirin A.; Pashaev, Oktay K.
2010-12-15
We construct a Madelung fluid model with time variable parameters as a dissipative quantum fluid and linearize it in terms of Schroedinger equation with time-dependent parameters. It allows us to find exact solutions of the nonlinear Madelung system in terms of solutions of the Schroedinger equation and the corresponding classical linear ordinary differential equation with variable frequency and damping. For the complex velocity field, the Madelung system takes the form of a nonlinear complex Schroedinger-Burgers equation, for which we obtain exact solutions using complex Cole-Hopf transformation. In particular, we give exact results for nonlinear Madelung systems related with Caldirola-Kanai-type dissipative harmonic oscillator. Collapse of the wave function in dissipative models and possible implications for the quantum cosmology are discussed.
The quantum probability equation: I. Bound state perturbation theory
NASA Astrophysics Data System (ADS)
Milward, Geoffrey C.; Wilkin, Colin
2000-10-01
The partial-wave Schrödinger equation with real boundary conditions is recast as an equation for the probability density. When a small additional potential is included, the changes in the bound-state energy eigenvalues are obtained, up to third order in the perturbation, purely in terms of the perturbing potential and the unperturbed probability density. Although the approach is different, our results are equivalent to those derived by Bender (Bender C M 1978 Advanced Mathematical Methods for Scientists and Engineers (New York: McGraw-Hill) p 330). Knowledge of neither the unperturbed energy spectrum nor the wavefunctions of excited states is required. Evaluations of the second-order energy shift are given for some soluble S-wave problems.
Digital quantum simulation of Dirac equation with a trapped ion
NASA Astrophysics Data System (ADS)
Shen, Yangchao; Zhang, Xiang; Zhang, Junhua; Casanova, Jorge; Lamata, Lucas; Solano, Enrique; Yung, Man-Hong; Zhang, Jingning; Kim, Kihwan; Department Of Physical Chemistry Collaboration
2014-05-01
Recently there has been growing interest in simulating relativistic effects in controllable physical system. We digitally simulate the Dirac equation in 3 +1 dimensions with a single trapped ion. We map four internal levels of 171Yb+ ion to the Dirac bispinor. The time evolution of the Dirac equation is implemented by trotter expansion. In the 3 +1 dimension, we can observe a helicoidal motion of a free Dirac particle which reduces to Zitterbewegung in 1 +1 dimension. This work was supported in part by the National Basic Research Program of China Grant 2011CBA00300, 2011CBA00301, the National Natural Science Foundation of China Grant 61033001, 61061130540. KK acknowledge the support from the recruitment program of global youth experts.
NASA Astrophysics Data System (ADS)
Donker, H. C.; Katsnelson, M. I.; De Raedt, H.; Michielsen, K.
2016-09-01
The logical inference approach to quantum theory, proposed earlier De Raedt et al. (2014), is considered in a relativistic setting. It is shown that the Klein-Gordon equation for a massive, charged, and spinless particle derives from the combination of the requirements that the space-time data collected by probing the particle is obtained from the most robust experiment and that on average, the classical relativistic equation of motion of a particle holds.
A parametric approach to supersymmetric quantum mechanics in the solution of Schrödinger equation
Tezcan, Cevdet; Sever, Ramazan
2014-03-15
We study exact solutions of the Schrödinger equation for some potentials. We introduce a parametric approach to supersymmetric quantum mechanics to calculate energy eigenvalues and corresponding wave functions exactly. As an application we solve Schrödinger equation for the generalized Morse potential, modified Hulthen potential, deformed Rosen-Morse potential and Poschl-Teller potential. The method is simple and effective to get the results.
Myers, R.E.; Riley, S.C.
1994-12-31
A state-wide network for Mathematics And Science Teaching Excellence Through Resources, Renewal, and Services, MASTER{sup 3}S Network is a grant-supported project designed to provide a comprehensive teacher support system for enhancing MST industry representatives, and MST professional system for enhancing MST industry representatives, and MST professional societies, a unique feature in the broad alliance of organizations involved. Made up of three inter-related projects, MASTER{sup 3}S facilitates the provision of resources, services, and opportunities for renewal for the instructional expert. Project One provides support through expert assistance as a cadre of scientists and engineers volunteer to serve as assistants in the classroom. Project Two provides support in the form of math/science summer courses, plus forums throughout the school year to offer ongoing collegial support. Project Three will soon provide support through information with the development of TROL (Teaching Resources on Line), our catalog database of locally available MST resources. The guiding principle of MASTER3S is the belief that by empowering, supporting and serving the teacher, we can most effectively impact student attitudes toward and achievement in MST subjects.
The stochastic radiative transfer equation: quantum damping, Kirchoff's law and NLTE
Graziani, F R
2005-01-24
A method is presented based on the theory of quantum damping, for deriving a self consistent but approximate form of the quantum transport for photons interacting with fully ionized electron plasma. Specifically, we propose in this paper a technique of approximately including the effects of background plasma on a photon distribution function without directly solving any kinetic equations for the plasma itself. The result is a quantum Langevin equation for the photon number operator; the quantum radiative transfer equation. A dissipation term appears which is the imaginary part of the dielectric function for an electron gas with photon mediated electron-electron interactions due to absorption and re-emission. It depends only on the initial state of the plasma. A quantum noise operator also appears as a result of spontaneous emission of photons from the electron plasma. The thermal expectation value of this noise operator yields the emissivity which is exactly of the form of the Kirchoff-Planck relation. This non-zero thermal expectation value is a direct consequence of a fluctuation-dissipation relation (FDR).
NASA Astrophysics Data System (ADS)
Levy, Amikam; Diósi, Lajos; Kosloff, Ronnie
2016-05-01
In this work we present the concept of a quantum flywheel coupled to a quantum heat engine. The flywheel stores useful work in its energy levels, while additional power is extracted continuously from the device. Generally, the energy exchange between a quantum engine and a quantized work repository is accompanied by heat, which degrades the charging efficiency. Specifically when the quantum harmonic oscillator acts as a work repository, quantum and thermal fluctuations dominate the dynamics. Quantum monitoring and feedback control are applied to the flywheel in order to reach steady state and regulate its operation. To maximize the charging efficiency one needs a balance between the information gained by measuring the system and the information fed back to the system. The dynamics of the flywheel are described by a stochastic master equation that accounts for the engine, the external driving, the measurement, and the feedback operations.
Theta function solutions of the quantum Knizhnik-Zamolodchikov-Bernard equation for a face model
NASA Astrophysics Data System (ADS)
Finch, Peter E.; Weston, Robert; Zinn-Justin, Paul
2016-02-01
We consider the quantum Knizhnik-Zamolodchikov-Bernard equation for a face model with elliptic weights, the SOS model. We provide explicit solutions as theta functions. On the so-called combinatorial line, in which the model is equivalent to the three-colour model, these solutions are shown to be eigenvectors of the transfer matrix with periodic boundary conditions.
The Schr{umlt o}dinger and Dirac free particle equations without quantum mechanics
Ord, G.N.
1996-08-01
Einstein{close_quote}s theory of Brownian Movement has provided a well accepted microscopic model of diffusion for many years. Until recently the relationship between this model and Quantum Mechanics has been completely formal. Brownian motion provides a microscopic model for diffusion, but quantum mechanics and diffusion are related by a formal analytic continuation, so the relationship between Brownian motion and Quantum Mechanics has been correspondingly vague. Some recent work has changed this picture somewhat and here we show that a random walk model of Brownian motion produces the diffusion equation or the telegraph equations as a descriptions of particle densities, while at the same time the correlations in the space-time geometry of these same Brownian particles obey the Schr{umlt o}dinger and Dirac equations respectively. This is of interest because the equations of Quantum Mechanics appear here naturally in a classical context without the problems of interpretation they have in the usual context. {copyright} 1996 Academic Press, Inc.
Cross, J. E.; Gregori, G.; Reville, B.
2014-11-01
We introduce the equations of magneto-quantum-radiative hydrodynamics. By rewriting them in a dimensionless form, we obtain a set of parameters that describe scale-dependent ratios of characteristic hydrodynamic quantities. We discuss how these dimensionless parameters relate to the scaling between astrophysical observations and laboratory experiments.
Dubinov, Alexander E.; Kitayev, Ilya N.
2014-02-15
New multiplicative solutions of the Zakharov's quantum system of equations using the separation of variables method are found. The found solutions are interpreted as spatial-periodical lattices of non-linear plasma bursts. It is shown that the bursts could be both symmetrical and asymmetrical by an electric field.
Hu Jie; Luo Meng; Jiang Feng; Xu Ruixue; Yan Yijing
2011-06-28
Pade spectrum decomposition is an optimal sum-over-poles expansion scheme of Fermi function and Bose function [J. Hu, R. X. Xu, and Y. J. Yan, J. Chem. Phys. 133, 101106 (2010)]. In this work, we report two additional members to this family, from which the best among all sum-over-poles methods could be chosen for different cases of application. Methods are developed for determining these three Pade spectrum decomposition expansions at machine precision via simple algorithms. We exemplify the applications of present development with optimal construction of hierarchical equations-of-motion formulations for nonperturbative quantum dissipation and quantum transport dynamics. Numerical demonstrations are given for two systems. One is the transient transport current to an interacting quantum-dots system, together with the involved high-order co-tunneling dynamics. Another is the non-Markovian dynamics of a spin-boson system.
The damped Pinney equation and its applications to dissipative quantum mechanics
NASA Astrophysics Data System (ADS)
Haas, F.
2010-02-01
The present work considers the damped Pinney equation, defined as the model arising when a linear in velocity damping term is included in the Pinney equation. In the general case, the resulting equation does not admit Lie point symmetries or reduction to a simpler form by any obvious coordinate transformation. In this context, the method of Kuzmak-Luke is applied to derive a perturbation solution, for weak damping and slow time dependence of the frequency function. The perturbative and numerical solutions are shown to be in good agreement. The results are applied to examine the time evolution of Gaussian-shaped wave functions in the Kostin formulation of dissipative quantum mechanics.
Bailey, M.J.
1987-12-01
In support of a Very High Speed Integrated Circuit (VHSIC) class processor for computation of a set of equations known as the Vector Wave Equations (VWE), certain elementary functions including sine, cosine, and division are required. These elementary functions are the bottlenecks in the VWE processor. Floating-point multipliers and adders comprise the remainder of the pipeline stages in the VWE processor. To speed up the computation of the elementary functions, pipelining within the functions is considered. To compute sine, cosine, and division, the CORDIC algorithm is presented. Another method for computation of sine and cosine is the expansion of the Chebyshev polynomials. The equations for the CORDIC processor are recursive and the resulting hardware is very simple, consisting of three adders, three shifters, and lookup table for some of the coefficients. The shifters replace the multiplies, because in binary, i right shifts is the same as multiplying by 2 to the 8th power. The expansion of the Chebyshev polynomials can be used to compute other trigonometric functions as well as the exponential and logarithmic functions. The expansion of the Chebyshev polynomials can be used as a mathematic coprocessor. From these equations, a pipelined architecture can be realized that results in very fast computation times. The transformation of these equations as a function of x instead of the Chebyshev polynomials produces an architecture that requires less hardware, resulting in even faster computation times.
NASA Astrophysics Data System (ADS)
Håkansson, Pär; Westlund, Per-Olof
2005-01-01
This paper discusses the process of energy migration transfer within reorientating chromophores using the stochastic master equation (SME) and the stochastic Liouville equation (SLE) of motion. We have found that the SME over-estimates the rate of the energy migration compared to the SLE solution for a case of weakly interacting chromophores. This discrepancy between SME and SLE is caused by a memory effect occurring when fluctuations in the dipole-dipole Hamiltonian ( H( t)) are on the same timescale as the intrinsic fast transverse relaxation rate characterized by (1/ T2). Thus the timescale critical for energy-transfer experiments is T2≈10 -13 s. An extended SME is constructed, accounting for the memory effect of the dipole-dipole Hamiltonian dynamics. The influence of memory on the interpretation of experiments is discussed.
Håkansson, Pär; Westlund, Per-Olof
2005-01-01
This paper discusses the process of energy migration transfer within reorientating chromophores using the stochastic master equation (SME) and the stochastic Liouville equation (SLE) of motion. We have found that the SME over-estimates the rate of the energy migration compared to the SLE solution for a case of weakly interacting chromophores. This discrepancy between SME and SLE is caused by a memory effect occurring when fluctuations in the dipole-dipole Hamiltonian (H(t)) are on the same timescale as the intrinsic fast transverse relaxation rate characterized by (1/T(2)). Thus the timescale critical for energy-transfer experiments is T(2) approximately 10(-13) s. An extended SME is constructed, accounting for the memory effect of the dipole-dipole Hamiltonian dynamics. The influence of memory on the interpretation of experiments is discussed. PMID:15556453
NASA Astrophysics Data System (ADS)
Hessian, H. A.; Mohammed, F. A.; Mohamed, A.-B. A.
2009-04-01
In this paper, we analytically solve the master equation for Jaynes-Cummings model in the dispersive regime including phase damping and the field is assumed to be initially in a superposition of coherent states. Using an established entanglement measure based on the negativity of the eigenvalues of the partially transposed density matrix we find a very strong sensitivity of the maximally generated entanglement to the amount of phase damping. Qualitatively this behavior is also reflected in alternative entanglement measures, but the quantitative agreement between different measures depends on the chosen noise model. The phase decoherence for this model results in monotonic increase in the total entropy while the atomic sub-entropy keeps its periodic behaviour without any effect.
NASA Astrophysics Data System (ADS)
Pelosi, A.; Schumer, R.; Parker, G.; Ferguson, R. I.
2016-03-01
Tracer pebbles are often used to study bed load transport processes in gravel bed rivers. Models have been proposed for their downstream dispersion, and also for vertical dispersion, but not for the combined effects of downstream and vertical movement. Here we use the Exner-Based Master Equation to characterize the transient coevolution of streamwise and vertical advection-diffusion of tracer pebbles under equilibrium transport conditions (no net aggradation or degradation). The coevolution of streamwise and vertical dispersion gives rise to behavior that can differ markedly from that associated with purely streamwise processes with no vertical exchange. One example is streamwise advective slowdown. Particles that are advected downward into zones where the probability of reentrainment becomes asymptotically small are essentially trapped and can no longer participate in streamwise advection. As a result, the mean streamwise velocity of the tracer plume declines in time. Qualitative and quantitative comparisons with two field experiments show encouraging agreement despite the simplified boundary conditions in the model.
Initial states in integrable quantum field theory quenches from an integral equation hierarchy
NASA Astrophysics Data System (ADS)
Horváth, D. X.; Sotiriadis, S.; Takács, G.
2016-01-01
We consider the problem of determining the initial state of integrable quantum field theory quenches in terms of the post-quench eigenstates. The corresponding overlaps are a fundamental input to most exact methods to treat integrable quantum quenches. We construct and examine an infinite integral equation hierarchy based on the form factor bootstrap, proposed earlier as a set of conditions determining the overlaps. Using quenches of the mass and interaction in Sinh-Gordon theory as a concrete example, we present theoretical arguments that the state has the squeezed coherent form expected for integrable quenches, and supporting an Ansatz for the solution of the hierarchy. Moreover we also develop an iterative method to solve numerically the lowest equation of the hierarchy. The iterative solution along with extensive numerical checks performed using the next equation of the hierarchy provides a strong numerical evidence that the proposed Ansatz gives a very good approximation for the solution.
On a derivation of the Boltzmann equation in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Leiler, Gregor
The Boltzmann equation (BE) is a commonly used tool for the study of non-equilibrium many particle systems. It has been introduced in 1872 by Ludwig Boltzmann and has been widely generalized throughout the years. Today it is commonly used in physical applications, from the study of ordinary fluids to problems in particle Cosmology where Quantum Field Theoretical techniques are essential. Despite its numerous experimental successes, the conceptual basis of the BE is not entirely clear. For instance, it is well known that it is not a fundamental equation of physics like, say, the Heisenberg equation (HE). A natural question then arises whether it is possible to derive the BE from physical first principles, i.e. the Heisenberg equation in Quantum Field Theory. In this work we attempted to answer this question and succeeded in deriving the BE from the HE, thus further clarifying its conceptual status. In particular, the results we have obtained are as follows. Firstly, we establish the non-perturbative validity of what we call the "pre-Boltzmann equation". The crucial point here is that this latter equation is equivalent to the Heisenberg equation. Secondly, we proceed to consider various limits of the pre-Boltzmann equation, namly the "low density" and the "weak coupling" limits, to obtain two equations that can be considered as generalizations of the BE. These limits are always taken together with the "long time" limit, which allows us to interpret the BE as an appropriate long time limit of the HE. The generalization we obtain consists in additional "correction" terms to the usual Boltzmann collision factor, and can be associated to multiple particle scattering. Unlike the pre-Boltzmann equation, these latter results are only valid pertubatively. Finally, we briefly consider the possibility to extend these results beyond said limits and outline some important aspects in this case.
Woesler, Richard
2007-02-21
The computations of the present text with non-relativistic quantum teleportation equations and special relativity are totally speculative, physically correct computations can be done using quantum field theory, which remain to be done in future. Proposals for what might be called statistical time loop experiments with, e.g., photon polarization states are described when assuming the simplified non-relativistic quantum teleportation equations and special relativity. However, a closed time loop would usually not occur due to phase incompatibilities of the quantum states. Histories with such phase incompatibilities are called inconsistent ones in the present text, and it is assumed that only consistent histories would occur. This is called an exclusion principle for inconsistent histories, and it would yield that probabilities for certain measurement results change. Extended multiple parallel experiments are proposed to use this statistically for transmission of classical information over distances, and regarding time. Experiments might be testable in near future. However, first a deeper analysis, including quantum field theory, remains to be done in future.
Derivation of quantum mechanics from the Boltzmann equation for the Planch aether
Winterberg, F.
1995-10-01
The Planck aether hypothesis assumes that space is densely filled with an equal number of locally interacting positive and negative Planck masses obeying an exactly nonrelativistic law of motion. The Planck masses can be described by a quantum mechanical two-component nonrelativistic operator field equation having the form of a two-component nonlinear Schroedinger equation, with a spectrum of quasiparticles obeying Lorentz invariance as a dynamic symmetry for energies small compared to the Planck energy. We show that quantum mechanics itself can be derived from the Newtonian mechanics of the Planck aether as an approximate solution of Boltzmann`s equation for the locally interacting positive and negative Planck masses, and that the validity of the nonrelativistic Schroedinger equation depends on Lorentz invariance as a dynamic symmetry. We also show how the many-body Schroedinger wave function can be factorized into a product of quasiparticles of the Planck aether with separable quantum potentials. Finally, we present a possible explanation of wave function collapse as a kind of enhanced gravitational collapse in the presence of the negative Planck masses.
Solutions to the Painlevé V equation through supersymmetric quantum mechanics
NASA Astrophysics Data System (ADS)
Bermudez, David; Fernández C, David J.; Negro, Javier
2016-08-01
In this paper we shall use the algebraic method known as supersymmetric quantum mechanics (SUSY QM) to obtain solutions to the Painlevé V (PV) equation, a second-order nonlinear ordinary differential equation. For this purpose, we will apply first the SUSY QM treatment to the radial oscillator. In addition, we will revisit the polynomial Heisenberg algebras (PHAs) and we will study the general systems ruled by them: for first-order PHAs we obtain the radial oscillator while for third-order PHAs the potential will be determined by solutions to the PV equation. This connection allows us to introduce a simple technique for generating solutions of the PV equation expressed in terms of confluent hypergeometric functions. Finally, we will classify them into several solution hierarchies.
NASA Astrophysics Data System (ADS)
Kojima, T.; Korepin, V. E.; Slavnov, N. A.
Painlevé analysis of correlation functions of the impenetrable Bose gas by M. Jimbo, T. Miwa, Y. Mori and M. Sato [1] was based on the determinant representation of these correlation functions obtained by A. Lenard [2]. The impenetrable Bose gas is the free fermionic case of the quantum nonlinear Schrödinger equation. In this paper we generalize the Lenard determinant representation for ψ (0,0)ψ (x,t)> to the non-free fermionic case. We also include time and temeprature dependence. In forthcoming publications we shall perform the JMMS analysis of this correlationl function. This will give us a completely integrable equation and asymptotic for the quantum correlation function of interacting fermions.
Astrophysical Applications of Quantum Corrections to the Equation of State of a Plasma
NASA Technical Reports Server (NTRS)
Heckler, Andrew F.
1994-01-01
The quantum electrodynamic correction to the equation of state of a plasma at finite temperature is applied to the areas of solar physics and cosmology. A previously neglected, purely quantum term in the correction is found to change the equation of state in the solar core by -0.37%, which is roughly estimated to decrease the calculated high energy neutrino flux by about 2.2%. We also show that a previous calculation of the effect of this correction on big bang nucleosynthesis is incomplete, and we estimate the correction to the primordial helium abundance Y to be Delta A= 1.4 x 10(exp -4). A physical explanation for the correction is found in terms of corrections to the dispersion relation of the electron, positron, and photon.
Positiveness and Pauli exception principle in raw Bloch equations for quantum boxes
NASA Astrophysics Data System (ADS)
Bidégaray-Fesquet, Brigitte
2010-10-01
The aim of this paper is to derive a raw Bloch model for the interaction of light with quantum boxes in the framework of a two-electron-species (conduction and valence) description. This requires a good understanding of the one-species case and of the treatment of level degeneracy. In contrast with some existing literature, we obtain a Liouville equation which induces the positiveness and the boundedness of solutions, that are necessary for future mathematical studies involving higher order phenomena.
Gauge invariant cosmological perturbation equations with corrections from loop quantum gravity
Bojowald, Martin; Hossain, Golam Mortuza; Kagan, Mikhail; Shankaranarayanan, S.
2009-02-15
A consistent implementation of quantum gravity is expected to change the familiar notions of space, time, and the propagation of matter in drastic ways. This will have consequences on very small scales, but also gives rise to correction terms in evolution equations of modes relevant for observations. In particular, the evolution of inhomogeneities in the very early Universe should be affected. In this paper consistent evolution equations for gauge-invariant perturbations in the presence of inverse triad corrections of loop quantum gravity are derived. Some immediate effects are pointed out, for instance, concerning conservation of power on large scales and nonadiabaticity. It is also emphasized that several critical corrections can only be seen to arise in a fully consistent treatment where the gauge freedom of canonical gravity is not fixed before implementing quantum corrections. In particular, metric modes must be allowed to be inhomogeneous: it is not consistent to assume only matter inhomogeneities on a quantum-corrected homogeneous background geometry. In this way, stringent consistency conditions arise for possible quantization ambiguities, which will eventually be further constrained observationally.
Quantum theory as a description of robust experiments: Derivation of the Pauli equation
De Raedt, Hans; Katsnelson, Mikhail I.; Donker, Hylke C.; Michielsen, Kristel
2015-08-15
It is shown that the Pauli equation and the concept of spin naturally emerge from logical inference applied to experiments on a charged particle under the conditions that (i) space is homogeneous (ii) the observed events are logically independent, and (iii) the observed frequency distributions are robust with respect to small changes in the conditions under which the experiment is carried out. The derivation does not take recourse to concepts of quantum theory and is based on the same principles which have already been shown to lead to e.g. the Schrödinger equation and the probability distributions of pairs of particles in the singlet or triplet state. Application to Stern–Gerlach experiments with chargeless, magnetic particles, provides additional support for the thesis that quantum theory follows from logical inference applied to a well-defined class of experiments. - Highlights: • The Pauli equation is obtained through logical inference applied to robust experiments on a charged particle. • The concept of spin appears as an inference resulting from the treatment of two-valued data. • The same reasoning yields the quantum theoretical description of neutral magnetic particles. • Logical inference provides a framework to establish a bridge between objective knowledge gathered through experiments and their description in terms of concepts.
Hunting the ghosts of a 'strictly quantum field': the Klein-Gordon equation
NASA Astrophysics Data System (ADS)
Bertozzi, Eugenio
2010-11-01
This paper aims to identify and tackle some problems related to teaching quantum field theory (QFT) at university level. In particular, problems arising from the canonical quantization are addressed by focusing on the Klein-Gordon equation (KGE). After a brief description of the status of the KGE in teaching as it emerges from an analysis of a selected sample of university textbooks, an analysis of the applications of the KGE in contexts different from the QFT is presented. The results of the analysis show that, while in the real case the solutions of the equation can be easily interpreted from a physical point of view, in the complex case the coherence with relativistic quantum mechanics and the electrodynamics framework brings to light interpretative problems related to the classical complex KG field. The comparison between the classical cases investigated and the QFT framework, where the equation finds a coherent particle interpretation, leads to share Ryder's statement asserting that the KG field is a 'strictly quantum field'. Implications of the results in terms of remarks about the canonical procedure currently utilized for teaching are underlined.
NASA Astrophysics Data System (ADS)
Jang, Seogjoo
2016-06-01
This work provides a detailed derivation of a generalized quantum Fokker-Planck equation (GQFPE) appropriate for photo-induced quantum dynamical processes. The path integral method pioneered by Caldeira and Leggett (CL) [Physica A 121, 587 (1983)] is extended by utilizing a nonequilibrium influence functional applicable to different baths for the ground and the excited electronic states. Both nonequilibrium and non-Markovian effects are accounted for consistently by expanding the paths in the exponents of the influence functional up to the second order with respect to time. This procedure results in approximations involving only single time integrations for the exponents of the influence functional but with additional time dependent boundary terms that have been ignored in previous works. The boundary terms complicate the derivation of a time evolution equation but do not affect position dependent physical observables or the dynamics in the steady state limit. For an effective density operator with the boundary terms factored out, a time evolution equation is derived, through short time expansion of the effective action and Gaussian integration in analytically continued complex domain of space. This leads to a compact form of the GQFPE with time dependent kernels and additional terms, which renders the resulting equation to be in the Dekker form [Phys. Rep. 80, 1 (1981)]. Major terms of the equation are analyzed for the case of Ohmic spectral density with Drude cutoff, which shows that the new GQFPE satisfies the positive definiteness condition in medium to high temperature limit. Steady state limit of the GQFPE is shown to approach the well-known expression derived by CL in the high temperature and Markovian bath limit and also provides additional corrections due to quantum and non-Markovian effects of the bath.
Jang, Seogjoo
2016-06-01
This work provides a detailed derivation of a generalized quantum Fokker-Planck equation (GQFPE) appropriate for photo-induced quantum dynamical processes. The path integral method pioneered by Caldeira and Leggett (CL) [Physica A 121, 587 (1983)] is extended by utilizing a nonequilibrium influence functional applicable to different baths for the ground and the excited electronic states. Both nonequilibrium and non-Markovian effects are accounted for consistently by expanding the paths in the exponents of the influence functional up to the second order with respect to time. This procedure results in approximations involving only single time integrations for the exponents of the influence functional but with additional time dependent boundary terms that have been ignored in previous works. The boundary terms complicate the derivation of a time evolution equation but do not affect position dependent physical observables or the dynamics in the steady state limit. For an effective density operator with the boundary terms factored out, a time evolution equation is derived, through short time expansion of the effective action and Gaussian integration in analytically continued complex domain of space. This leads to a compact form of the GQFPE with time dependent kernels and additional terms, which renders the resulting equation to be in the Dekker form [Phys. Rep. 80, 1 (1981)]. Major terms of the equation are analyzed for the case of Ohmic spectral density with Drude cutoff, which shows that the new GQFPE satisfies the positive definiteness condition in medium to high temperature limit. Steady state limit of the GQFPE is shown to approach the well-known expression derived by CL in the high temperature and Markovian bath limit and also provides additional corrections due to quantum and non-Markovian effects of the bath. PMID:27276940
A 3+1 formalism for quantum electrodynamical corrections to Maxwell equations in general relativity
NASA Astrophysics Data System (ADS)
Pétri, J.
2015-08-01
Magnetized neutron stars constitute a special class of compact objects harbouring gravitational fields that deviate strongly from the Newtonian weak field limit. Moreover, strong electromagnetic fields anchored into the star give rise to non-linear corrections to Maxwell equations described by quantum electrodynamics (QED). Electromagnetic fields close to or above the critical value of BQ = 4.4 × 109 T are probably present in some pulsars and for most of the magnetars. To account properly for emission emanating from the neutron star surface like for instance thermal radiation and its polarization properties, it is important to include general relativistic (GR) effects simultaneously with non-linear electrodynamics. This can be achieved through a 3+1 formalism known in general relativity and that incorporates QED perturbations to Maxwell equations. Starting from the lowest order corrections to the Lagrangian for the electromagnetic field, as given for instance by Born-Infeld or Euler-Heisenberg theory, we derive the non-linear Maxwell equations in general relativity including quantum vacuum effects. We also derive a prescription for the force-free limit and show that these equations can be solved with classical finite volume methods for hyperbolic conservation laws. It is therefore straightforward to include general relativity and QED in the description of neutron star magnetospheres by using standard classical numerical techniques borrowed from Maxwell and Newton theory. As an application, we show that spin-down luminosity corrections associated with QED effects are negligible with respect to GR corrections.
Nonlinear quantum-mechanical system associated with Sine-Gordon equation in (1 + 2) dimensions
Zarmi, Yair
2014-10-15
Despite the fact that it is not integrable, the (1 + 2)-dimensional Sine-Gordon equation has N-soliton solutions, whose velocities are lower than the speed of light (c = 1), for all N ≥ 1. Based on these solutions, a quantum-mechanical system is constructed over a Fock space of particles. The coordinate of each particle is an angle around the unit circle. U, a nonlinear functional of the particle number-operators, which obeys the Sine-Gordon equation in (1 + 2) dimensions, is constructed. Its eigenvalues on N-particle states in the Fock space are the slower-than-light, N-soliton solutions of the equation. A projection operator (a nonlinear functional of U), which vanishes on the single-particle subspace, is a mass-density generator. Its eigenvalues on multi-particle states play the role of the mass density of structures that emulate free, spatially extended, relativistic particles. The simplicity of the quantum-mechanical system allows for the incorporation of perturbations with particle interactions, which have the capacity to “annihilate” and “create” solitons – an effect that does not have an analog in perturbed classical nonlinear evolution equations.
Reduced Dirac equation and Lamb shift as off-mass-shell effect in quantum electrodynamics
NASA Astrophysics Data System (ADS)
Ni, Guang-Jiong; Xu, Jian-Jun; Lou, Sen-Yue
2011-02-01
Based on the accurate experimental data of energy-level differences in hydrogen-like atoms, especially the 1S—2S transitions of hydrogen and deuterium, the necessity of introducing a reduced Dirac equation with reduced mass as the substitution of original electron mass is stressed. Based on new cognition about the essence of special relativity, we provide a reasonable argument for the reduced Dirac equation to have two symmetries, the invariance under the (newly defined) space-time inversion and that under the pure space inversion, in a noninertial frame. By using the reduced Dirac equation and within the framework of quantum electrodynamics in covariant form, the Lamb shift can be evaluated (at one-loop level) as the radiative correction on a bound electron staying in an off-mass-shell state—-a new approach eliminating the infrared divergence. Hence the whole calculation, though with limited accuracy, is simplified, getting rid of all divergences and free of ambiguity.
Orbital HP-Clouds for Solving Schr?dinger Equation inQuantum Mechanics
Chen, J; Hu, W; Puso, M
2006-10-19
Solving Schroedinger equation in quantum mechanics presents a challenging task in numerical methods due to the high order behavior and high dimension characteristics in the wave functions, in addition to the highly coupled nature between wave functions. This work introduces orbital and polynomial enrichment functions to the partition of unity for solution of Schroedinger equation under the framework of HP-Clouds. An intrinsic enrichment of orbital function and extrinsic enrichment of monomial functions are proposed. Due to the employment of higher order basis functions, a higher order stabilized conforming nodal integration is developed. The proposed methods are implemented using the density functional theory for solution of Schroedinger equation. Analysis of several single and multi-electron/nucleus structures demonstrates the effectiveness of the proposed method.
Ishizaki, Akihito; Fleming, Graham R
2009-06-21
A new quantum dynamic equation for excitation energy transfer is developed which can describe quantum coherent wavelike motion and incoherent hopping in a unified manner. The developed equation reduces to the conventional Redfield theory and Forster theory in their respective limits of validity. In the regime of coherent wavelike motion, the equation predicts several times longer lifetime of electronic coherence between chromophores than does the conventional Redfield equation. Furthermore, we show quantum coherent motion can be observed even when reorganization energy is large in comparison to intersite electronic coupling (the Forster incoherent regime). In the region of small reorganization energy, slow fluctuation sustains longer-lived coherent oscillation, whereas the Markov approximation in the Redfield framework causes infinitely fast fluctuation and then collapses the quantum coherence. In the region of large reorganization energy, sluggish dissipation of reorganization energy increases the time electronic excitation stays above an energy barrier separating chromophores and thus prolongs delocalization over the chromophores. PMID:19548715
A new functional flow equation for Einstein-Cartan quantum gravity
NASA Astrophysics Data System (ADS)
Harst, U.; Reuter, M.
2015-03-01
We construct a special-purpose functional flow equation which facilitates non-perturbative renormalization group (RG) studies on theory spaces involving a large number of independent field components that are prohibitively complicated using standard methods. Its main motivation are quantum gravity theories in which the gravitational degrees of freedom are carried by a complex system of tensor fields, a prime example being Einstein-Cartan theory, possibly coupled to matter. We describe a sequence of approximation steps leading from the functional RG equation of the Effective Average Action to the new flow equation which, as a consequence, is no longer fully exact on the untruncated theory space. However, it is by far more "user friendly" when it comes to projecting the abstract equation on a concrete (truncated) theory space and computing explicit beta-functions. The necessary amount of (tensor) algebra reduces drastically, and the usually very hard problem of diagonalizing the pertinent Hessian operator is sidestepped completely. In this paper we demonstrate the reliability of the simplified equation by applying it to a truncation of the Einstein-Cartan theory space. It is parametrized by a scale dependent Holst action, depending on a O(4) spin-connection and the tetrad as the independent field variables. We compute the resulting RG flow, focusing in particular on the running of the Immirzi parameter, and compare it to the results of an earlier computation where the exact equation had been applied to the same truncation. We find consistency between the two approaches and provide further evidence for the conjectured non-perturbative renormalizability (asymptotic safety) of quantum Einstein-Cartan gravity. We also investigate a duality symmetry relating small and large values of the Immirzi parameter (γ → 1 / γ) which is displayed by the beta-functions in the absence of a cosmological constant.
Bouten, Luc; Stockton, John; Sarma, Gopal; Mabuchi, Hideo
2007-05-15
We propose a model, based on a quantum stochastic differential equation (QSDE), to describe the scattering of polarized laser light by an atomic gas. The gauge terms in the QSDE account for the direct scattering of the laser light into different field channels. Once the model has been set, we can rigorously derive quantum filtering equations for balanced polarimetry and homodyne detection experiments, study the statistics of output processes, and investigate a strong driving, weak coupling limit.
Qian, Hong; Bishop, Lisa M.
2010-01-01
We develop the stochastic, chemical master equation as a unifying approach to the dynamics of biochemical reaction systems in a mesoscopic volume under a living environment. A living environment provides a continuous chemical energy input that sustains the reaction system in a nonequilibrium steady state with concentration fluctuations. We discuss the linear, unimolecular single-molecule enzyme kinetics, phosphorylation-dephosphorylation cycle (PdPC) with bistability, and network exhibiting oscillations. Emphasis is paid to the comparison between the stochastic dynamics and the prediction based on the traditional approach based on the Law of Mass Action. We introduce the difference between nonlinear bistability and stochastic bistability, the latter has no deterministic counterpart. For systems with nonlinear bistability, there are three different time scales: (a) individual biochemical reactions, (b) nonlinear network dynamics approaching to attractors, and (c) cellular evolution. For mesoscopic systems with size of a living cell, dynamics in (a) and (c) are stochastic while that with (b) is dominantly deterministic. Both (b) and (c) are emergent properties of a dynamic biochemical network; We suggest that the (c) is most relevant to major cellular biochemical processes such as epi-genetic regulation, apoptosis, and cancer immunoediting. The cellular evolution proceeds with transitions among the attractors of (b) in a “punctuated equilibrium” manner. PMID:20957107
Qian, Hong; Bishop, Lisa M
2010-01-01
We develop the stochastic, chemical master equation as a unifying approach to the dynamics of biochemical reaction systems in a mesoscopic volume under a living environment. A living environment provides a continuous chemical energy input that sustains the reaction system in a nonequilibrium steady state with concentration fluctuations. We discuss the linear, unimolecular single-molecule enzyme kinetics, phosphorylation-dephosphorylation cycle (PdPC) with bistability, and network exhibiting oscillations. Emphasis is paid to the comparison between the stochastic dynamics and the prediction based on the traditional approach based on the Law of Mass Action. We introduce the difference between nonlinear bistability and stochastic bistability, the latter has no deterministic counterpart. For systems with nonlinear bistability, there are three different time scales: (a) individual biochemical reactions, (b) nonlinear network dynamics approaching to attractors, and (c) cellular evolution. For mesoscopic systems with size of a living cell, dynamics in (a) and (c) are stochastic while that with (b) is dominantly deterministic. Both (b) and (c) are emergent properties of a dynamic biochemical network; We suggest that the (c) is most relevant to major cellular biochemical processes such as epi-genetic regulation, apoptosis, and cancer immunoediting. The cellular evolution proceeds with transitions among the attractors of (b) in a "punctuated equilibrium" manner. PMID:20957107
Hasenauer, J; Wolf, V; Kazeroonian, A; Theis, F J
2014-09-01
The time-evolution of continuous-time discrete-state biochemical processes is governed by the Chemical Master Equation (CME), which describes the probability of the molecular counts of each chemical species. As the corresponding number of discrete states is, for most processes, large, a direct numerical simulation of the CME is in general infeasible. In this paper we introduce the method of conditional moments (MCM), a novel approximation method for the solution of the CME. The MCM employs a discrete stochastic description for low-copy number species and a moment-based description for medium/high-copy number species. The moments of the medium/high-copy number species are conditioned on the state of the low abundance species, which allows us to capture complex correlation structures arising, e.g., for multi-attractor and oscillatory systems. We prove that the MCM provides a generalization of previous approximations of the CME based on hybrid modeling and moment-based methods. Furthermore, it improves upon these existing methods, as we illustrate using a model for the dynamics of stochastic single-gene expression. This application example shows that due to the more general structure, the MCM allows for the approximation of multi-modal distributions. PMID:23918091
Cruz, Hans; Schuch, Dieter; Castaños, Octavio; Rosas-Ortiz, Oscar
2015-09-15
The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems with exact analytic solutions with the form of Gaussian wave packets. In particular, one-dimensional conservative systems with at most quadratic Hamiltonians are studied.
NASA Astrophysics Data System (ADS)
Nakamura, Katsuhiro; Sobirov, Zarifboy A.; Matrasulov, Davron U.; Avazbaev, Sanat K.
2012-12-01
We study a nonequilibrium equation of states of an ideal quantum gas confined in the cavity under a moving piston with a small but finite velocity in the case in which the cavity wall suddenly begins to move at the time origin. Confining ourselves to the thermally isolated process, the quantum nonadiabatic (QNA) contribution to Poisson's adiabatic equations and to Bernoulli's formula which bridges the pressure and internal energy is elucidated. We carry out a statistical mean of the nonadiabatic (time-reversal-symmetric) force operator found in our preceding paper [Nakamura , Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.83.041133 83, 041133 (2011)] in both the low-temperature quantum-mechanical and high-temperature quasiclassical regimes. The QNA contribution, which is proportional to the square of the piston's velocity and to the inverse of the longitudinal size of the cavity, has a coefficient that is dependent on the temperature, gas density, and dimensionality of the cavity. The investigation is done for a unidirectionally expanding three-dimensional (3D) rectangular parallelepiped cavity as well as its 1D version. Its relevance in a realistic nanoscale heat engine is discussed.
Wave front-ray synthesis for solving the multidimensional quantum Hamilton-Jacobi equation.
Wyatt, Robert E; Chou, Chia-Chun
2011-08-21
A Cauchy initial-value approach to the complex-valued quantum Hamilton-Jacobi equation (QHJE) is investigated for multidimensional systems. In this approach, ray segments foliate configuration space which is laminated by surfaces of constant action. The QHJE incorporates all quantum effects through a term involving the divergence of the quantum momentum function (QMF). The divergence term may be expressed as a sum of two terms, one involving displacement along the ray and the other incorporating the local curvature of the action surface. It is shown that curvature of the wave front may be computed from coefficients of the first and second fundamental forms from differential geometry that are associated with the surface. Using the expression for the divergence, the QHJE becomes a Riccati-type ordinary differential equation (ODE) for the complex-valued QMF, which is parametrized by the arc length along the ray. In order to integrate over possible singularities in the QMF, a stable and accurate Möbius propagator is introduced. This method is then used to evolve rays and wave fronts for four systems in two and three dimensions. From the QMF along each ray, the wave function can be easily computed. Computational difficulties that may arise are described and some ways to circumvent them are presented. PMID:21861551
Wave front-ray synthesis for solving the multidimensional quantum Hamilton-Jacobi equation
Wyatt, Robert E.; Chou, Chia-Chun
2011-08-21
A Cauchy initial-value approach to the complex-valued quantum Hamilton-Jacobi equation (QHJE) is investigated for multidimensional systems. In this approach, ray segments foliate configuration space which is laminated by surfaces of constant action. The QHJE incorporates all quantum effects through a term involving the divergence of the quantum momentum function (QMF). The divergence term may be expressed as a sum of two terms, one involving displacement along the ray and the other incorporating the local curvature of the action surface. It is shown that curvature of the wave front may be computed from coefficients of the first and second fundamental forms from differential geometry that are associated with the surface. Using the expression for the divergence, the QHJE becomes a Riccati-type ordinary differential equation (ODE) for the complex-valued QMF, which is parametrized by the arc length along the ray. In order to integrate over possible singularities in the QMF, a stable and accurate Moebius propagator is introduced. This method is then used to evolve rays and wave fronts for four systems in two and three dimensions. From the QMF along each ray, the wave function can be easily computed. Computational difficulties that may arise are described and some ways to circumvent them are presented.
Production of a sterile species: Quantum kinetics
Ho, Chiu Man; Boyanovsky, D.; Ho, C.M.
2007-04-23
Production of a sterile species is studied within an effective model of active-sterile neutrino mixing in a medium in thermal equilibrium. The quantum kinetic equations for the distribution functions and coherences are obtained from two independent methods: the effective action and the quantum master equation. The decoherence time scale for active-sterile oscillations is tau(dec)=2/Gamma(aa), but the evolution of the distribution functions is determined by the two different time scales associated with the damping rates of the quasiparticle modes in the medium: Gamma(1)=Gamma(aa)cos^2theta(m); Gamma(2)=Gamma(aa)sin^2theta(m) where Gamma(aa) is the interaction rate of the active species in the absence of mixing and theta(m) the mixing angle in the medium. These two time scales are widely different away from Mikheyev-Smirnov-Wolfenstein resonances and preclude the kinetic description of active-sterile production in terms of a simple rate equation. We give the complete set of quantum kinetic equations for the active and sterile populations and coherences and discuss in detail the various approximations. A generalization of the active-sterile transition probability in a medium is provided via the quantum master equation. We derive explicitly the usual quantum kinetic equations in terms of the"polarization vector" and show their equivalence to those obtained from the quantum master equation and effective action.
Non-relativistic Limit of Dirac Equations in Gravitational Field and Quantum Effects of Gravity
NASA Astrophysics Data System (ADS)
Wu, Ning
2006-03-01
Based on unified theory of electromagnetic interactions and gravitational interactions, the non-relativistic limit of the equation of motion of a charged Dirac particle in gravitational field is studied. From the Schrödinger equation obtained from this non-relativistic limit, we can see that the classical Newtonian gravitational potential appears as a part of the potential in the Schrödinger equation, which can explain the gravitational phase effects found in COW experiments. And because of this Newtonian gravitational potential, a quantum particle in the earth's gravitational field may form a gravitationally bound quantized state, which has already been detected in experiments. Three different kinds of phase effects related to gravitational interactions are studied in this paper, and these phase effects should be observable in some astrophysical processes. Besides, there exists direct coupling between gravitomagnetic field and quantum spin, and radiation caused by this coupling can be used to directly determine the gravitomagnetic field on the surface of a star.
Quantum many-body dynamics in a Lagrangian frame: I. Equations of motion and conservation laws
NASA Astrophysics Data System (ADS)
Tokatly, I. V.
2005-04-01
We formulate equations of motion and conservation laws for a quantum many-body system in a co-moving Lagrangian reference frame. It is shown that generalized inertia forces in the co-moving frame are described by Green’s deformation tensor gμν(ξ,t) and a skew-symmetric vorticity tensor Ftilde μν(ξ,t) , where ξ in the Lagrangian coordinate. Equations of motion are equivalent to those for a quantum many-body system in a space with time-dependent metric gμν(ξ,t) in the presence of an effective magnetic field Ftilde μν(ξ,t) . To illustrate the general formalism we apply it to the proof of the harmonic potential theorem. As another example of application we consider a fast long wavelength dynamics of a Fermi system in the dynamic Hartree approximation. In this case the kinetic equation in the Lagrangian frame can be solved explicitly. This allows us to formulate the description of a Fermi gas in terms of an effective nonlinear elasticity theory. We also discuss a relation of our results to time-dependent density functional theory.
NASA Astrophysics Data System (ADS)
Stumpf, H.
2003-01-01
Generalized de Broglie-Bargmann-Wigner (BBW) equations are relativistically invariant quantum mechanical many body equations with nontrivial interaction, selfregularization and probability interpretation. Owing to these properties these equations are a suitable means for describing relativistic bound states of fermions. In accordance with de Broglie's fusion theory and modern assumptions about the partonic substructure of elementary fermions, i.e., leptons and quarks, the three-body generalized BBW-equations are investigated. The transformation properties and quantum numbers of the three-parton equations under the relevant group actions are elaborated in detail. Section 3 deals with the action of the isospin group SU(2), a U(1) global gauge group for the fermion number, the hypercharge and charge generators. The resulting quantum numbers of the composite partonic systems can be adapted to those of the phenomenological particles to be described. The space-time transformations and in particular rotations generated by angular momentum operators are considered in Section 4. Based on the compatibility of the BBW-equations and the group theoretical constraints, in Sect. 5 integral equations are formulated in a representation with diagonal energy and total angular momentum variables. The paper provides new insight into the solution space and quantum labels of resulting integral equations for three parton states and prepares the ground for representing leptons and quarks as composite systems.
Quantum Coherence of Optomechanical Systems in the Single-photon Strong Coupling Regime
NASA Astrophysics Data System (ADS)
Hu, Dan; Huang, Shang-Yu; Liao, Jie-Qiao; Tian, Lin; Goan, Hsi-Sheng
2015-03-01
Optomechanical systems with ultrastrong coupling could demonstrate nonlinear optical effects such as photon blockade. The system-bath couplings in these systems play an essential role in observing these effects. In this work, we use a dressed-state master equation approach to study the quantum coherence of an optomechanical system. In this approach, the system-bath couplings are decomposed in terms of the eigenbasis of the optomechanical system, where the mechanical state is displaced by finite photon occupation. Compared with the standard master equation often seen in the literature, our master equation includes photon-number-dependent terms that induce dephasing. We calculate cavity dephasing, second-order photon correlation, and two-cavity entanglement using the dressed-state master equation. At high temperature, our master equation predicts faster decay of the quantum coherence than with the standard master equation. The second-order photon correlation derived with our master equation shows less antibunching than that with the standard master equation. This work is supported by awards from DARPA, NSF, JSPS (Japan), MOST (Taiwan) and NTU (Taiwan).
Increasing the accuracy of measurements based on the solution of Pauli's quantum equation
NASA Astrophysics Data System (ADS)
Ermishin, Sergey; Korol, Alexandra
2013-05-01
There is a measurements principle that ensures the increase of accuracy of measurements based on redundant measurements. Main properties of the solution are: a discrete method with a surge of probability within the parent entity and comparison of the graph of the probability distribution for the diffraction grids with the graph of probability density function. Method based on the analog of Pauli equation solution. The method of electronic reference measurements with quantum computing applied to mathematical data processing allows to greatly increase the credibility and accuracy of measurements at low cost, which is confirmed by simulation.
Minami, Takuya; Nakano, Masayoshi
2015-01-22
Electromagnetically induced transparency (EIT), which is known as an efficient control method of optical absorption property, is investigated using the polarizability spectra and population dynamics obtained by solving the quantum Liouville equation. In order to clarify the intermolecular interaction effect on EIT, we examine several molecular aggregate models composed of three-state monomers with the dipole-dipole coupling. On the basis of the present results, we discuss the applicability of EIT in molecular aggregate systems to a new type of optical switch.
Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion
Lamata, L.; Leon, J.; Schaetz, T.; Solano, E.
2007-06-22
We present a method of simulating the Dirac equation in 3+1 dimensions for a free spin-1/2 particle in a single trapped ion. The Dirac bispinor is represented by four ionic internal states, and position and momentum of the Dirac particle are associated with the respective ionic variables. We show also how to simulate the simplified 1+1 case, requiring the manipulation of only two internal levels and one motional degree of freedom. Moreover, we study relevant quantum-relativistic effects, like the Zitterbewegung and Klein's paradox, the transition from massless to massive fermions, and the relativistic and nonrelativistic limits, via the tuning of controllable experimental parameters.
Rate equation analysis of frequency chirp in optically injection-locked quantum cascade lasers
NASA Astrophysics Data System (ADS)
Wang, C.; Grillot, F.; Kovanis, V. I.; Bodyfelt, J. D.; Even, J.
2014-03-01
The frequency chirp characteristics of an optically injection-locked quantum cascade laser are theoretically investigated. The key parameter chirp-to-power ratio (CPR) is analytically derived from a full rate equation model. The CPR value can be efficiently reduced by increasing optical injection strength, especially at modulation frequencies less than 10 GHz. In contrast to interband lasers, both positive and negative frequency detuning increase the CPR. Since the frequency detuning is also predicted to enhance the intensity modulation response, a trade-off is required in the optical injection to simultaneously obtain a large modulation bandwidth and low frequency chirp.
NASA Technical Reports Server (NTRS)
Sharafeddin, Omar A.; Judson, Richard S.; Kouri, Donald J.; Hoffman, David K.
1990-01-01
The novel wave-packet propagation scheme presented is based on the time-dependent form of the Lippman-Schwinger integral equation and does not require extensive matrix inversions, thereby facilitating application to systems in which some degrees of freedom express the potential in a basis expansion. The matrix to be inverted is a function of the kinetic energy operator, and is accordingly diagonal in a Bessel function basis set. Transition amplitudes for various orbital angular momentum quantum numbers are obtainable via either Fourier transform of the amplitude density from the time to the energy domain, or the direct analysis of the scattered wave packet.
Dong, Jianping
2014-03-15
The 2D space-fractional Schrödinger equation in the time-independent and time-dependent cases for the scattering problems in the fractional quantum mechanics is studied. We define the Green's functions for the two cases and give the mathematical expression of them in infinite series form and in terms of some special functions. The asymptotic formulas of the Green's functions are also given, and applied to get the approximate wave functions for the fractional quantum scattering problems. These results contain those in the standard (integer) quantum mechanics as special cases, and can be applied to study the complex quantum systems.
NASA Astrophysics Data System (ADS)
Chandra, Rishabh
Partial differential equation-constrained combinatorial optimization (PDECCO) problems are a mixture of continuous and discrete optimization problems. PDECCO problems have discrete controls, but since the partial differential equations (PDE) are continuous, the optimization space is continuous as well. Such problems have several applications, such as gas/water network optimization, traffic optimization, micro-chip cooling optimization, etc. Currently, no efficient classical algorithm which guarantees a global minimum for PDECCO problems exists. A new mapping has been developed that transforms PDECCO problem, which only have linear PDEs as constraints, into quadratic unconstrained binary optimization (QUBO) problems that can be solved using an adiabatic quantum optimizer (AQO). The mapping is efficient, it scales polynomially with the size of the PDECCO problem, requires only one PDE solve to form the QUBO problem, and if the QUBO problem is solved correctly and efficiently on an AQO, guarantees a global optimal solution for the original PDECCO problem.
The quantum equations of state of plasma under the influence of a weak magnetic field
Hussein, N. A.; Eisa, D. A.; Eldin, M. G.
2012-05-15
The aim of this paper is to calculate the magnetic quantum equations of state of plasma, the calculation is based on the magnetic binary Slater sum in the case of low density. We consider only the thermal equilibrium plasma in the case of n{lambda}{sub ab}{sup 3} Much-Less-Than 1, where {lambda}{sub ab}{sup 2}=( Planck-Constant-Over-Two-Pi {sup 2}/m{sub ab}KT) is the thermal De Broglie wave length between two particles. The formulas contain the contributions of the magnetic field effects. Using these results we compute the magnetization and the magnetic susceptibility. Our equation of state is compared with others.
Classical and quantum equations of motion of an n-dimensional BTZ black hole
NASA Astrophysics Data System (ADS)
Greenwood, Eric
2016-05-01
We investigate the gravitational collapse of a non-rotating n-dimensional BTZ black hole in AdS space in the context of both classical and quantum mechanics. This is done by first deriving the conserved mass of a "spherically" symmetric domain wall, which is taken as the classical Hamiltonian of the black hole. Upon deriving the conserved mass, we also point out that, for a "spherically" symmetric shell, there is an easy and straight-forward way of determining the conserved mass, which is related to the proper time derivative of the interior and exterior times. This method for determining the conserved mass is generic to any situation (i.e. any equation of state), since it only depends on the energy per unit area, σ, of the shell. Classically, we show that the time taken for gravitational collapse follows that of the typical formation of a black hole via gravitational collapse; that is, an asymptotic observer will see that the collapse takes an infinite amount of time to occur, while an infalling observer will see the collapse to both the horizon and the classical singularity occur in a finite amount of time. Quantum mechanically, we take primary interest in the behavior of the collapse near the horizon and near the classical singularity from the point of view of both asymptotic and infalling observers. In the absence of radiation and fluctuations of the metric, quantum effects near the horizon do not change the classical conclusions for an asymptotic observer. The most interesting quantum mechanical effect comes in when investigating near the classical singularity. Here, we find, that the quantum effects in this region are able to remove the classical singularity at the origin, since the wave function is non-singular, and it also displays non-local effects, which depend on the energy density of the domain wall.
Chakraborty, Debdutta; Kar, Susmita; Chattaraj, Pratim Kumar
2015-12-21
The orbital free density functional theory and the single density equation approach are formally equivalent. An orbital free density based quantum dynamical strategy is used to study the quantum-classical correspondence in both weakly and strongly coupled van der Pol and Duffing oscillators in the presence of an external electric field in one dimension. The resulting quantum hydrodynamic equations of motion are solved through an implicit Euler type real space method involving a moving weighted least square technique. The Lagrangian framework used here allows the numerical grid points to follow the wave packet trajectory. The associated classical equations of motion are solved using a sixth order Runge-Kutta method and the Ehrenfest dynamics is followed through the solution of the time dependent Schrodinger equation using a time dependent Fourier Grid Hamiltonian technique. Various diagnostics reveal a close parallelism between classical regular as well as chaotic dynamics and that obtained from the Bohmian mechanics. PMID:26033095
Real-time and imaginary-time quantum hierarchal Fokker-Planck equations
Tanimura, Yoshitaka
2015-04-14
We consider a quantum mechanical system represented in phase space (referred to hereafter as “Wigner space”), coupled to a harmonic oscillator bath. We derive quantum hierarchal Fokker-Planck (QHFP) equations not only in real time but also in imaginary time, which represents an inverse temperature. This is an extension of a previous work, in which we studied a spin-boson system, to a Brownian system. It is shown that the QHFP in real time obtained from a correlated thermal equilibrium state of the total system possesses the same form as those obtained from a factorized initial state. A modified terminator for the hierarchal equations of motion is introduced to treat the non-Markovian case more efficiently. Using the imaginary-time QHFP, numerous thermodynamic quantities, including the free energy, entropy, internal energy, heat capacity, and susceptibility, can be evaluated for any potential. These equations allow us to treat non-Markovian, non-perturbative system-bath interactions at finite temperature. Through numerical integration of the real-time QHFP for a harmonic system, we obtain the equilibrium distributions, the auto-correlation function, and the first- and second-order response functions. These results are compared with analytically exact results for the same quantities. This provides a critical test of the formalism for a non-factorized thermal state and elucidates the roles of fluctuation, dissipation, non-Markovian effects, and system-bath coherence. Employing numerical solutions of the imaginary-time QHFP, we demonstrate the capability of this method to obtain thermodynamic quantities for any potential surface. It is shown that both types of QHFP equations can produce numerical results of any desired accuracy. The FORTRAN source codes that we developed, which allow for the treatment of Wigner space dynamics with any potential form (TanimuranFP15 and ImTanimuranFP15), are provided as the supplementary material.
Real-time and imaginary-time quantum hierarchal Fokker-Planck equations.
Tanimura, Yoshitaka
2015-04-14
We consider a quantum mechanical system represented in phase space (referred to hereafter as "Wigner space"), coupled to a harmonic oscillator bath. We derive quantum hierarchal Fokker-Planck (QHFP) equations not only in real time but also in imaginary time, which represents an inverse temperature. This is an extension of a previous work, in which we studied a spin-boson system, to a Brownian system. It is shown that the QHFP in real time obtained from a correlated thermal equilibrium state of the total system possesses the same form as those obtained from a factorized initial state. A modified terminator for the hierarchal equations of motion is introduced to treat the non-Markovian case more efficiently. Using the imaginary-time QHFP, numerous thermodynamic quantities, including the free energy, entropy, internal energy, heat capacity, and susceptibility, can be evaluated for any potential. These equations allow us to treat non-Markovian, non-perturbative system-bath interactions at finite temperature. Through numerical integration of the real-time QHFP for a harmonic system, we obtain the equilibrium distributions, the auto-correlation function, and the first- and second-order response functions. These results are compared with analytically exact results for the same quantities. This provides a critical test of the formalism for a non-factorized thermal state and elucidates the roles of fluctuation, dissipation, non-Markovian effects, and system-bath coherence. Employing numerical solutions of the imaginary-time QHFP, we demonstrate the capability of this method to obtain thermodynamic quantities for any potential surface. It is shown that both types of QHFP equations can produce numerical results of any desired accuracy. The FORTRAN source codes that we developed, which allow for the treatment of Wigner space dynamics with any potential form (TanimuranFP15 and ImTanimuranFP15), are provided as the supplementary material. PMID:25877565
Real-time and imaginary-time quantum hierarchal Fokker-Planck equations
NASA Astrophysics Data System (ADS)
Tanimura, Yoshitaka
2015-04-01
We consider a quantum mechanical system represented in phase space (referred to hereafter as "Wigner space"), coupled to a harmonic oscillator bath. We derive quantum hierarchal Fokker-Planck (QHFP) equations not only in real time but also in imaginary time, which represents an inverse temperature. This is an extension of a previous work, in which we studied a spin-boson system, to a Brownian system. It is shown that the QHFP in real time obtained from a correlated thermal equilibrium state of the total system possesses the same form as those obtained from a factorized initial state. A modified terminator for the hierarchal equations of motion is introduced to treat the non-Markovian case more efficiently. Using the imaginary-time QHFP, numerous thermodynamic quantities, including the free energy, entropy, internal energy, heat capacity, and susceptibility, can be evaluated for any potential. These equations allow us to treat non-Markovian, non-perturbative system-bath interactions at finite temperature. Through numerical integration of the real-time QHFP for a harmonic system, we obtain the equilibrium distributions, the auto-correlation function, and the first- and second-order response functions. These results are compared with analytically exact results for the same quantities. This provides a critical test of the formalism for a non-factorized thermal state and elucidates the roles of fluctuation, dissipation, non-Markovian effects, and system-bath coherence. Employing numerical solutions of the imaginary-time QHFP, we demonstrate the capability of this method to obtain thermodynamic quantities for any potential surface. It is shown that both types of QHFP equations can produce numerical results of any desired accuracy. The FORTRAN source codes that we developed, which allow for the treatment of Wigner space dynamics with any potential form (TanimuranFP15 and ImTanimuranFP15), are provided as the supplementary material.
... levels. But watch out! The wrong choice could end the game. Survive all 7 levels plus a turn in the hot seat and become a Disaster Master! Print ... 6 - Tsunami/Earthquake Level 7: Thunderstorm/Lightning ...
NASA Astrophysics Data System (ADS)
Sato, Masatoshi; Tobe, Daijiro; Kohmoto, Mahito
2008-12-01
We consider a tight-binding model with the nearest-neighbor hopping integrals on the honeycomb lattice in a magnetic field. Assuming one of the three hopping integrals, which we denote by ta , can take a different value from the two others, we study quantum phase structures controlled by the anisotropy of the honeycomb lattice. For weak and strong ta regions, the Hall conductances are calculated algebraically by using the Diophantine equation. Except for a few specific gaps, we completely determine the Hall conductances in these two regions including those for subband gaps. In a weak magnetic field, it is found that the weak ta region shows the unconventional quantization of the Hall conductance, σxy=-(e2/h)(2n+1) (n=0,±1,±2,…) , near the half filling, while the strong ta region shows only the conventional one, σxy=-(e2/h)n (n=0,±1,±2,…) . From the topological nature of the Hall conductance, the existence of gap closing points and quantum phase transitions in the intermediate ta region is concluded. We also study numerically the quantum phase structure in detail and find that even when ta=1 , namely, in graphene case, the system is in the weak ta phase except when the Fermi energy is located near the Van Hove singularity or the lower and upper edges of the spectrum.
Investigating non-Markovian dynamics of quantum open systems
NASA Astrophysics Data System (ADS)
Chen, Yusui
Quantum open system coupled to a non-Markovian environment has recently attracted widespread interest for its important applications in quantum information processing and quantum dissipative systems. New phenomena induced by the non-Markovian environment have been discovered in variety of research areas ranging from quantum optics, quantum decoherence to condensed matter physics. However, the study of the non-Markovian quantum open system is known a difficult problem due to its technical complexity in deriving the fundamental equation of motion and elusive conceptual issues involving non-equilibrium dynamics for a strong coupled environment. The main purpose of this thesis is to introduce several new techniques of solving the quantum open systems including a systematic approach to dealing with non-Markovian master equations from a generic quantum-state diffusion (QSD) equation. In the first part of this thesis, we briefly introduce the non-Markovian quantum-state diffusion approach, and illustrate some pronounced non-Markovian quantum effects through numerical investigation on a cavity-QED model. Then we extend the non-Markovian QSD theory to an interesting model where the environment has a hierarchical structure, and find out the exact non-Markovian QSD equation of this model system. We observe the generation of quantum entanglement due to the interplay between the non-Markovian environment and the cavity. In the second part, we show an innovative method to obtain the exact non-Markovian master equations for a set of generic quantum open systems based on the corresponding non-Markovian QSD equations. Multiple-qubit systems and multilevel systems are discussed in details as two typical examples. Particularly, we derive the exact master equation for a model consisting of a three-level atom coupled to an optical cavity and controlled by an external laser field. Additionally, we discuss in more general context the mathematical similarity between the multiple
Chiral transport equation from the quantum Dirac Hamiltonian and the on-shell effective field theory
NASA Astrophysics Data System (ADS)
Manuel, Cristina; Torres-Rincon, Juan M.
2014-10-01
We derive the relativistic chiral transport equation for massless fermions and antifermions by performing a semiclassical Foldy-Wouthuysen diagonalization of the quantum Dirac Hamiltonian. The Berry connection naturally emerges in the diagonalization process to modify the classical equations of motion of a fermion in an electromagnetic field. We also see that the fermion and antifermion dispersion relations are corrected at first order in the Planck constant by the Berry curvature, as previously derived by Son and Yamamoto for the particular case of vanishing temperature. Our approach does not require knowledge of the state of the system, and thus it can also be applied at high temperature. We provide support for our result by an alternative computation using an effective field theory for fermions and antifermions: the on-shell effective field theory. In this formalism, the off-shell fermionic modes are integrated out to generate an effective Lagrangian for the quasi-on-shell fermions/antifermions. The dispersion relation at leading order exactly matches the result from the semiclassical diagonalization. From the transport equation, we explicitly show how the axial and gauge anomalies are not modified at finite temperature and density despite the incorporation of the new dispersion relation into the distribution function.
The master T-operator for the Gaudin model and the KP hierarchy
NASA Astrophysics Data System (ADS)
Alexandrov, Alexander; Leurent, Sebastien; Tsuboi, Zengo; Zabrodin, Anton
2014-06-01
Following the approach of [1], we construct the master T-operator for the quantum Gaudin model with twisted boundary conditions and show that it satisfies the bilinear identity and Hirota equations for the classical KP hierarchy. We also characterize the class of solutions to the KP hierarchy that correspond to eigenvalues of the master T-operator and study dynamics of their zeros as functions of the spectral parameter. This implies a remarkable connection between the quantum Gaudin model and the classical Calogero-Moser system of particles. The quantum Gaudin model, The classical Kadomtsev-Petviashvili (KP) hierarchy, The classical Calogero-Moser (CM) system of particles. The link (i)-(ii) is a limiting case of the correspondence between quantum spin chains with the Yangian Y(gl(N))-invariant rational R-matrices and the classical modified KP hierarchy based on the construction of the master T-operator [1,2]. The link (ii)-(iii) is a well-known story about dynamics of poles of rational solutions to soliton equations started by Airault, McKean and Moser [3] for the KdV equation, developed by Krichever [4] for the KP equation and extended to the whole KP hierarchy by Shiota [5]. The composition of (i)-(ii) and (ii)-(iii) implies the connection between the quantum Gaudin model and the classical CM model which is a limiting case of the connection between quantum spin chains and classical Ruijsenaars systems found in [1]. The link (i)-(iii) was also earlier established in [6] from a different reasoning.The master T-operator was introduced in [1]. We construct commuting integrals of motion for the gl(N) Gaudin model, with twisted boundary conditions and vector representations at the marked points in the quantum space, corresponding to arbitrary representations in the auxiliary space. They are presented in an explicit form using the matrix derivative operation. We also find functional relations satisfied by them. The master T-operator for the gl(N) Gaudin model is the
NASA Astrophysics Data System (ADS)
Wieser, Robert
2015-03-01
The classical Landau-Lifshitz equation has been derived from quantum mechanics. Starting point is the assumption of a non-Hermitian Hamilton operator to take the energy dissipation into account. The corresponding quantum mechanical spin dynamics along with the time dependent Schrödinger, Liouville and Heisenberg equation has been described and the similarities and differences between classical and quantum mechanical spin dynamics have been discussed. Furthermore, a time dependent Schrödinger equation corresponding to the classical Landau-Lifshitz-Gilbert equation and two ways to include temperature into the quantum mechanical spin dynamics have been proposed.
Matuttis, Hans-Georg; Wang, Xiaoxing
2015-03-10
Decomposition methods of the Suzuki-Trotter type of various orders have been derived in different fields. Applying them both to classical ordinary differential equations (ODEs) and quantum systems allows to judge their effectiveness and gives new insights for many body quantum mechanics where reference data are scarce. Further, based on data for 6 × 6 system we conclude that sampling with sign (minus-sign problem) is probably detrimental to the accuracy of fermionic simulations with determinant algorithms.
Garcia-Ravelo, J.; Trujillo, A. L.; Schulze-Halberg, A.
2012-10-15
We obtain explicit formulas for perturbative corrections of the infinite quantum well model. The formulas we obtain are based on a class of matrix elements that we construct by means of two-parameter ladder operators associated with the infinite quantum well system. Our approach can be used to construct solutions to Schroedinger-type equations that involve generalized harmonic perturbations of their potentials, such as cosine powers, Fourier series, and more general functions. As a particular case, we obtain characteristic values for odd periodic solutions of the Mathieu equation.
Decoherence and dissipation for a quantum system coupled to a local environment
NASA Technical Reports Server (NTRS)
Gallis, Michael R.
1994-01-01
Decoherence and dissipation in quantum systems has been studied extensively in the context of Quantum Brownian Motion. Effective decoherence in coarse grained quantum systems has been a central issue in recent efforts by Zurek and by Hartle and Gell-Mann to address the Quantum Measurement Problem. Although these models can yield very general classical phenomenology, they are incapable of reproducing relevant characteristics expected of a local environment on a quantum system, such as the characteristic dependence of decoherence on environment spatial correlations. I discuss the characteristics of Quantum Brownian Motion in a local environment by examining aspects of first principle calculations and by the construction of phenomenological models. Effective quantum Langevin equations and master equations are presented in a variety of representations. Comparisons are made with standard results such as the Caldeira-Leggett master equation.
NASA Astrophysics Data System (ADS)
Rovelli, Carlo
Hamiltonian mechanics of field theory can be formulated in a generally covariant and background independent manner over a finite dimensional extended configuration space. I study the physical symplectic structure of the theory in this framework. This structure can be defined over a space of three-dimensional surfaces without boundary, in the extended configuration space. These surfaces provide a preferred over-coordinatization of phase space. I consider the covariant form of the Hamilton-Jacobi equation on , and a canonical function S on which is a preferred solution of the Hamilton-Jacobi equation. The application of this formalism to general relativity is fully covariant and yields directly the Ashtekar-Wheeler-DeWitt equation, the basic equation of canonical quantum gravity. Finally, I apply this formalism to discuss the partial observables of a covariant field theory and the role of the spin networks -basic objects in quantum gravity- in the classical theory.
NASA Astrophysics Data System (ADS)
Rovelli, Carlo
Hamiltonian mechanics of field theory can be formulated in a generally covariant and background independent manner over a finite dimensional extended configuration space. I study the physical symplectic structure of the theory in this framework. This structure can be defined over a space G of three-dimensional surfaces without boundary, in the extended configuration space. These surfaces provide a preferred over-coordinatization of phase space. I consider the covariant form of the Hamilton-Jacobi equation on G, and a canonical function S on G which is a preferred solution of the Hamilton-Jacobi equation. The application of this formalism to general relativity is fully covariant and yields directly the Ashtekar-Wheeler-DeWitt equation, the basic equation of canonical quantum gravity. Finally, I apply this formalism to discuss the partial observables of a covariant field theory and the role of the spin networks -basic objects in quantum gravity- in the classical theory.
NASA Astrophysics Data System (ADS)
Rhyner, Reto; Luisier, Mathieu
2013-12-01
We propose to check and validate the approximations made in dissipative quantum transport (QT) simulations solved in the Non-equilibrium Green's Function formalism by comparing them with the exact solution of the linearized Boltzmann Transport Equation (LB) in the stationary regime. For that purpose, we calculate the phonon-limited electron and hole mobility in bulk Si and ultra-scaled Si nanowires for different crystal orientations ⟨100⟩, ⟨110⟩, and ⟨111⟩. In both QT and LB simulations, we use the same sp3d5s* tight-binding model to describe the electron/hole properties and the same valence-force-field approach to account for the phonon properties. It is found that the QT simplifications work well for electrons, but are less accurate for holes, where a renormalization of the phonon scattering strength is proved useful to improve the results.
Equation of state for a trapped quantum gas: remnant of zero-point energy effects
NASA Astrophysics Data System (ADS)
Castilho, P. C. M.; Poveda-Cuevas, F. J.; Seman, J. A.; Shiozaki, R. F.; Roati, G.; Muniz, S. R.; Magalhães, D. V.; Bagnato, V. S.
2016-02-01
The study of the thermodynamic properties of trapped gases has attracted great attention during the last few years and can be used as a tool to characterize such clouds in the presence of other phenomena. Here, we obtain an equation of state for a harmonically trapped Bose-Einstein condensate taking the limit of T\\to 0 by means of global themodynamic variables. These variables allow us to explore limits in which the standard thermodynamics are not defined. Our results are taken in the high density limit, and the extrapolation for N\\to 1 is done later. Even in this situation, we qualitatively observe the well known existence of a zero-point energy for harmonic potentials in which the determination of conjugated variables is limited by the quantum nature of the system.
Perturbative approach to Markovian open quantum systems
Li, Andy C. Y.; Petruccione, F.; Koch, Jens
2014-01-01
The exact treatment of Markovian open quantum systems, when based on numerical diagonalization of the Liouville super-operator or averaging over quantum trajectories, is severely limited by Hilbert space size. Perturbation theory, standard in the investigation of closed quantum systems, has remained much less developed for open quantum systems where a direct application to the Lindblad master equation is desirable. We present such a perturbative treatment which will be useful for an analytical understanding of open quantum systems and for numerical calculation of system observables which would otherwise be impractical. PMID:24811607
Comment on "Fractional quantum mechanics" and "Fractional Schrödinger equation".
Wei, Yuchuan
2016-06-01
In this Comment we point out some shortcomings in two papers [N. Laskin, Phys. Rev. E 62, 3135 (2000)10.1103/PhysRevE.62.3135; N. Laskin, Phys. Rev. E 66, 056108 (2002)10.1103/PhysRevE.66.056108]. We prove that the fractional uncertainty relation does not hold generally. The probability continuity equation in fractional quantum mechanics has a missing source term, which leads to particle teleportation, i.e., a particle can teleport from a place to another. Since the relativistic kinetic energy can be viewed as an approximate realization of the fractional kinetic energy, the particle teleportation should be an observable relativistic effect in quantum mechanics. With the help of this concept, superconductivity could be viewed as the teleportation of electrons from one side of a superconductor to another and superfluidity could be viewed as the teleportation of helium atoms from one end of a capillary tube to the other. We also point out how to teleport a particle to an arbitrary destination. PMID:27415397
Comment on "Fractional quantum mechanics" and "Fractional Schrödinger equation"
NASA Astrophysics Data System (ADS)
Wei, Yuchuan
2016-06-01
In this Comment we point out some shortcomings in two papers [N. Laskin, Phys. Rev. E 62, 3135 (2000), 10.1103/PhysRevE.62.3135; N. Laskin, Phys. Rev. E 66, 056108 (2002), 10.1103/PhysRevE.66.056108]. We prove that the fractional uncertainty relation does not hold generally. The probability continuity equation in fractional quantum mechanics has a missing source term, which leads to particle teleportation, i.e., a particle can teleport from a place to another. Since the relativistic kinetic energy can be viewed as an approximate realization of the fractional kinetic energy, the particle teleportation should be an observable relativistic effect in quantum mechanics. With the help of this concept, superconductivity could be viewed as the teleportation of electrons from one side of a superconductor to another and superfluidity could be viewed as the teleportation of helium atoms from one end of a capillary tube to the other. We also point out how to teleport a particle to an arbitrary destination.
ERIC Educational Resources Information Center
Miranda, Maria Eugenia
2011-01-01
Dr. Carole Berotte Joseph, the new president of Bronx Community College, or BCC, has been training to lead an institution of higher education since grade school, taking on the role of master teacher since she played on her parents' stoop with the neighborhood children in Brooklyn. Growing up, she didn't play with dolls much. She played with real…
Koller, Andrew; Olshanii, Maxim
2011-12-15
We present a case demonstrating the connection between supersymmetric quantum mechanics (SUSYQM), reflectionless scattering, and soliton solutions of integrable partial differential equations. We show that the members of a class of reflectionless Hamiltonians, namely, Akulin's Hamiltonians, are connected via supersymmetric chains to a potential-free Hamiltonian, explaining their reflectionless nature. While the reflectionless property in question has been mentioned in the literature for over two decades, the enabling algebraic mechanism was previously unknown. Our results indicate that the multisoliton solutions of the sine-Gordon and nonlinear Schroedinger equations can be systematically generated via the supersymmetric chains connecting Akulin's Hamiltonians. Our findings also explain a well-known but little-understood effect in laser physics: when a two-level atom, initially in the ground state, is subjected to a laser pulse of the form V(t)=(n({h_bar}/2{pi})/{tau})/cosh(t/{tau}), with n being an integer and {tau} being the pulse duration, it remains in the ground state after the pulse has been applied, for any choice of the laser detuning.
Quantum Operator Approach Applied to the Position-Dependent Mass Schrödinger Equation
NASA Astrophysics Data System (ADS)
Ovando, G.; Peña, J. J.; Morales, J.
2014-03-01
In this work, the quantum operator approach is applied to both, the position-dependent mass Schrödinger equation (PDMSE) and the Schrodinger equation with constant mass (CMSE). This fact enable us to find the factorization operators that relates both Hamiltonians by means of a kinetic energy operator that comes from the proposal of Morrow and Brownstein. With this approach is possible to find the exactly-solvable PDMSE, for any value of the parameters α and γ in the von Roos's Hamiltonian. For that, our proposal can be considered as a unified treatment of the PDMSE because it contains as particular cases, the kinetic energy operators of various authors such as BenDaniel-Duke, Gora-Williams, Zhu-Kroemer and Li-Kuhn among others. To show the usefulness of our result, we show the solvable PDMSE that comes from the harmonic oscillator potential model for the CMSE. The proposal is general and can easily be extended to other potential models and mass distributions which will be given in the extended paper.
Solution of the quantum fluid dynamical equations with radial basis function interpolation
Hu, Xu-Guang; Ho, Tak-San; Rabitz, Herschel; Askar, Attila
2000-05-01
The paper proposes a numerical technique within the Lagrangian description for propagating the quantum fluid dynamical (QFD) equations in terms of the Madelung field variables R and S, which are connected to the wave function via the transformation {psi}=exp{l_brace}(R+iS)/({Dirac_h}/2{pi})(right brace). The technique rests on the QFD equations depending only on the form, not the magnitude, of the probability density {rho}=|{psi}|{sup 2} and on the structure of R=({Dirac_h}/2{pi})/2 ln {rho} generally being simpler and smoother than {rho}. The spatially smooth functions R and S are especially suitable for multivariate radial basis function interpolation to enable the implementation of a robust numerical scheme. Examples of two-dimensional model systems show that the method rivals, in both efficiency and accuracy, the split-operator and Chebychev expansion methods. The results on a three-dimensional model system indicates that the present method is superior to the existing ones, especially, for its low storage requirement and its uniform accuracy. The advantage of the new algorithm is expected to increase for higher dimensional systems to provide a practical computational tool. (c) 2000 The American Physical Society.
NASA Astrophysics Data System (ADS)
Acevedo, Ramiro, Jr.
Wavelet-based algorithms are developed for solution of quantum and electromagnetic differential equations. Wavelets offer orthonormal localized bases with built-in multiscale properties for the representation of functions, differential operators, and multiplicative operators. The work described here is part of a series of tools for use in the ultimate goal of general, efficient, accurate and automated wavelet-based algorithms for solution of differential equations. The most recent work, and the focus here, is the elimination of operator matrices in wavelet bases. For molecular quantum eigenvalue and dynamics calculations in multiple dimensions, it is the coupled potential energy matrices that generally dominate storage requirements. A Coefficient Product Approximation (CPA) for the potential operator and wave function wavelet expansions dispenses with the matrix, reducing storage and coding complexity. New developments are required, however. It is determined that the CPA is most accurate for specific choices of wavelet families, and these are given here. They have relatively low approximation order (number of vanishing wavelet function moments), which would ordinarily be thought to compromise both wavelet reconstruction and differentiation accuracy. Higher-order convolutional coefficient filters are determined that overcome both apparent problems. The result is a practical wavelet method where the effect of applying the Hamiltonian matrix to a coefficient vector can be calculated accurately without constructing the matrix. The long-familiar Lanczos propagation algorithm, wherein one constructs and diagonalizes a symmetric tridiagonal matrix, uses both eigenvalues and eigenvectors. We show here that time-reversal-invariance for Hermitian Hamiltonians allows a new algorithm that avoids the usual need to keep a number Lanczos vectors around. The resulting Conjugate Symmetric Lanczos (CSL) method, which will apply for wavelets or other choices of basis or grid
NASA Astrophysics Data System (ADS)
Plane, J. M. C.; Whalley, C. L.; Frances-Soriano, L.; Goddard, A.; Harvey, J. N.; Glowacki, D. R.; Viggiano, A. A.
2012-07-01
utilized density functional theory along with multireference and explicitly correlated CCSD(T)-F12 electronic structure calculations to examine the lowest lying singlet and triplet surfaces. In addition to mapping stationary points, we used a genetic algorithm to locate minimum energy crossing points between the two surfaces. Simulations of the Ca + O2(a) kinetics were then carried out using a combination of both standard and non-adiabatic Rice-Ramsperger-Kassel-Marcus (RRKM) theory implemented within a weak collision, multiwell master equation model. In terms of atmospheric significance, only in the case of Ca does reaction with O2(a) compete with O3 during the daytime between 85 and 110 km.
NASA Astrophysics Data System (ADS)
Barchielli, Alberto
2016-06-01
The quantum stochastic Schrödinger equation or Hudson-Parthasarathy (HP) equation is a powerful tool to construct unitary dilations of quantum dynamical semigroups and to develop the theory of measurements in continuous time via the construction of output fields. An important feature of such an equation is that it allows to treat not only absorption and emission of quanta, but also scattering processes, which however had very few applications in physical modelling. Moreover, recent developments have shown that also some non-Markovian dynamics can be generated by suitable choices of the state of the quantum noises involved in the HP-equation. This paper is devoted to an application involving these two features, non-Markovianity and scattering process. We consider a micro-mirror mounted on a vibrating structure and reflecting a laser beam, a process giving rise to a radiation-pressure force on the mirror. We show that this process needs the scattering part of the HP-equation to be described. On the other side, non-Markovianity is introduced by the dissipation due to the interaction with some thermal environment which we represent by a phonon field, with a nearly arbitrary excitation spectrum, and by the introduction of phase noise in the laser beam. Finally, we study the full power spectrum of the reflected light and we show how the laser beam can be used as a temperature probe.
Complex master slave interferometry.
Rivet, Sylvain; Maria, Michael; Bradu, Adrian; Feuchter, Thomas; Leick, Lasse; Podoleanu, Adrian
2016-02-01
A general theoretical model is developed to improve the novel Spectral Domain Interferometry method denoted as Master/Slave (MS) Interferometry. In this model, two functions, g and h are introduced to describe the modulation chirp of the channeled spectrum signal due to nonlinearities in the decoding process from wavenumber to time and due to dispersion in the interferometer. The utilization of these two functions brings two major improvements to previous implementations of the MS method. A first improvement consists in reducing the number of channeled spectra necessary to be collected at Master stage. In previous MSI implementation, the number of channeled spectra at the Master stage equated the number of depths where information was selected from at the Slave stage. The paper demonstrates that two experimental channeled spectra only acquired at Master stage suffice to produce A-scans from any number of resolved depths at the Slave stage. A second improvement is the utilization of complex signal processing. Previous MSI implementations discarded the phase. Complex processing of the electrical signal determined by the channeled spectrum allows phase processing that opens several novel avenues. A first consequence of such signal processing is reduction in the random component of the phase without affecting the axial resolution. In previous MSI implementations, phase instabilities were reduced by an average over the wavenumber that led to reduction in the axial resolution. PMID:26906857
Ayvaz, Muzaffer; Demiralp, Metin
2012-12-10
This study focuses on the construction of the optimal control equations for one dimensional quantum harmonic oscillator under the influence of external dipol effects and the solution of these equations by using Fluctuationlessness Theorem and a recently developed scheme called Characteristic Evolutions Method. The dipole function of the system has been taken as odd cubic spatial polynomial. Optimal control equations of the system under consideration are constructed by using expectation values of the position and the momentum operators instead of the wave and costate evolutions. It is shown that, the resulting equations are systems of ordinary differential equations and there are infinitely many ODEs. The solution strategy is based on the approximation of the expectation values for the operator products in the sense of Fluctuationlessness Theorem.
Dynamics of open bosonic quantum systems in coherent state representation
Dalvit, D. A. R.; Berman, G. P.; Vishik, M.
2006-01-15
We consider the problem of decoherence and relaxation of open bosonic quantum systems from a perspective alternative to the standard master equation or quantum trajectories approaches. Our method is based on the dynamics of expectation values of observables evaluated in a coherent state representation. We examine a model of a quantum nonlinear oscillator with a density-density interaction with a collection of environmental oscillators at finite temperature. We derive the exact solution for dynamics of observables and demonstrate a consistent perturbation approach.
Non-Markovian dynamics without using a quantum trajectory
Wu Chengjun; Li Yang; Zhu Mingyi; Guo Hong
2011-05-15
Open quantum systems interacting with structured environments is important and manifests non-Markovian behavior, which was conventionally studied using a quantum trajectory stochastic method. In this paper, by dividing the effects of the environment into two parts, we propose a deterministic method without using a quantum trajectory. This method is more efficient and accurate than the stochastic method in most Markovian and non-Markovian cases. We also extend this method to the generalized Lindblad master equation.
NASA Astrophysics Data System (ADS)
Vélez, Mario; Ospina, Juan
2007-04-01
Using the Kauffman-Lomonaco method, some two-qutrits universal quantum gates are derived from the nine-dimensional unitary solutions of the Yang-Baxter equations associated with algebraic structures like the partial transpose operator and the dihedral group, which admit three dimensional representations. The Yang-Baxterization method given by Zhang-Kauffman-Ge is continuously used to obtain two-qutrits quantum gates and certain Hamiltonians for the evolution of the quantum gates are obtained, being such Hamiltonians interpreted as physical Hamiltonians of chain of particles of spin 1. Finally, the generalization for systems of two qudits is presented in the case of Yang-Baxterization of representations of braided monoidal algebra like the BH algebra and the bicolored Birman-Wenzl-Muraki algebra. For these algebras the corresponding two-qudits quantum gates are constructed jointly with the associated Hamiltonians interpreted like physical chains of particles with spin d. It is conjectured that the derived two-qdits quantum gates and the Hamiltonians may be implemented over bi-dimensional lattice systems like anyons systems or more generally over any physical systems ruled by the Yang-Baxter equations.
NASA Astrophysics Data System (ADS)
Li, Zhi-Guo; Cheng, Yan; Chen, Qi-Feng; Chen, Xiang-Rong
2016-05-01
The equation of state, self-diffusion, and viscosity coefficients of helium have been investigated by quantum molecular dynamics (QMD) simulations in the warm dense matter regime. Our simulations are validated through the comparison with the reliable experimental data. The calculated principal and reshock Hugoniots of liquid helium are in good agreement with the gas-gun data. On this basis, we revisit the issue for helium, i.e., the possibility of the instabilities predicted by chemical models at around 2000 GPa and 10 g/cm3 along the pressure isotherms of 6309, 15 849, and 31 623 K. Our calculations show no indications of instability in this pressure-temperature region, which reconfirm the predictions of previous QMD simulations. The self-diffusion and viscosity coefficients of warm dense helium have been systematically investigated by the QMD simulations. We carefully test the finite-size effects and convergences of statistics, and obtain numerically converged self-diffusion and viscosity coefficients by using the Kubo-Green formulas. The present results have been used to evaluate the existing one component plasma models. Finally, the validation of the Stokes-Einstein relationship for helium in the warm dense regime is discussed.
NASA Astrophysics Data System (ADS)
Reinisch, Gilbert C.; Gazeau, Maxime
2016-07-01
In this paper we consider a basic two-level nonlinear quantum model consisting in a two-particle interacting bound-state system. It is described by means of two different approaches: i) the mean-field stationary nonlinear Schrödinger-Poisson equation with classical Coulomb interaction and harmonic potential; ii) the linear quantum electrodynamics Hamiltonian of a quantized field coupled to two fixed charges. Computing numerically the ground state and the first excited state about the maximum eigenstate overlap (which is not zero because of eigenstate non-orthogonality), we numerically demonstrate that these two descriptions coincide at first order. As a consequence, a specific definition of the fine-structure constant α is provided within 99.95% accuracy by the present first-order non-relativistic and nonlinear quantum description. This result also means that the internal Coulomb interaction commutes with external particle confinement for the calculation of the ground state. Consequently peculiar nonlinear quantum properties become observable (an experiment with GaAs quantum-dot helium is suggested).
NASA Astrophysics Data System (ADS)
Zhang, Yong; Zhang, Kun; Pang, Jinglong
2016-01-01
This paper focuses on the study of topological features in teleportation-based quantum computation and aims at presenting a detailed review on teleportation-based quantum computation (Gottesman and Chuang in Nature 402: 390, 1999). In the extended Temperley-Lieb diagrammatical approach, we clearly show that such topological features bring about the fault-tolerant construction of both universal quantum gates and four-partite entangled states more intuitive and simpler. Furthermore, we describe the Yang-Baxter gate by its extended Temperley-Lieb configuration and then study teleportation-based quantum circuit models using the Yang-Baxter gate. Moreover, we discuss the relationship between the extended Temperley-Lieb diagrammatical approach and the Yang-Baxter gate approach. With these research results, we propose a worthwhile subject, the extended Temperley-Lieb diagrammatical approach, for physicists in quantum information and quantum computation.
Quantum lattice-gas model for the many-particle Schr{umlt o}dinger equation in d dimensions
Boghosian, B.M.; Taylor, W. IV
1998-01-01
We consider a general class of discrete unitary dynamical models on the lattice. We show that generically such models give rise to a wave function satisfying a Schr{umlt o}dinger equation in the continuum limit, in any number of dimensions. There is a simple mathematical relationship between the mass of the Schr{umlt o}dinger particle and the eigenvalues of a unitary matrix describing the local evolution of the model. Second quantized versions of these unitary models can be defined, describing in the continuum limit the evolution of a nonrelativistic quantum many-body theory. An arbitrary potential is easily incorporated into these systems. The models we describe fall in the class of quantum lattice-gas automata and can be implemented on a quantum computer with a speedup exponential in the number of particles in the system. This gives an efficient algorithm for simulating general nonrelativistic interacting quantum many-body systems on a quantum computer. {copyright} {ital 1998} {ital The American Physical Society}
NASA Astrophysics Data System (ADS)
Srisangyingcharoen, P.; Klinkla, R.; Boonchui, S.
2015-11-01
The quantum history approach is applied to investigate the first-photon emission of a quantum dot induced by propagating surface plasmons. The dynamics of the emission is described through the partitioning dynamics of a quantum system. The extended probability distribution which correspond to the photon emission rate is directly calculated. In the case that the Markov's approximation is satisfied, the well known double decay character of the first-photon emission is obtained accompanying with the analytic expression of decay amplitudes which has never been derived before. This is a merit of our approach which allows us to analytically investigate this interacting quantum system and goes beyond the master equation approach.
Edwards, D M; Wessely, O
2009-04-01
An extended Landau-Lifshitz-Gilbert (LLG) equation is introduced to describe the dynamics of inhomogeneous magnetization in a current-carrying wire. The coefficients of all the terms in this equation are calculated quantum-mechanically for a simple model which includes impurity scattering. This is done by comparing the energies and lifetimes of a spin wave calculated from the LLG equation and from the explicit model. Two terms are of particular importance since they describe non-adiabatic spin-transfer torque and damping processes which do not rely on spin-orbit coupling. It is shown that these terms may have a significant influence on the velocity of a current-driven domain wall and they become dominant in the case of a narrow wall. PMID:21825349
NASA Astrophysics Data System (ADS)
Edwards, D. M.; Wessely, O.
2009-04-01
An extended Landau-Lifshitz-Gilbert (LLG) equation is introduced to describe the dynamics of inhomogeneous magnetization in a current-carrying wire. The coefficients of all the terms in this equation are calculated quantum-mechanically for a simple model which includes impurity scattering. This is done by comparing the energies and lifetimes of a spin wave calculated from the LLG equation and from the explicit model. Two terms are of particular importance since they describe non-adiabatic spin-transfer torque and damping processes which do not rely on spin-orbit coupling. It is shown that these terms may have a significant influence on the velocity of a current-driven domain wall and they become dominant in the case of a narrow wall.
NASA Astrophysics Data System (ADS)
Bommier, Véronique
2016-06-01
Context. We discuss the case of lines formed by scattering, which comprises both coherent and incoherent scattering. Both processes contribute to form the line profiles in the so-called second solar spectrum, which is the spectrum of the linear polarization of such lines observed close to the solar limb. However, most of the lines cannot be simply modeled with a two-level or two-term atom model, and we present a generalized formalism for this purpose. Aims: The aim is to obtain a formalism that is able to describe scattering in line centers (resonant scattering or incoherent scattering) and in far wings (Rayleigh/Raman scattering or coherent scattering) for a multilevel and multiline atom. Methods: The method is designed to overcome the Markov approximation, which is often performed in the atom-photon interaction description. The method was already presented in the two first papers of this series, but the final equations of those papers were for a two-level atom. Results: We present here the final equations generalized for the multilevel and multiline atom. We describe the main steps of the theoretical development, and, in particular, how we performed the series development to overcome the Markov approximation. Conclusions: The statistical equilibrium equations for the atomic density matrix and the radiative transfer equation coefficients are obtained with line profiles. The Doppler redistribution is also taken into account because we show that the statistical equilibrium equations must be solved for each atomic velocity class.
Multi-band Bloch equations and gain spectra of highly excited II-VI semiconductor quantum wells
Girndt, A.; Jahnke, F.; Knorr, A.; Koch, S.W.; Chow, W.W.
1997-04-21
Quasi-equilibrium excitation dependent optical probe spectra of II-VI semiconductor quantum wells at room temperature are investigated within the framework of multi-band semiconductor Bloch equations. The calculations include correlation effects beyond the Hartree-Fock level which describe dephasing, interband Coulomb correlations and band-gap renormalization in second Born approximation. In addition to the carrier-Coulomb interaction, the influence of carrier-phonon scattering and inhomogeneous broadening is considered. The explicit calculation of single particle properties like band structure and dipole matrix elements using k {center_dot} p theory makes it possible to investigate various II-VI material combinations. Numerical results are presented for CdZnSe/ZnSe and CdZnSe/MnZnSSe semiconductor quantum-well systems.
Cooper, J. D.; Valavanis, A.; Ikonic, Z.; Harrison, P.; Cunningham, J. E.
2010-12-01
The nonparabolic Schroedinger equation for electrons in quantum cascade lasers (QCLs) is a cubic eigenvalue problem (EVP) which cannot be solved directly. While a method for linearizing this cubic EVP has been proposed in principle for quantum dots [Hwang et al., Math. Comput. Modell., 40, 519 (2004)] it was deemed too computationally expensive because of the three-dimensional geometry under consideration. We adapt this linearization approach to the one-dimensional geometry of QCLs, and arrive at a direct and exact solution to the cubic EVP. The method is then compared with the well established shooting method, and it is shown to be more accurate and reliable for calculating the bandstructure of mid-infrared QCLs.
The Master T-Operator for Inhomogeneous XXX Spin Chain and mKP Hierarchy
NASA Astrophysics Data System (ADS)
Zabrodin, Anton
2014-01-01
Following the approach of [Alexandrov A., Kazakov V., Leurent S., Tsuboi Z., Zabrodin A., J. High Energy Phys. 2013 (2013), no. 9, 064, 65 pages, arXiv:1112.3310], we show how to construct the master T-operator for the quantum inhomogeneous GL(N) XXX spin chain with twisted boundary conditions. It satisfies the bilinear identity and Hirota equations for the classical mKP hierarchy. We also characterize the class of solutions to the mKP hierarchy that correspond to eigenvalues of the master T-operator and study dynamics of their zeros as functions of the spectral parameter. This implies a remarkable connection between the quantum spin chain and the classical Ruijsenaars-Schneider system of particles.
Quantum theory of multiwave mixing - Squeezed-vacuum model
NASA Astrophysics Data System (ADS)
An, Sunghyuck; Sargent, Murray, III
1989-12-01
The present paper combines a Langevin quantum-regression method with a denisty-operator approach to derive the master equation for the quantum theory of multiwave mixing in a very efficient way. The approach is quite general and is particularly valuable for analyzing complicated media such as semiconductors. It is used in the present paper to derive the quantum multiwave-mixing equations in a squeezed vacuum. Improved formulas are found for resonance fluorescence in a squeezed vacuum as well as the squeezing coefficients in a squeezed vacuum. Comparing squeezing spectra in squeezed and ordinary vacuums, significantly enhanced squeezing for the appropriate pump-vacuum relative phase is found.
NASA Astrophysics Data System (ADS)
Topalović, D. B.; Arsoski, V. V.; Pavlović, S.; Čukarić, N. A.; Tadić, M. Ž.; Peeters, F. M.
2016-01-01
We use the Galerkin approach and the finite-element method to numerically solve the effective-mass Schrödinger equation. The accuracy of the solution is explored as it varies with the range of the numerical domain. The model potentials are those of interdiffused semiconductor quantum wells and axially symmetric quantum wires. Also, the model of a linear harmonic oscillator is considered for comparison reasons. It is demonstrated that the absolute error of the electron ground state energy level exhibits a minimum at a certain domain range, which is thus considered to be optimal. This range is found to depend on the number of mesh nodes N approximately as α0 logeα1(α2N), where the values of the constants α0, α1, and α2 are determined by fitting the numerical data. And the optimal range is found to be a weak function of the diffusion length. Moreover, it was demonstrated that a domain range adaptation to the optimal value leads to substantial improvement of accuracy of the solution of the Schrödinger equation. Supported by the Ministry of Education, Science, and Technological Development of Serbia and the Flemish fund for Scientific Research (FWO Vlaanderen)
Alemgadmi, Khaled I. K. Suparmi; Cari; Deta, U. A.
2015-09-30
The approximate analytical solution of Schrodinger equation for Q-Deformed Rosen-Morse potential was investigated using Supersymmetry Quantum Mechanics (SUSY QM) method. The approximate bound state energy is given in the closed form and the corresponding approximate wave function for arbitrary l-state given for ground state wave function. The first excited state obtained using upper operator and ground state wave function. The special case is given for the ground state in various number of q. The existence of Rosen-Morse potential reduce energy spectra of system. The larger value of q, the smaller energy spectra of system.
NASA Astrophysics Data System (ADS)
Daviau, Claude; Bertrand, Jacques
A wave equation with mass term is studied for all particles and antiparticles of the first generation: electron and its neutrino, positron and antineutrino, quarks $u$ and $d$ with three states of color and antiquarks $\\overline{u}$ and $\\overline{d}$. This wave equation is form invariant under the $Cl_3^*$ group generalizing the relativistic invariance. It is gauge invariant under the $U(1)\\times SU(2) \\times SU(3)$ group of the standard model of quantum physics. The wave is a function of space and time with value in the Clifford algebra $Cl_{1,5}$. All features of the standard model, charge conjugation, color, left waves, Lagrangian formalism, are linked to the geometry of this extended space-time.
Marconcini, Paolo; Logoteta, Demetrio; Macucci, Massimo
2013-11-07
The solution of differential problems, and in particular of quantum wave equations, can in general be performed both in the direct and in the reciprocal space. However, to achieve the same accuracy, direct-space finite-difference approaches usually involve handling larger algebraic problems with respect to the approaches based on the Fourier transform in reciprocal space. This is the result of the errors that direct-space discretization formulas introduce into the treatment of derivatives. Here, we propose an approach, relying on a set of sinc-based functions, that allows us to achieve an exact representation of the derivatives in the direct space and that is equivalent to the solution in the reciprocal space. We apply this method to the numerical solution of the Dirac equation in an armchair graphene nanoribbon with a potential varying only in the transverse direction.
NASA Astrophysics Data System (ADS)
Marconcini, Paolo; Logoteta, Demetrio; Macucci, Massimo
2013-11-01
The solution of differential problems, and in particular of quantum wave equations, can in general be performed both in the direct and in the reciprocal space. However, to achieve the same accuracy, direct-space finite-difference approaches usually involve handling larger algebraic problems with respect to the approaches based on the Fourier transform in reciprocal space. This is the result of the errors that direct-space discretization formulas introduce into the treatment of derivatives. Here, we propose an approach, relying on a set of sinc-based functions, that allows us to achieve an exact representation of the derivatives in the direct space and that is equivalent to the solution in the reciprocal space. We apply this method to the numerical solution of the Dirac equation in an armchair graphene nanoribbon with a potential varying only in the transverse direction.
Quantum Monte Carlo Calculation for the Equation of State of MgSiO3 perovskite at high pressures
NASA Astrophysics Data System (ADS)
Lin, Yangzheng; Cohen, R. E.; Driver, Kevin P.; Militzer, Burkhard; Shulenburger, Luke; Kim, Jeongnim
2014-03-01
Magnesium silicate (MgSiO3) is among the most abundant minerals in the Earth's mantle. Its phase behavior under high pressure has important implications for the physical properties of deep Earth and the core-mantle boundary. A number of experiments and density functional theory calculations have studied perovskite and its transition to the post-perovskite phase. Here, we present our initial work on the equation of state of perovskite at pressures up to 200 GPa using quantum Monte Carlo (QMC), a benchmark ab initio method. Our QMC calculations optimize electron correlation by using a Slater-Jastrow type wave function with a single determinant comprised of single-particle orbitals extracted from fully converged DFT calculations. The equation of state obtained from QMC calculations agrees with experimental data. E-mail: rcohen@carnegiescience.edu; This work is supported by NSF.
Hashimoto, K; Kanki, K; Tanaka, S; Petrosky, T
2016-02-01
Irreversible processes of weakly coupled one-dimensional quantum perfect Lorentz gas are studied on the basis of the fundamental laws of physics in terms of the complex spectral analysis associated with the resonance state of the Liouville-von Neumann operator. Without any phenomenological operations, such as a coarse-graining of space-time, or a truncation of the higher order correlation, we obtained irreversible processes in a purely dynamical basis in all space and time scale including the microscopic atomic interaction range that is much smaller than the mean-free length. Based on this solution, a limitation of the usual phenomenological Boltzmann equation, as well as an extension of the Boltzmann equation to entire space-time scale, is discussed. PMID:26986313
NASA Astrophysics Data System (ADS)
Hashimoto, K.; Kanki, K.; Tanaka, S.; Petrosky, T.
2016-02-01
Irreversible processes of weakly coupled one-dimensional quantum perfect Lorentz gas are studied on the basis of the fundamental laws of physics in terms of the complex spectral analysis associated with the resonance state of the Liouville-von Neumann operator. Without any phenomenological operations, such as a coarse-graining of space-time, or a truncation of the higher order correlation, we obtained irreversible processes in a purely dynamical basis in all space and time scale including the microscopic atomic interaction range that is much smaller than the mean-free length. Based on this solution, a limitation of the usual phenomenological Boltzmann equation, as well as an extension of the Boltzmann equation to entire space-time scale, is discussed.
NASA Astrophysics Data System (ADS)
Gainutdinov, Azat M.; Hao, Wenrui; Nepomechie, Rafael I.; Sommese, Andrew J.
2015-12-01
We consider the {U}q{sl}(2)-invariant open spin-1/2 XXZ quantum spin chain of finite length N. For the case that q is a root of unity, we propose a formula for the number of admissible solutions of the Bethe ansatz equations in terms of dimensions of irreducible representations of the Temperley-Lieb algebra; and a formula for the degeneracies of the transfer matrix eigenvalues in terms of dimensions of tilting {U}q{sl}(2)-modules. These formulas include corrections that appear if two or more tilting modules are spectrum-degenerate. For the XX case (q={{{e}}}{{i}π /2}), we give explicit formulas for the number of admissible solutions and degeneracies. We also consider the cases of generic q and the isotropic (q\\to 1) limit. Numerical solutions of the Bethe equations up to N = 8 are presented. Our results are consistent with the Bethe ansatz solution being complete.
Quantum correlations among optical and vibrational quanta
NASA Astrophysics Data System (ADS)
Carlig, Sergiu; Macovei, Mihai A.
2014-05-01
We investigate the feasibility of correlating an optical cavity field and a vibrational phonon mode. A laser pumped quantum dot fixed on a nanomechanical resonator beam interacts as a whole with the optical resonator mode. When the quantum dot variables are faster than the optical and phonon ones, we obtain a final master equation describing the involved modes only. Increasing the temperature, which directly affects the vibrational degrees of freedom, one can as well influence the cavity photon intensity, i.e., the optical and phonon modes are correlated. Furthermore, the corresponding Cauchy-Schwarz inequality is violated demonstrating the quantum nature of those correlations.
Honey, D.A.
1989-12-01
The collisional Boltzmann equation was solved numerically to obtain excitation rates for use in a CO{sub 2} laser design program. The program was written in Microsoft QuickBasic for use on the IBM Personal Computer or equivalent. Program validation involved comparisons of computed transport coefficients with experimental data and previous theoretical work. Four different numerical algorithms were evaluated in terms of accuracy and efficiency. L-U decomposition was identified as the preferred approach. The calculated transport coefficients were found to agree with empirical data within one to five percent. The program was integrated into a CO{sub 2} laser design program. Studies were then performed to evaluate the effects on predicted laser output power and energy density as parameters affecting electron kinetics were changed. Plotting routines were written for both programs.
Mkrtchyan, A. R.; Hayrapetyan, A. G.; Khachatryan, B. V.; Petrosyan, R. G.; Avakyan, R. M.
2009-08-15
The fourth order linear differential equation is obtained for the probability density considering the non-Hermitian Hamiltonian (the case of quasistationary states - complexity of energy). Third order nonlinear differential equation for the square of the modulus of the order parameter and for the phase is obtained by making use of Ginzburg-Landau equations. Three integrals of 'motion' are found in the absence of the external magnetic field and two integrals are found in the presence of the external magnetic field. The analysis of these integrals is conducted. New analytical solutions are obtained.
NASA Astrophysics Data System (ADS)
Privalov, T.; Shalagin, A.
1999-06-01
The interaction of a plane monochromatic traveling wave with two-level particles suffering collisions with buffer-gas particles is considered. Collision rates are assumed to be velocity dependent. The collision integral is obtained on the basis of the strong-collision model, generalized to the case of velocity-dependent collision rates (the so-called ``kangaroo'' model). We obtained the exact analytical solution of the problem for arbitrary intensity of radiation, arbitrary ratio of homogeneous and Doppler widths of the absorption line, and arbitrary mass ratio between absorbing- and buffer-gas particles. The obtained analytical solutions of the quantum kinetic equations allowed us to analyze the spectral shape of the strong-field absorption line as well as the probe-field absorption line (the nonlinear part of the work done by the probe field) and the frequency dependence of the light-induced drift (LID) velocity. A comprehensive comparative analysis for the three- and one-dimensional versions of the model is given. On the basis of this analysis, we reach the conclusion that the one-dimensional quantum kinetic equation has quite a wide range of application. We also reveal the conditions for the strongest manifestation of the velocity dependence of the collision rates, which affects most strongly the anomalous LID.
Spin field equations and Heun's equations
NASA Astrophysics Data System (ADS)
Jiang, Min; Wang, Xuejing; Li, Zhongheng
2015-06-01
The Kerr-Newman-(anti) de Sitter metric is the most general stationary black hole solution to the Einstein-Maxwell equation with a cosmological constant. We study the separability of the equations of the massless scalar (spin s=0), neutrino ( s=1/2), electromagnetic ( s=1), Rarita-Schwinger ( s=3/2), and gravitational ( s=2) fields propagating on this background. We obtain the angular and radial master equations, and show that the master equations are transformed to Heun's equation. Meanwhile, we give the condition of existence of event horizons for Kerr-Newman-(anti) de Sitter spacetime by using Sturm theorem.
Quantum limit for nuclear spin polarization in semiconductor quantum dots
NASA Astrophysics Data System (ADS)
Hildmann, Julia; Kavousanaki, Eleftheria; Burkard, Guido; Ribeiro, Hugo
2014-05-01
A recent experiment [E. A. Chekhovich et al., Phys. Rev. Lett. 104, 066804 (2010), 10.1103/PhysRevLett.104.066804] has demonstrated that high nuclear spin polarization can be achieved in self-assembled quantum dots by exploiting an optically forbidden transition between a heavy hole and a trion state. However, a fully polarized state is not achieved as expected from a classical rate equation. Here, we theoretically investigate this problem with the help of a quantum master equation and we demonstrate that a fully polarized state cannot be achieved due to formation of a nuclear dark state. Moreover, we show that the maximal degree of polarization depends on structural properties of the quantum dot.
Efficient quantum state transfer in an engineered chain of quantum bits
NASA Astrophysics Data System (ADS)
Sandberg, Martin; Knill, Emanuel; Kapit, Eliot; Vissers, Michael R.; Pappas, David P.
2016-03-01
We present a method of performing quantum state transfer in a chain of superconducting quantum bits. Our protocol is based on engineering the energy levels of the qubits in the chain and tuning them all simultaneously with an external flux bias. The system is designed to allow sequential adiabatic state transfers, resulting in on-demand quantum state transfer from one end of the chain to the other. Numerical simulations of the master equation using realistic parameters for capacitive nearest-neighbor coupling, energy relaxation, and dephasing show that fast, high-fidelity state transfer should be feasible using this method.
Non-Perturbative, Unitary Quantum-Particle Scattering Amplitudes from Three-Particle Equations
Lindesay, James V
2002-03-19
We here use our non-perturbative, cluster decomposable relativistic scattering formalism to calculate photon-spinor scattering, including the related particle-antiparticle annihilation amplitude. We start from a three-body system in which the unitary pair interactions contain the kinematic possibility of single quantum exchange and the symmetry properties needed to identify and substitute antiparticles for particles. We extract from it unitary two-particle amplitude for quantum-particle scattering. We verify that we have done this correctly by showing that our calculated photon-spinor amplitude reduces in the weak coupling limit to the usual lowest order, manifestly covariant (QED) result with the correct normalization. That we are able to successfully do this directly demonstrates that renormalizability need not be a fundamental requirement for all physically viable models.
NASA Astrophysics Data System (ADS)
Pogrosheva, T.; Vladimirov, V.; Lipunov, V.; Lopez, R. Rebolo; Buckley, D.; Gorbovskoy, E.; Tiurina, N.; Kuznetsov, A.; Balanutsa, P.; Kornilov, V.; Gorbunov, I.; Gress, O.; Shumkov, V.; Ricart, M. Serra; Israelian, G.; Potter, S.; Kniazev, A.
2016-06-01
MASTER-IAC auto-detection system( Lipunov et al., "MASTER Global Robotic Net", Advances in Astronomy, 2010, 30L ) discovered OT source at (RA, Dec) = 20h 58m 16.98s +23d 58m 12.6s on 2016-06-09.03890 UT. The OT unfiltered magnitude is 17.5m (limit 19.4m).
Quantum algorithm for simulating the dynamics of an open quantum system
Wang Hefeng; Ashhab, S.; Nori, Franco
2011-06-15
In the study of open quantum systems, one typically obtains the decoherence dynamics by solving a master equation. The master equation is derived using knowledge of some basic properties of the system, the environment, and their interaction: One basically needs to know the operators through which the system couples to the environment and the spectral density of the environment. For a large system, it could become prohibitively difficult to even write down the appropriate master equation, let alone solve it on a classical computer. In this paper, we present a quantum algorithm for simulating the dynamics of an open quantum system. On a quantum computer, the environment can be simulated using ancilla qubits with properly chosen single-qubit frequencies and with properly designed coupling to the system qubits. The parameters used in the simulation are easily derived from the parameters of the system + environment Hamiltonian. The algorithm is designed to simulate Markovian dynamics, but it can also be used to simulate non-Markovian dynamics provided that this dynamics can be obtained by embedding the system of interest into a larger system that obeys Markovian dynamics. We estimate the resource requirements for the algorithm. In particular, we show that for sufficiently slow decoherence a single ancilla qubit could be sufficient to represent the entire environment, in principle.
NASA Astrophysics Data System (ADS)
Sakurai, Atsunori; Tanimura, Yoshitaka
2013-03-01
The quantum dissipative dynamics of a tunneling process through double barrier structures is investigated on the basis of a rigorous treatment for the first time. We employ a Caldeira--Leggett Hamiltonian with an effective potential calculated self-consistently, accounting for the electron distribution. With this Hamiltonian, we use the reduced hierarchy equations of motion in the Wigner space representation to study the effects of non-Markovian thermal fluctuations and dissipation at finite temperature in a rigorous manner. Hysteresis, double plateau-like behavior, and self-excited current oscillation are observed in a negative differential resistance (NDR) region of the current--voltage curve. We find that while most of the current oscillations decay in time in the NDR region, there is a steady oscillation characterized by a tornado-like rotation in the Wigner space in the upper plateau of the NDR region.
Space-time versus particle-hole symmetry in quantum Enskog equations.
Spicka, V; Morawetz, K; Lipavský, P
2001-10-01
The nonlocal scattering-in and scattering-out integrals of the Enskog equation have reversed displacements of colliding particles reflecting that the scattering-in and -out processes are conjugated by the space and time inversions. Generalizations of the Enskog equation to Fermi liquid systems are hindered by the need for particle-hole symmetry which contradicts the reversed displacements. We resolve this problem with the help of the optical theorem. It is found that space-time and particle-hole symmetry can be fulfilled simultaneously only for the Bruckner type of internal Pauli blocking while the Feynman-Galitskii form allows only for particle-hole symmetry but not for space-time symmetry due to a stimulated emission of bosons. PMID:11690090
The Wasserstein Gradient Flow of the Fisher Information and the Quantum Drift-diffusion Equation
NASA Astrophysics Data System (ADS)
Gianazza, Ugo; Savaré, Giuseppe; Toscani, Giuseppe
2009-10-01
We prove the global existence of non-negative variational solutions to the “drift diffusion” evolution equation {{partial_t} u+ div left(u{D}left(2 Δ sqrt u/sqrt u-{f}right)right)=0} under variational boundary condition. Despite the lack of a maximum principle for fourth order equations, non-negative solutions can be obtained as a limit of a variational approximation scheme by exploiting the particular structure of this equation, which is the gradient flow of the (perturbed) Fisher information functional {fancyscript F^f(u):=frac 12int left|{D} log uright|^2 {u} dx+int fu dx} with respect to the Kantorovich-Rubinstein-Wasserstein distance between probability measures. We also study long-time behavior of the solutions, proving their exponential decay to the equilibrium state g = e- V characterized by {-Δ V+frac12 left|{D} Vright|^2=f,quad int e^{-V} dx=int u0dx,} when the potential V is uniformly convex: in this case the functional {fancyscript F^f} coincides with the relative Fisher information {fancyscript F^f(u)=frac12fancyscript I(u|g)= int left|{D}log(u/g)right|^2u dx}.
Liu, Hao; Zhu, Lili; Bai, Shuming; Shi, Qiang
2014-04-07
We investigated applications of the hierarchical equation of motion (HEOM) method to perform high order perturbation calculations of reduced quantum dynamics for a harmonic bath with arbitrary spectral densities. Three different schemes are used to decompose the bath spectral density into analytical forms that are suitable to the HEOM treatment: (1) The multiple Lorentzian mode model that can be obtained by numerically fitting the model spectral density. (2) The combined Debye and oscillatory Debye modes model that can be constructed by fitting the corresponding classical bath correlation function. (3) A new method that uses undamped harmonic oscillator modes explicitly in the HEOM formalism. Methods to extract system-bath correlations were investigated for the above bath decomposition schemes. We also show that HEOM in the undamped harmonic oscillator modes can give detailed information on the partial Wigner transform of the total density operator. Theoretical analysis and numerical simulations of the spin-Boson dynamics and the absorption line shape of molecular dimers show that the HEOM formalism for high order perturbations can serve as an important tool in studying the quantum dissipative dynamics in the intermediate coupling regime.
Koller, Andrew; Olshanii, Maxim
2011-12-01
We present a case demonstrating the connection between supersymmetric quantum mechanics (SUSYQM), reflectionless scattering, and soliton solutions of integrable partial differential equations. We show that the members of a class of reflectionless Hamiltonians, namely, Akulin's Hamiltonians, are connected via supersymmetric chains to a potential-free Hamiltonian, explaining their reflectionless nature. While the reflectionless property in question has been mentioned in the literature for over two decades, the enabling algebraic mechanism was previously unknown. Our results indicate that the multisoliton solutions of the sine-Gordon and nonlinear Schrödinger equations can be systematically generated via the supersymmetric chains connecting Akulin's Hamiltonians. Our findings also explain a well-known but little-understood effect in laser physics: when a two-level atom, initially in the ground state, is subjected to a laser pulse of the form V(t) = (nh/τ)/cosh(t/τ), with n being an integer and τ being the pulse duration, it remains in the ground state after the pulse has been applied, for any choice of the laser detuning. PMID:22304205
Caruso, F.; Martins, J.; Oguri, V.
2014-08-15
The effects on the non-relativistic dynamics of a system compound by two electrons interacting by a Coulomb potential and with an external harmonic oscillator potential, confined to move in a two dimensional Euclidean space, are investigated. In particular, it is shown that it is possible to determine exactly and in a closed form a finite portion of the energy spectrum and the associated eigenfunctions for the Schrödinger equation describing the relative motion of the electrons, by putting it into the form of a biconfluent Heun equation. In the same framework, another set of solutions of this type can be straightforwardly obtained for the case when the two electrons are submitted also to an external constant magnetic field. - Highlights: • Exact solution of a quantum dot model. • Determination of the energy levels. • Investigation of how the radial wave functions depend on the external excitation frequency. • Characteristic length between the two-electrons are found to be compatible with the semiconductor lattice parameter.
The quantum mechanical two-Coulomb-centre problem in the Dirac equation framework
NASA Astrophysics Data System (ADS)
Reity, O. K.; Lazur, V. Yu; Katernoha, A. V.
2002-01-01
The asymptotic expansions (at small and large internuclear distances R) of the eigenvalues (potential curves) E(R) of the two-Coulomb-centre problem are obtained. The Dirac equation with an axially symmetrical potential, not allowing complete separation of variables, is solved analytically by the Wentzel-Kramers-Brillouin approach and boundary-layer method. In the framework of this scheme, the relativistic two-Coulomb-centre wavefunction is constructed. The first two terms of the asymptotic (at large internuclear distance) behaviour of the exchange interaction potential for an ion with an atom are calculated.
Danel, J.-F.; Blottiau, P.; Kazandjian, L.; Piron, R.; Torrent, M.
2014-10-15
The applicability of quantum molecular dynamics to the calculation of the equation of state of a dense plasma is limited at high temperature by computational cost. Orbital-free molecular dynamics, based on a semiclassical approximation and possibly on a gradient correction, is a simulation method available at high temperature. For a high-Z element such as lutetium, we examine how orbital-free molecular dynamics applied to the equation of state of a dense plasma can be regarded as the limit of quantum molecular dynamics at high temperature. For the normal mass density and twice the normal mass density, we show that the pressures calculated with the quantum approach converge monotonically towards those calculated with the orbital-free approach; we observe a faster convergence when the orbital-free approach includes the gradient correction. We propose a method to obtain an equation of state reproducing quantum molecular dynamics results up to high temperatures where this approach cannot be directly implemented. With the results already obtained for low-Z plasmas, the present study opens the way for reproducing the quantum molecular dynamics pressure for all elements up to high temperatures.
Szymański, S
2009-12-28
The damped quantum rotation (DQR) theory describes manifestations in nuclear magnetic resonance spectra of the coherent and stochastic dynamics of N-fold molecular rotors composed of indistinguishable particles. The standard jump model is only a limiting case of the DQR approach; outside this limit, the stochastic motions of such rotors have no kinematic description. In this paper, completing the previous two of this series, consequences of nuclear permutation symmetry for the properties of the DQR line shape equation are considered. The systems addressed are planar rotors, such as aromatic hydrocarbons' rings, occurring inside of molecular crystals oriented in the magnetic field. Under such conditions, oddfold rotors can have nontrivial permutation symmetries only for peculiar orientations while evenfold ones always retain their intrinsic symmetry element, which is rotation by 180 degrees about the N-fold axis; in specific orientations the latter can gain two additional symmetry elements. It is shown that the symmetry selection rules applicable to the classical rate processes in fluids, once recognized as having two diverse aspects, macroscopic and microscopic, are also rigorously valid for the DQR processes in the solid state. However, formal justification of these rules is different because the DQR equation is based on the Pauli principle, which is ignored in the jump model. For objects like the benzene ring, exploitation of these rules in simulations of spectra using the DQR equation can be of critical significance for the feasibility of the calculations. Examples of such calculations for the proton system of the benzene ring in a general orientation are provided. It is also shown that, because of the intrinsic symmetries of the evenfold rotors, many of the DQR processes, which such rotors can undergo, are unobservable in NMR spectra. PMID:20059076
Solving non-Markovian open quantum systems with multi-channel reservoir coupling
Broadbent, Curtis J.; Jing, Jun; Yu, Ting; Eberly, Joseph H.
2012-08-15
We extend the non-Markovian quantum state diffusion (QSD) equation to open quantum systems which exhibit multi-channel coupling to a harmonic oscillator reservoir. Open quantum systems which have multi-channel reservoir coupling are those in which canonical transformation of reservoir modes cannot reduce the number of reservoir operators appearing in the interaction Hamiltonian to one. We show that the non-Markovian QSD equation for multi-channel reservoir coupling can, in some cases, lead to an exact master equation which we derive. We then derive the exact master equation for the three-level system in a vee-type configuration which has multi-channel reservoir coupling and give the analytical solution. Finally, we examine the evolution of the three-level vee-type system with generalized Ornstein-Uhlenbeck reservoir correlations numerically. - Highlights: Black-Right-Pointing-Pointer The concept of multi-channel vs. single-channel reservoir coupling is rigorously defined. Black-Right-Pointing-Pointer The non-Markovian quantum state diffusion equation for arbitrary multi-channel reservoir coupling is derived. Black-Right-Pointing-Pointer An exact time-local master equation is derived under certain conditions. Black-Right-Pointing-Pointer The analytical solution to the three-level system in a vee-type configuration is found. Black-Right-Pointing-Pointer The evolution of the three-level system under generalized Ornstein-Uhlenbeck noise is plotted for many parameter regimes.
Semenov, Alexander; Babikov, Dmitri
2015-12-17
The mixed quantum classical theory, MQCT, for inelastic scattering of two molecules is developed, in which the internal (rotational, vibrational) motion of both collision partners is treated with quantum mechanics, and the molecule-molecule scattering (translational motion) is described by classical trajectories. The resultant MQCT formalism includes a system of coupled differential equations for quantum probability amplitudes, and the classical equations of motion in the mean-field potential. Numerical tests of this theory are carried out for several most important rotational state-to-state transitions in the N2 + H2 system, in a broad range of collision energies. Besides scattering resonances (at low collision energies) excellent agreement with full-quantum results is obtained, including the excitation thresholds, the maxima of cross sections, and even some smaller features, such as slight oscillations of energy dependencies. Most importantly, at higher energies the results of MQCT are nearly identical to the full quantum results, which makes this approach a good alternative to the full-quantum calculations that become computationally expensive at higher collision energies and for heavier collision partners. Extensions of this theory to include vibrational transitions or general asymmetric-top rotor (polyatomic) molecules are relatively straightforward. PMID:26323089
The optomechanical instability in the quantum regime
NASA Astrophysics Data System (ADS)
Ludwig, Max; Kubala, Björn; Marquardt, Florian
2008-09-01
We consider a generic optomechanical system, consisting of a driven optical cavity and a movable mirror attached to a cantilever. Systems of this kind (and analogues) have been realized in many recent experiments. It is well known that these systems can exhibit an instability towards a regime where the cantilever settles into self-sustained oscillations. In this paper, we briefly review the classical theory of the optomechanical instability, and then discuss the features arising in the quantum regime. We solve numerically a full quantum master equation for the coupled system, and use it to analyze the photon number, the cantilever's mechanical energy, the phonon probability distribution and the mechanical Wigner density, as a function of experimentally accessible control parameters. When a suitable dimensionless 'quantum parameter' is sent to zero, the results of the quantum mechanical model converge towards the classical predictions. We discuss this quantum-to-classical transition in some detail.
High power diode laser Master Oscillator-Power Amplifier (MOPA)
NASA Technical Reports Server (NTRS)
Andrews, John R.; Mouroulis, P.; Wicks, G.
1994-01-01
High power multiple quantum well AlGaAs diode laser master oscillator - power amplifier (MOPA) systems were examined both experimentally and theoretically. For two pass operation, it was found that powers in excess of 0.3 W per 100 micrometers of facet length were achievable while maintaining diffraction-limited beam quality. Internal electrical-to-optical conversion efficiencies as high as 25 percent were observed at an internal amplifier gain of 9 dB. Theoretical modeling of multiple quantum well amplifiers was done using appropriate rate equations and a heuristic model of the carrier density dependent gain. The model gave a qualitative agreement with the experimental results. In addition, the model allowed exploration of a wider design space for the amplifiers. The model predicted that internal electrical-to-optical conversion efficiencies in excess of 50 percent should be achievable with careful system design. The model predicted that no global optimum design exists, but gain, efficiency, and optical confinement (coupling efficiency) can be mutually adjusted to meet a specific system requirement. A three quantum well, low optical confinement amplifier was fabricated using molecular beam epitaxial growth. Coherent beam combining of two high power amplifiers injected from a common master oscillator was also examined. Coherent beam combining with an efficiency of 93 percent resulted in a single beam having diffraction-limited characteristics. This beam combining efficiency is a world record result for such a system. Interferometric observations of the output of the amplifier indicated that spatial mode matching was a significant factor in the less than perfect beam combining. Finally, the system issues of arrays of amplifiers in a coherent beam combining system were investigated. Based upon experimentally observed parameters coherent beam combining could result in a megawatt-scale coherent beam with a 10 percent electrical-to-optical conversion efficiency.
The Quantum World of Ultra-Cold Atoms and Light - Book 1: Foundations of Quantum Optics
NASA Astrophysics Data System (ADS)
Gardiner, Crispin; Zoller, Peter
2014-03-01
Abstract The Table of Contents is as follows: * I - THE PHYSICAL BACKGROUND * 1. Controlling the Quantum World * 1.1 Quantum Optics * 1.2 Quantum Information * 2. Describing the Quantum World * 2.1 Classical Stochastic Processes * 2.2. Theoretical Quantum Optics * 2.3. Quantum Stochastic Methods * 2.4. Ultra-Cold Atoms * II - CLASSICAL STOCHASTIC METHODS * 3. Physics in a Noisy World * 3.1. Brownian Motion and the Thermal Origin of Noise * 3.2. Brownian Motion, Friction, Noise and Temperature * 3.3. Measurement in a Fluctuating System * 4. Stochastic Differential Equations * 4.1. Ito Stochastic Differential Equation * 4.2. The Fokker-Planck Equation * 4.3. The Stratonovich Stochastic Differential Equation * 4.4. Systems with Many Variables * 4.5. Numerical Simulation of Stochastic Differential Equations * 5. The Fokker-Planck Equation * 5.1. Fokker-Planck Equation in One Dimension * 5.2. Eigenfunctions of the Fokker-Planck Equation * 5.3. Many-Variable Fokker-Planck Equations * 6. Master Equations and Jump Processes * 6.1. The Master Equation * 7. Applications of Random Processes * 7.1. The Ornstein-Uhlenbeck Process * 7.2. Johnson Noise * 7.3. Complex Variable Oscillator Processes * 8. The Markov Limit * 8.1. The White Noise Limit * 8.2. Interpretation and Generalizations of the White Noise Limit * 8.3. Linear Non-Markovian Stochastic Differential Equations * 9. Adiabatic Elimination of Fast Variables * 9.1 Slow and Fast Variables * 9.2. Other Applications of the Adiabatic Elimination Method * III - FIELDS, QUANTA AND ATOMS * 10. Ideal Bose and Fermi Systems * 10.1. The Quantum Gas * 10.2. Thermal States * 10.3. Fluctuations in the Ideal Bose Gas * 10.4. Bosonic Quantum Gaussian Systems * 10.5. Coherent States * 10.6. Fluctuations in Systems of Fermions * 10.7. Two-Level Systems and Pauli Matrices * 11. Quantum Fields * 11.1 Kinds of Quantum Field * 11.2 Coherence and Correlation Functions * 12. Atoms, Light and their Interaction * 12.1. Interaction with the
Quantum Simulation of Dissipative Processes without Reservoir Engineering
Di Candia, R.; Pedernales, J. S.; del Campo, A.; Solano, E.; Casanova, J.
2015-01-01
We present a quantum algorithm to simulate general finite dimensional Lindblad master equations without the requirement of engineering the system-environment interactions. The proposed method is able to simulate both Markovian and non-Markovian quantum dynamics. It consists in the quantum computation of the dissipative corrections to the unitary evolution of the system of interest, via the reconstruction of the response functions associated with the Lindblad operators. Our approach is equally applicable to dynamics generated by effectively non-Hermitian Hamiltonians. We confirm the quality of our method providing specific error bounds that quantify its accuracy. PMID:26024437
Quantum simulation of dissipative processes without reservoir engineering
Di Candia, R.; Pedernales, J. S.; del Campo, A.; Solano, E.; Casanova, J.
2015-05-29
We present a quantum algorithm to simulate general finite dimensional Lindblad master equations without the requirement of engineering the system-environment interactions. The proposed method is able to simulate both Markovian and non-Markovian quantum dynamics. It consists in the quantum computation of the dissipative corrections to the unitary evolution of the system of interest, via the reconstruction of the response functions associated with the Lindblad operators. Our approach is equally applicable to dynamics generated by effectively non-Hermitian Hamiltonians. We confirm the quality of our method providing specific error bounds that quantify its accuracy.
Sargsyan, V. V.; Kanokov, Z.; Adamian, G. G.; Antonenko, N. V.; Scheid, W.
2009-10-15
Using the reduced-density-matrix formalism, the interaction time of two heavy nuclei is studied. In the reactions {sup 136}Xe+{sup 136}Xe and {sup 238}U+{sup 238}U, the mean interaction time and variance of interaction time distribution are calculated and compared with those of other treatments.
MASTER TELEVISION ANTENNA SYSTEM.
ERIC Educational Resources Information Center
Rhode Island State Dept. of Education, Providence.
SPECIFICATIONS FOR THE FURNISHING AND INSTALLATION OF TELEVISION MASTER ANTENNA SYSTEMS FOR SECONDARY AND ELEMENTARY SCHOOLS ARE GIVEN. CONTRACTOR REQUIREMENTS, EQUIPMENT, PERFORMANCE STANDARDS, AND FUNCTIONS ARE DESCRIBED. (MS)
NASA Astrophysics Data System (ADS)
Winterberg, Friedwardt
2016-01-01
An explanation of the quantum-mechanical particle-wave duality is given by the watt-less emission of gravitational waves from a particle described by the Dirac equation. This explanation is possible through the existence of negative energy, and hence negative mass solutions of Einstein's gravitational field equations. They permit to understand the Dirac equation as the equation for a gravitationally bound positive-negative mass (pole-dipole particle) two-body configuration, with the mass of the Dirac particle equal to the positive mass of the gravitational field binding the positive with the negative mass particle, and with the mass particles making a luminal "Zitterbewegung" (quivering motion), emitting a watt-less oscillating positive-negative space curvature wave. It is shown that this thusly produced "Zitterbewegung" reproduces the quantum potential of the Madelung-transformed Schrödinger equation. The watt-less gravitational wave emitted by the quivering particles is conjectured to be de Broglie's pilot wave. The hypothesised connection of the Dirac equation to gravitational wave physics could, with the failure to detect gravitational waves by the LIGO antennas and pulsar timing arrays, give a clue to extended theories of gravity, or a correction of astrophysical models for the generation of such waves.
Subotnik, Joseph E. Ouyang, Wenjun; Landry, Brian R.
2013-12-07
In this article, we demonstrate that Tully's fewest-switches surface hopping (FSSH) algorithm approximately obeys the mixed quantum-classical Liouville equation (QCLE), provided that several conditions are satisfied – some major conditions, and some minor. The major conditions are: (1) nuclei must be moving quickly with large momenta; (2) there cannot be explicit recoherences or interference effects between nuclear wave packets; (3) force-based decoherence must be added to the FSSH algorithm, and the trajectories can no longer rigorously be independent (though approximations for independent trajectories are possible). We furthermore expect that FSSH (with decoherence) will be most robust when nonadiabatic transitions in an adiabatic basis are dictated primarily by derivative couplings that are presumably localized to crossing regions, rather than by small but pervasive off-diagonal force matrix elements. In the end, our results emphasize the strengths of and possibilities for the FSSH algorithm when decoherence is included, while also demonstrating the limitations of the FSSH algorithm and its inherent inability to follow the QCLE exactly.
Factorized three-body S-matrix restrained by the Yang–Baxter equation and quantum entanglements
Yu, Li-Wei; Zhao, Qing; Ge, Mo-Lin
2014-09-15
This paper investigates the physical effects of the Yang–Baxter equation (YBE) to quantum entanglements through the 3-body S-matrix in entangling parameter space. The explicit form of 3-body S-matrix Ř{sub 123}(θ,φ) based on the 2-body S-matrices is given due to the factorization condition of YBE. The corresponding chain Hamiltonian has been obtained and diagonalized, also the Berry phase for 3-body system is given. It turns out that by choosing different spectral parameters the Ř(θ,φ)-matrix gives GHZ and W states respectively. The extended 1-D Kitaev toy model has been derived. Examples of the role of the model in entanglement transfer are discussed. - Highlights: • We give the relation between 3-body S-matrix and 3-qubit entanglement. • The relation between 3-qubit and 2-qubit entanglements is investigated via YBE. • 1D Kitaev toy model is derived by the Type-II solution of YBE. • The condition of YBE kills the “Zero boundary mode” in our chain model.
NASA Astrophysics Data System (ADS)
Mazziotti, David A.
1998-06-01
The contracted Schrödinger equation (CSE) technique through its direct determination of the two-particle reduced density matrix (2RDM) without the wave function may offer a fresh alternative to traditional many-body quantum calculations. Without additional information the CSE, also known as the density equation, cannot be solved for the 2RDM because it also requires a knowledge of the 4RDM. We provide theoretical foundations through a reconstruction theorem for recent attempts at generating higher RDMs from the 2RDM to remove the indeterminacy of the CSE. With Grassmann algebra a more concise representation for Valdemoro's reconstruction functionals [F. Colmenero, C. Perez del Valle, and C. Valdemoro, Phys. Rev. A 47, 971 (1993)] is presented. From the perspective of the particle-hole equivalence we obtain Nakatsuji and Yasuda's correction for the 4RDM formula [H. Nakatsuji and K. Yasuda, Phys. Rev. Lett. 76, 1039 (1996)] as well as a corrective approach for the 3RDM functional. A different reconstruction strategy, the ensemble representability method (ERM), is introduced to build the 3- and 4-RDMs by enforcing four-ensemble representability and contraction conditions. We derive the CSE in second quantization without Valdemoro's matrix contraction mapping and offer the first proof of Nakatsuji's theorem for the second-quantized CSE. Both the functional and ERM reconstruction strategies are employed with the CSE to solve for the energies and the 2RDMs of a quasispin model without wave functions. We elucidate the iterative solution of the CSE through an analogy with the power method for eigenvalue equations. Resulting energies of the CSE methods are comparable to single-double configuration-interaction (SDCI) energies, and the 2RDMs are more accurate by an order of magnitude than those from SDCI. While the CSE has been applied to systems with 14 electrons, we present results for as many as 40 particles. Results indicate that the 2RDM remains accurate as the number
NASA Astrophysics Data System (ADS)
Balanutsa, P.; Gress, O.; Lipunov, V.; Buckley, D.; Lopez, R. Rebolo; Serra-Ricart, M.; Gorbovskoy, E.; Popova, E.; Kuvshinov, D.; Kuznetsov, A.; Kornilov, V.; Vlasenko, D.; Gress, O.; Shurpakov, S.; Potter, S.; Kniazev, A.
2016-07-01
MASTER-IAC auto-detection system ( Lipunov et al., "MASTER Global Robotic Net", Advances in Astronomy, 2010, 349171 ) discovered OT source at (RA, Dec) = 19h 45m 07.47s -20d 07m 20.5s on 2016-07-11.00663 UT. The OT unfiltered magnitude is (limit 18.8m).
NASA Astrophysics Data System (ADS)
Vladimirov, V.; Shumkov, V.; Lipunov, V.; Buckley, D.; Lopez, R. Rebolo; Serra-Ricart, M.; Gorbovskoy, E.; Tiurina, N.; Balanutsa, P.; Kornilov, V.; Kuvshinov, D.; Kuznetsov, A.; Chazov, V.
2016-08-01
MASTER-SAAO auto-detection system ( Lipunov et al., "MASTER Global Robotic Net", Advances in Astronomy, 2010, 30L ) discovered OT source at (RA, Dec) = 15h 25m 39.43s -70d 22m 45.1s on 2016-08-16.80259 UT. The OT unfiltered magnitude is 17.0m (mlim=17.9m).
NASA Astrophysics Data System (ADS)
Balanutsa, P.; Lipunov, V.; Buckley, D.; Tlatov, A.; Gorbovskoy, E.; Tyurina, N.; Kuznetsov, A.; Kornilov, V.; Kuvshinov, D.; Popova, E.; Vlasenko, D.; Shumkov, V.; Potter, S.; Kniazev, A.; Budnev, N.; Gress, O.; Ivanov, K.; Senik, V.; Dormidontov, D.; Parhomenko, A. V.
2016-08-01
MASTER-Kislovodsk auto-detection system ( Lipunov et al., "MASTER Global Robotic Net", Advances in Astronomy, 2010, 30L ) discovered OT source at (RA, Dec) = 21h 33m 50.58s +06d 51m 22.5s on 2016-07-27.94690 UT. The OT unfiltered magnitude is 17.8m (limit 18.0m).
NASA Astrophysics Data System (ADS)
Balanutsa, P.; Pogrosheva, T.; Lipunov, V.; Buckley, D.; Gorbovskoy, E.; Tiurina, N.; Kuznetsov, A.; Kornilov, V.; Shumkov, V.; Gorbunov, I.; Gress, O.; Kniazev, S. Potter A.
2016-04-01
MASTER-SAAO auto-detection system ( Lipunov et al., "MASTER Global Robotic Net", Advances in Astronomy, 2010, 349171 ) discovered OT source at (RA, Dec) = 10h 34m 32.65s -38d 51m 35.3s on 2016-04-15.84756 UT. The OT unfiltered magnitude is 17.5m (limit 19.3m).
NASA Astrophysics Data System (ADS)
Gress, O.; Balanutsa, P.; Vladimirov, V.; Lipunov, V.; Buckley, D.; Tlatov, A.; Gorbovskoy, E.; Tiurina, N.; Kuznetsov, A.; Kornilov, V.; Gorbunov, I.; Shumkov, V.; Kochutina, N.; Potter, S.; Kniazev, A.; Senik, V.; Dormidontov, D.; Parkhomenko, A.
2016-06-01
MASTER-IAC auto-detection system (Lipunov et al., "MASTER Global Robotic Net", Advances in Astronomy, 2010, 30L) discovered OT source at (RA, Dec) = 20h 03m 08.64s +02d 34m 10.4s on 2016-06-02.14910 UT with unfiltered m_OT=16.3m (mlim=18.8m).
NASA Astrophysics Data System (ADS)
Balanutsa, P.; Shumkov, V.; Gorbovskoy, E.; Lipunov, V.; Buckley, D.; Potter, S.; Rebolo, R.; Serra-Ricart, M.; Israelyan, G.; Tiurina, N.; Kornilov, V.; Gorbunv, I.; Popova, E.; Vladimirov, V.; Kuvshinov, D.; Budnev, N.; Gress, O.; Ivanov, K.
2016-05-01
MASTER-SAAO auto-detection system ( Lipunov et al., "MASTER Global Robotic Net", Advances in Astronomy, 2010, 349171 ) discovered OT source at (RA, Dec) = 15h 31m 05.22s -26d 04m 37.2s on 2016-05-07.99397 UT. The OT unfiltered magnitude is 17.7m (limit 20.0m).
Master Teachers. Fastback 201.
ERIC Educational Resources Information Center
Moore, Richard W.
A nationwide interest in master-teacher plans has arisen as a response to the general malaise in education, but the viability of such plans depends on finding answers to certain crucial problems. Some basic issues must be addressed before master teachers can even be identified: whether a heirarchy of teachers should be established, or prior…
NASA Astrophysics Data System (ADS)
Gress, O.; Vladimirov, V.; Lipunov, V.; Gorbovskoy, E.; Buckley, D.; Balanutsa, P.; Tiurina, N.; Kornilov, V.; Kuznetsov, A.; Gorbunov, I.; Vlasenko, D.; Kuvshinov, D.; Popova, E.; Potter, S.; Kotze, M.; Budnev, N.; Poleschuk, V.; Ivanov, K.
2016-01-01
MASTER-SAAO auto-detection system ( Lipunov et al., "MASTER Global Robotic Net", Advances in Astronomy, 2010, 349171 ) discovered OT source at (RA, Dec) = 14h 50m 56.15s -25d 55m 26.9s on 2016-01-27.02773 UT. The OT unfiltered magnitude is 16.3 (limit 18.4m).
One-step implementation of the 1->3 orbital state quantum cloning machine via quantum Zeno dynamics
Shao Xiaoqiang; Wang Hongfu; Zhang Shou; Chen Li; Zhao Yongfang; Yeon, Kyu-Hwang
2009-12-15
We present an approach for implementation of a 1->3 orbital state quantum cloning machine based on the quantum Zeno dynamics via manipulating three rf superconducting quantum interference device (SQUID) qubits to resonantly interact with a superconducting cavity assisted by classical fields. Through appropriate modulation of the coupling constants between rf SQUIDs and classical fields, the quantum cloning machine can be realized within one step. We also discuss the effects of decoherence such as spontaneous emission and the loss of cavity in virtue of master equation. The numerical simulation result reveals that the quantum cloning machine is especially robust against the cavity decay, since all qubits evolve in the decoherence-free subspace with respect to cavity decay due to the quantum Zeno dynamics.
Adiabaticity in open quantum systems
NASA Astrophysics Data System (ADS)
Venuti, Lorenzo Campos; Albash, Tameem; Lidar, Daniel A.; Zanardi, Paolo
2016-03-01
We provide a rigorous generalization of the quantum adiabatic theorem for open systems described by a Markovian master equation with time-dependent Liouvillian L (t ) . We focus on the finite system case relevant for adiabatic quantum computing and quantum annealing. Adiabaticity is defined in terms of closeness to the instantaneous steady state. While the general result is conceptually similar to the closed-system case, there are important differences. Namely, a system initialized in the zero-eigenvalue eigenspace of L (t ) will remain in this eigenspace with a deviation that is inversely proportional to the total evolution time T . In the case of a finite number of level crossings, the scaling becomes T-η with an exponent η that we relate to the rate of the gap closing. For master equations that describe relaxation to thermal equilibrium, we show that the evolution time T should be long compared to the corresponding minimum inverse gap squared of L (t ) . Our results are illustrated with several examples.
Quantum localization of classical mechanics
NASA Astrophysics Data System (ADS)
Batalin, Igor A.; Lavrov, Peter M.
2016-07-01
Quantum localization of classical mechanics within the BRST-BFV and BV (or field-antifield) quantization methods are studied. It is shown that a special choice of gauge fixing functions (or BRST-BFV charge) together with the unitary limit leads to Hamiltonian localization in the path integral of the BRST-BFV formalism. In turn, we find that a special choice of gauge fixing functions being proportional to extremals of an initial non-degenerate classical action together with a very special solution of the classical master equation result in Lagrangian localization in the partition function of the BV formalism.
Plimak, L.I.; Stenholm, S.
2013-11-15
The general structure of electromagnetic interactions in the so-called response representation of quantum electrodynamics (QED) is analysed. A formal solution to the general quantum problem of the electromagnetic field interacting with matter is found. Independently, a formal solution to the corresponding problem in classical stochastic electrodynamics (CSED) is constructed. CSED and QED differ only in the replacement of stochastic averages of c-number fields and currents by time-normal averages of the corresponding Heisenberg operators. All relations of QED connecting quantum field to quantum current lack Planck’s constant, and thus coincide with their counterparts in CSED. In Feynman’s terms, one encounters complete disentanglement of the potential and current operators in response picture. Based on this parallelism between QED and CSED, it is natural to expect validity of the Lorentz condition and Maxwell’s equations for the time-normal averages of the potential and current. Things however turn out to be more complicated. Maxwell’s equations under the time-normal ordering can only be demonstrated subject to cancellation of the so-called Schwinger terms by gauge-invariant regularisations. We presume this pattern to be general, formulating this as “commutativity conjecture”. Consistency of the latter with the Heisenberg uncertainty principle is discussed. -- Highlights: •The general structure of interaction in quantum electrodynamics (QED) is analysed. •A detailed parallelism between QED and classical stochastic electrodynamics is shown. •Validity of Maxwell’s equations for fluctuations of the field is discussed. •This validity turns out to be in essence a renormalisation postulate.
NASA Astrophysics Data System (ADS)
Barraud, Sylvain
2009-09-01
Various theoretical formulations are proposed for investigating the carrier transport in nanoscale electronic devices. In this paper, a discrete formulation of the Wigner transport equation (WTE) for the self-consistent simulation of phase-coherent quantum transport in silicon nanowire metal-oxide-semiconductor field-effect transistor (MOSFET) devices is presented. The device is simulated using an effective-mass Hamiltonian within the mode-space approximation. The numerical scheme proposed in this work solves self-consistently three dimensional Poisson's equation, two dimensional Schrödinger's equation in each cross-sectional plane of the nanowire, and the steady-state one dimensional WTE for each conduction mode to handle the quantum transport along the channel. Details on numerical implementation of the Wigner function method are given, and the results are compared with those of the nonequilibrium Green's function (NEGF) method in the ballistic limit. The calculations of current-voltage electrical characteristics of surround-gated silicon nanowires are performed using both NEGF and WTE formulations. The good agreement observed between these approaches means that a direct solution of the WTE is an accurate simulation method for modeling the ballistic quantum transport in silicon nanowire MOSFETs.
Assessing non-Markovian quantum dynamics.
Wolf, M M; Eisert, J; Cubitt, T S; Cirac, J I
2008-10-10
We investigate what a snapshot of a quantum evolution--a quantum channel reflecting open system dynamics--reveals about the underlying continuous time evolution. Remarkably, from such a snapshot, and without imposing additional assumptions, it can be decided whether or not a channel is consistent with a time (in)dependent Markovian evolution, for which we provide computable necessary and sufficient criteria. Based on these, a computable measure of "Markovianity" is introduced. We discuss how the consistency with Markovian dynamics can be checked in quantum process tomography. The results also clarify the geometry of the set of quantum channels with respect to being solutions of time (in)dependent master equations. PMID:18999575
Decoherence and dissipation of a quantum harmonic oscillator coupled to two-level systems
Schlosshauer, Maximilian; Hines, A. P.; Milburn, G. J.
2008-02-15
We derive and analyze the Born-Markov master equation for a quantum harmonic oscillator interacting with a bath of independent two-level systems. This hitherto virtually unexplored model plays a fundamental role as one of the four 'canonical' system-environment models for decoherence and dissipation. To investigate the influence of further couplings of the environmental spins to a dissipative bath, we also derive the master equation for a harmonic oscillator interacting with a single spin coupled to a bosonic bath. Our models are experimentally motivated by quantum-electromechanical systems and micron-scale ion traps. Decoherence and dissipation rates are found to exhibit temperature dependencies significantly different from those in quantum Brownian motion. In particular, the systematic dissipation rate for the central oscillator decreases with increasing temperature and goes to zero at zero temperature, but there also exists a temperature-independent momentum-diffusion (heating) rate.
Linear Equations: Equivalence = Success
ERIC Educational Resources Information Center
Baratta, Wendy
2011-01-01
The ability to solve linear equations sets students up for success in many areas of mathematics and other disciplines requiring formula manipulations. There are many reasons why solving linear equations is a challenging skill for students to master. One major barrier for students is the inability to interpret the equals sign as anything other than…
1995-06-01
This document is a master list of acronyms and other abbreviations that are used by or could be useful to, the personnel at Los Alamos National Laboratory. Many specialized and well-known abbreviations are not included in this list.
ERIC Educational Resources Information Center
Sippola, Arne E.
1997-01-01
Describes a set of activities and materials using Language Master machines, combined with more traditional listening-while-reading procedures that helped emergent readers grow rapidly in reading ability and motivation to read. (SR)
MASTER HOME ENVIRONMENTALIST PROGRAM
The Master Home Environmentalist (MHE) program is an innovative approach to address issues of indoor pollution, such as molds and biological contaminants that cause allergies and asthma, dust, indoor air pollution (including asbestos, formaldehyde, radon, combustion sources, tob...
NASA Astrophysics Data System (ADS)
Toh, Kok-Aun; Tsoi, Mun-Fie
2008-11-01
The dire need of some schools to boost the academic performance of their students inevitably rests with their ability to attract highly qualified teachers. As such, the UK has put in place the Advanced Skills Teacher (AST) scheme, while the US has set the ball rolling in laying down standards for the certification of the master science teacher, to distil the best teachers from this pool of highly qualified science teachers. This article examines some of the practices in the teaching-learning process one would associate with those of master science teachers. It argues for the master science teacher to have a well-developed pedagogical content knowledge rather than be an expert in content knowledge. It argues for the master science teacher to be someone who has moved 'from personal comprehension to preparing for the comprehension of others' (Shulman 1987 Harv. Educ. Rev. 75 1-22).
Quantum to classical transition in quantum field theory
NASA Astrophysics Data System (ADS)
Lombardo, Fernando C.
1998-12-01
We study the quatum to classical transition process in the context of quantum field theory. Extending the influence functional formalism of Feynman and Vernon, we study the decoherence process for self-interacting quantum fields in flat space. We also use this formalism for arbitrary geometries to analyze the quantum to classical transition in quantum gravity. After summarizing the main results known for the quantum Brownian motion, we consider a self-interacting field theory in Minkowski spacetime. We compute a coarse grained effective action by integrating out the field modes with wavelength shorter than a critical value. From this effective action we obtain the evolution equation for the reduced density matrix (master equation). We compute the diffusion coefficients for this equation and analyze the decoherence induced on the long-wavelength modes. We generalize the results to the case of a conformally coupled scalar field in de Sitter spacetime. We show that the decoherence is effective as long as the critical wavelength is taken to be not shorter than the Hubble radius. On the other hand, we study the classical limit for scalar-tensorial models in two dimensions. We consider different couplings between the dilaton and the scalar field. We discuss the Hawking radiation process and, from an exact evaluation of the influence functional, we study the conditions by which decoherence ensures the validity of the semiclassical approximation in cosmological metrics. Finally we consider four dimensional models with massive scalar fields, arbitrary coupled to the geometry. We compute the Einstein-Langevin equations in order to study the effect of the fluctuations induced by the quantum fields on the classical geometry.
Ganguly, A. E-mail: aganguly@maths.iitkgp.ernet.in; Das, A.
2014-11-15
We consider one-dimensional stationary position-dependent effective mass quantum model and derive a generalized Korteweg-de Vries (KdV) equation in (1+1) dimension through Lax pair formulation, one being the effective mass Schrödinger operator and the other being the time-evolution of wave functions. We obtain an infinite number of conserved quantities for the generated nonlinear equation and explicitly show that the new generalized KdV equation is an integrable system. Inverse scattering transform method is applied to obtain general solution of the nonlinear equation, and then N-soliton solution is derived for reflectionless potentials. Finally, a special choice has been made for the variable mass function to get mass-deformed soliton solution. The influence of position and time-dependence of mass and also of the different representations of kinetic energy operator on the nature of such solitons is investigated in detail. The remarkable features of such solitons are demonstrated in several interesting figures and are contrasted with the conventional KdV-soliton associated with constant-mass quantum model.
Mine, Makoto Okumura, Masahiko Sunaga, Tomoka Yamanaka, Yoshiya
2007-10-15
The Bogoliubov-de Gennes equations are used for a number of theoretical works on the trapped Bose-Einstein condensates. These equations are known to give the energies of the quasi-particles when all the eigenvalues are real. We consider the case in which these equations have complex eigenvalues. We give the complete set including those modes whose eigenvalues are complex. The quantum fields which represent neutral atoms are expanded in terms of the complete set. It is shown that the state space is an indefinite metric one and that the free Hamiltonian is not diagonalizable in the conventional bosonic representation. We introduce a criterion to select quantum states describing the metastablity of the condensate, called the physical state conditions. In order to study the instability, we formulate the linear response of the density against the time-dependent external perturbation within the regime of Kubo's linear response theory. Some states, satisfying all the physical state conditions, give the blow-up and damping behavior of the density distributions corresponding to the complex eigenmodes. It is qualitatively consistent with the result of the recent analyses using the time-dependent Gross-Pitaevskii equation.
Clifford, David J.; Harris, James M.
2014-12-01
This is the IDC Re-Engineering Phase 2 project Integrated Master Plan (IMP). The IMP presents the major accomplishments planned over time to re-engineer the IDC system. The IMP and the associate Integrated Master Schedule (IMS) are used for planning, scheduling, executing, and tracking the project technical work efforts. REVISIONS Version Date Author/Team Revision Description Authorized by V1.0 12/2014 IDC Re- engineering Project Team Initial delivery M. Harris
Lin, Yangzheng; Cohen, Ronald E.; Stackhouse, Stephen; Driver, Kevin P.; Militzer, Burkhard; Shulenburger, Luke; Kim, Jeongnim
2014-11-10
In this study, we have performed quantum Monte Carlo (QMC) simulations and density functional theory calculations to study the equations of state of MgSiO_{3} perovskite (Pv, bridgmanite) and post-perovskite (PPv) up to the pressure and temperature conditions of the base of Earth's lower mantle. The ground-state energies were derived using QMC simulations and the temperature-dependent Helmholtz free energies were calculated within the quasiharmonic approximation and density functional perturbation theory. The equations of state for both phases of MgSiO_{3} agree well with experiments, and better than those from generalized gradient approximation calculations. The Pv-PPv phase boundary calculated from our QMC equations of state is also consistent with experiments, and better than previous local density approximation calculations. Lastly, we discuss the implications for double crossing of the Pv-PPv boundary in the Earth.
Evolution of quantum-like modeling in decision making processes
NASA Astrophysics Data System (ADS)
Khrennikova, Polina
2012-12-01
The application of the mathematical formalism of quantum mechanics to model behavioral patterns in social science and economics is a novel and constantly emerging field. The aim of the so called 'quantum like' models is to model the decision making processes in a macroscopic setting, capturing the particular 'context' in which the decisions are taken. Several subsequent empirical findings proved that when making a decision people tend to violate the axioms of expected utility theory and Savage's Sure Thing principle, thus violating the law of total probability. A quantum probability formula was devised to describe more accurately the decision making processes. A next step in the development of QL-modeling in decision making was the application of Schrödinger equation to describe the evolution of people's mental states. A shortcoming of Schrödinger equation is its inability to capture dynamics of an open system; the brain of the decision maker can be regarded as such, actively interacting with the external environment. Recently the master equation, by which quantum physics describes the process of decoherence as the result of interaction of the mental state with the environmental 'bath', was introduced for modeling the human decision making. The external environment and memory can be referred to as a complex 'context' influencing the final decision outcomes. The master equation can be considered as a pioneering and promising apparatus for modeling the dynamics of decision making in different contexts.
Evolution of quantum-like modeling in decision making processes
Khrennikova, Polina
2012-12-18
The application of the mathematical formalism of quantum mechanics to model behavioral patterns in social science and economics is a novel and constantly emerging field. The aim of the so called 'quantum like' models is to model the decision making processes in a macroscopic setting, capturing the particular 'context' in which the decisions are taken. Several subsequent empirical findings proved that when making a decision people tend to violate the axioms of expected utility theory and Savage's Sure Thing principle, thus violating the law of total probability. A quantum probability formula was devised to describe more accurately the decision making processes. A next step in the development of QL-modeling in decision making was the application of Schroedinger equation to describe the evolution of people's mental states. A shortcoming of Schroedinger equation is its inability to capture dynamics of an open system; the brain of the decision maker can be regarded as such, actively interacting with the external environment. Recently the master equation, by which quantum physics describes the process of decoherence as the result of interaction of the mental state with the environmental 'bath', was introduced for modeling the human decision making. The external environment and memory can be referred to as a complex 'context' influencing the final decision outcomes. The master equation can be considered as a pioneering and promising apparatus for modeling the dynamics of decision making in different contexts.
Ferenczy, György G
2013-04-01
Mixed quantum mechanics/quantum mechanics (QM/QM) and quantum mechanics/molecular mechanics (QM/MM) methods make computations feasible for extended chemical systems by separating them into subsystems that are treated at different level of sophistication. In many applications, the subsystems are covalently bound and the use of frozen localized orbitals at the boundary is a possible way to separate the subsystems and to ensure a sensible description of the electronic structure near to the boundary. A complication in these methods is that orthogonality between optimized and frozen orbitals has to be warranted and this is usually achieved by an explicit orthogonalization of the basis set to the frozen orbitals. An alternative to this approach is proposed by calculating the wave-function from the Huzinaga equation that guaranties orthogonality to the frozen orbitals without basis set orthogonalization. The theoretical background and the practical aspects of the application of the Huzinaga equation in mixed methods are discussed. Forces have been derived to perform geometry optimization with wave-functions from the Huzinaga equation. Various properties have been calculated by applying the Huzinaga equation for the central QM subsystem, representing the environment by point charges and using frozen strictly localized orbitals to connect the subsystems. It is shown that a two to three bond separation of the chemical or physical event from the frozen bonds allows a very good reproduction (typically around 1 kcal/mol) of standard Hartree-Fock-Roothaan results. The proposed scheme provides an appropriate framework for mixed QM/QM and QM/MM methods. PMID:23281055
Quantum inflationary minisuperspace cosmological models
Kim Sangpyo.
1991-01-01
The Wheeler-DeWitt equations for the Friedmann-Robertson-Walker cosmology conformally and minimally coupled to scalar fields with power-lay potential are expanded in the eigenstates of the scalar field parts. The gravitational parts become a diagonal matrix-valued differential equation for a conformal scalar field, and a coupled matrix-valued differential equation for a minimally coupled scalar field. The Cauchy initial value problem is defined with respect to the intrinsic timelike coordinate, and the wavefunctions incorporating initial data are constructed using the product integral formulation. The packetlike wavefunctions around classical turning points are shown possible in the product integral formulation, and the returning wavepackets near the returning point of the classical Friedmann-Robertson-Walker cosmology are constructed. The wavefunctions to the Wheeler-DeWitt equation minimally coupled to the scaler field are constructed by two differential methods, the master equation and the enlarged matrix equation. The spectrum for the wavefunctions regular at the infinite size of universe is found, and these are interpreted as the Hawking-Page spectrum of wormholes connecting two asymptotically Euclidean regions. The quantum Friedmann-Robertson-Walker cosmology is extended to the minimal scalar field with the inflationary potential having a first order phase transition. The Wheeler-DeWitt equation is expanded in the eigenstates of the scalar field, and the gravitational part becomes a coupled matrix-valued differential equation.
Zhang, Xiao; Wei, Chaozhen; Liu, Yingming; Luo, Maokang
2014-11-15
In this paper we use Dirac function to construct a fractional operator called fractional corresponding operator, which is the general form of momentum corresponding operator. Then we give a judging theorem for this operator and with this judging theorem we prove that R–L, G–L, Caputo, Riesz fractional derivative operator and fractional derivative operator based on generalized functions, which are the most popular ones, coincide with the fractional corresponding operator. As a typical application, we use the fractional corresponding operator to construct a new fractional quantization scheme and then derive a uniform fractional Schrödinger equation in form. Additionally, we find that the five forms of fractional Schrödinger equation belong to the particular cases. As another main result of this paper, we use fractional corresponding operator to generalize fractional quantization scheme by using Lévy path integral and use it to derive the corresponding general form of fractional Schrödinger equation, which consequently proves that these two quantization schemes are equivalent. Meanwhile, relations between the theory in fractional quantum mechanics and that in classic quantum mechanics are also discussed. As a physical example, we consider a particle in an infinite potential well. We give its wave functions and energy spectrums in two ways and find that both results are the same.
BOOK REVIEW Quantum Measurement and Control Quantum Measurement and Control
NASA Astrophysics Data System (ADS)
Kiefer, Claus
2010-12-01
In the last two decades there has been an enormous progress in the experimental investigation of single quantum systems. This progress covers fields such as quantum optics, quantum computation, quantum cryptography, and quantum metrology, which are sometimes summarized as `quantum technologies'. A key issue there is entanglement, which can be considered as the characteristic feature of quantum theory. As disparate as these various fields maybe, they all have to deal with a quantum mechanical treatment of the measurement process and, in particular, the control process. Quantum control is, according to the authors, `control for which the design requires knowledge of quantum mechanics'. Quantum control situations in which measurements occur at important steps are called feedback (or feedforward) control of quantum systems and play a central role here. This book presents a comprehensive and accessible treatment of the theoretical tools that are needed to cope with these situations. It also provides the reader with the necessary background information about the experimental developments. The authors are both experts in this field to which they have made significant contributions. After an introduction to quantum measurement theory and a chapter on quantum parameter estimation, the central topic of open quantum systems is treated at some length. This chapter includes a derivation of master equations, the discussion of the Lindblad form, and decoherence - the irreversible emergence of classical properties through interaction with the environment. A separate chapter is devoted to the description of open systems by the method of quantum trajectories. Two chapters then deal with the central topic of quantum feedback control, while the last chapter gives a concise introduction to one of the central applications - quantum information. All sections contain a bunch of exercises which serve as a useful tool in learning the material. Especially helpful are also various separate
NASA Astrophysics Data System (ADS)
Fu, Houqiang; Lu, Zhijian; Zhao, Yuji
2016-06-01
We study the low efficiency droop characteristics of semipolar InGaN light-emitting diodes (LEDs) using modified rate equation incoporating the phase-space filling (PSF) effect where the results on c-plane LEDs are also obtained and compared. Internal quantum efficiency (IQE) of LEDs was simulated using a modified ABC model with different PSF filling (n0), Shockley-Read-Hall (A), radiative (B), Auger (C) coefficients and different active layer thickness (d), where the PSF effect showed a strong impact on the simulated LED efficiency results. A weaker PSF effect was found for low-droop semipolar LEDs possibly due to small quantum confined Stark effect, short carrier lifetime, and small average carrier density. A very good agreement between experimental data and the theoretical modeling was obtained for low-droop semipolar LEDs with weak PSF effect. These results suggest the low droop performance may be explained by different mechanisms for semipolar LEDs.
Curchod, Basile F E; Tavernelli, Ivano; Rothlisberger, Ursula
2011-02-28
The non-relativistic quantum dynamics of nuclei and electrons is solved within the framework of quantum hydrodynamics using the adiabatic representation of the electronic states. An on-the-fly trajectory-based nonadiabatic molecular dynamics algorithm is derived, which is also able to capture nuclear quantum effects that are missing in the traditional trajectory surface hopping approach based on the independent trajectory approximation. The use of correlated trajectories produces quantum dynamics, which is in principle exact and computationally very efficient. The method is first tested on a series of model potentials and then applied to study the molecular collision of H with H(2) using on-the-fly TDDFT potential energy surfaces and nonadiabatic coupling vectors. PMID:21264437
Natural approach to quantum dissipation
NASA Astrophysics Data System (ADS)
Taj, David; Öttinger, Hans Christian
2015-12-01
The dissipative dynamics of a quantum system weakly coupled to one or several reservoirs is usually described in terms of a Lindblad generator. The popularity of this approach is certainly due to the linear character of the latter. However, while such linearity finds justification from an underlying Hamiltonian evolution in some scaling limit, it does not rely on solid physical motivations at small but finite values of the coupling constants, where the generator is typically used for applications. The Markovian quantum master equations we propose are instead supported by very natural thermodynamic arguments. They themselves arise from Markovian master equations for the system and the environment which preserve factorized states and mean energy and generate entropy at a non-negative rate. The dissipative structure is driven by an entropic map, called modular, which introduces nonlinearity. The generated modular dynamical semigroup (MDS) guarantees for the positivity of the time evolved state the correct steady state properties, the positivity of the entropy production, and a positive Onsager matrix with symmetry relations arising from Green-Kubo formulas. We show that the celebrated Davies Lindblad generator, obtained through the Born and the secular approximations, generates a MDS. In doing so we also provide a nonlinear MDS which is supported by a weak coupling argument and is free from the limitations of the Davies generator.
Kroemer, H.
1981-06-15
The dissipation processes by which electrons and holes lose energy after being trapped in quantum wells might, in a sufficiently heavily pumped quantum well laser, lead to the buildup of such a high phonon population that phonon-assisted laser action by doubly stimulated emission of photons and phonons acquires a higher gain than unassisted laser action. The resulting mode switching exhibits a pronounced hysteresis with pump rate, which should be a characteristic identifying feature of phonon-assisted laser action.
NASA Astrophysics Data System (ADS)
Popova, E.; Gress, O.; Lipunov, V.; Gabovich, A.; Yurkov, V.; Sergienko, Yu.; Budnev, N.; Ivanov, K.; Gorbovskoy, E.; Tiurina, N.; Balanutsa, P.; Kuznetsov, A.; Kornilov, V.
2016-07-01
MASTER-Amur auto-detection system ( Lipunov et al., "MASTER Global Robotic Net", Advances in Astronomy, 2010, 349171 ) discovered OT source at (RA, Dec) = 05h 00m 02.2s +74d 04m 07.4s on 2016-07-06 16:47:02.264UT with unfiltered(0.2B2+0.8R2 calibrated to USNO B1) m_OT=16.9. The OT is seen on 6 images. There is no minor planet at this place.
ELECTRONIC MASTER SLAVE MANIPULATOR
Goertz, R.C.; Thompson, Wm.M.; Olsen, R.A.
1958-08-01
A remote control manipulator is described in which the master and slave arms are electrically connected to produce the desired motions. A response signal is provided in the master unit in order that the operator may sense a feel of the object and may not thereby exert such pressures that would ordinarily damage delicate objects. This apparatus will permit the manipulation of objects at a great distance, that may be viewed over a closed TV circuit, thereby permitting a remote operator to carry out operations in an extremely dangerous area with complete safety.
NASA Astrophysics Data System (ADS)
Liu, De-Yin; Tian, Bo; Sun, Wen-Rong; Wang, Yun-Po
2015-04-01
In this paper, an integrable higher-order nonlinear Schrödinger equation for a density-modulated quantum condensate is investigated. Based on the Ablowitz-Kaup-Newell-Segur system, an infinite number of conservation laws are obtained. Introducing an auxiliary function, we derive the bilinear forms and construct the dark-soliton solutions with the help of the Hirota method and symbolic computation. Dark one, two, and three solitons are analyzed graphically. Via asymptotic analysis, interactions between the two dark solitons are proved to be elastic. We see that the coefficients in the equation only affect the soliton velocity. We analyze the linear stability of the plane wave solutions in the presence of a small perturbation.
Lin, Yangzheng; Cohen, Ronald E.; Stackhouse, Stephen; Driver, Kevin P.; Militzer, Burkhard; Shulenburger, Luke; Kim, Jeongnim
2014-11-10
In this study, we have performed quantum Monte Carlo (QMC) simulations and density functional theory calculations to study the equations of state of MgSiO3 perovskite (Pv, bridgmanite) and post-perovskite (PPv) up to the pressure and temperature conditions of the base of Earth's lower mantle. The ground-state energies were derived using QMC simulations and the temperature-dependent Helmholtz free energies were calculated within the quasiharmonic approximation and density functional perturbation theory. The equations of state for both phases of MgSiO3 agree well with experiments, and better than those from generalized gradient approximation calculations. The Pv-PPv phase boundary calculated from our QMC equationsmore » of state is also consistent with experiments, and better than previous local density approximation calculations. Lastly, we discuss the implications for double crossing of the Pv-PPv boundary in the Earth.« less
Plane, J. M. C.; Whalley, C. L.; Goddard, A.; Frances-Soriano, L.; Harvey, J. N.; Glowacki, D. R.; Viggiano, A. A.
2012-07-07
complex, suggesting that this reaction proceeds mostly by near-resonant electronic energy transfer to Fe(a{sup 5}F) + O{sub 2}(X). The reaction of Ca + O{sub 2}(a) occurs in an intermediate regime with two competing pressure dependent channels: (1) a recombination to produce CaO{sub 2}({sup 1}A{sub 1}), and (2) a singlet/triplet non-adiabatic hopping channel leading to CaO + O({sup 3}P). In order to interpret the Ca + O{sub 2}(a) results, we utilized density functional theory along with multireference and explicitly correlated CCSD(T)-F12 electronic structure calculations to examine the lowest lying singlet and triplet surfaces. In addition to mapping stationary points, we used a genetic algorithm to locate minimum energy crossing points between the two surfaces. Simulations of the Ca + O{sub 2}(a) kinetics were then carried out using a combination of both standard and non-adiabatic Rice-Ramsperger-Kassel-Marcus (RRKM) theory implemented within a weak collision, multiwell master equation model. In terms of atmospheric significance, only in the case of Ca does reaction with O{sub 2}(a) compete with O{sub 3} during the daytime between 85 and 110 km.
ERIC Educational Resources Information Center
Clemson Univ., SC. Vocational Education Media Center.
This document is a collection of 43 overhead transparency masters to be used as teaching aids in a course of study involving soils such as geology, agronomy, hydrology, earth science, or land use study. Some transparencies are in color. Selected titles of transparencies may give the reader a better understanding of the graphic content. Titles are:…
ERIC Educational Resources Information Center
Kanter, Rosabeth Moss
1984-01-01
The change masters are identified as corporate managers who have the resources and the vision to effect an economic renaissance in the United States. Strategies for change should emphasize horizontal as well as vertical communication, and should reward enterprise and innovation at all levels. (JB)
ERIC Educational Resources Information Center
Comer, Gary L.
The Master Watershed Stewards (MWS) Program is a pilot project (developed through the cooperation of the Ohio State University Extension Logan and Hardin County Offices and the Indian Lake Watershed Project) offering the opportunity for communities to get involved at the local level to protect their water quality. The program grew out of the…
ERIC Educational Resources Information Center
Mulrooney, Virginia F.
The State of California, as it seeks to revise the Master Plan for Higher Education, is grappling with circumstances similar to those underpinning the revision of the United States' original Articles of Confederation. The delegates to the 1787 Constitutional Convention had to identify the task before them; determine how the country would be…
William Brickman, Master Teacher
ERIC Educational Resources Information Center
Swing, Elizabeth Sherman
2010-01-01
In this article, the author shares her encounter and relationship with William Brickman as her master teacher. William Brickman was her professor, her dissertation advisor, her mentor, and her friend. Her pursuit of a Ph.D. in late middle age may have seemed strange to friends, family, and some of her professors, but not to Brickman. She enrolled…
NASA Astrophysics Data System (ADS)
Balanutsa, P.; Lipunov, V.; Gorbovskoy, E.; Buckley, D.; Tiurina, N.; Kornilov, V.; Gress, O.; Kuznetsov, A.; Shumkov, V.; Vladimirov, V.; Gorbunov, I.; Vlasenko, D.; Potter, S.; Kotze, M.; Tlatov, A.; Senik, V.; Dormidontov, D.; Parkhomenko, A.
2016-02-01
MASTER-Kislovodsk auto-detection system ( Lipunov et al., 2010 ) discovered OT source at (RA, Dec) = 06h 33m 29.26s +38d 55m 09.2s on 2016-01-30.80899 UT. The OT unfiltered magnitude is 17.3 (the limit is 19.9m).
ERIC Educational Resources Information Center
Toh, Kok-Aun; Tsoi, Mun-Fie
2008-01-01
The dire need of some schools to boost the academic performance of their students inevitably rests with their ability to attract highly qualified teachers. As such, the UK has put in place the Advanced Skills Teacher (AST) scheme, while the US has set the ball rolling in laying down standards for the certification of the master science teacher, to…
Monitoring quantum transport: Backaction and measurement correlations
NASA Astrophysics Data System (ADS)
Hussein, Robert; Gómez-García, Jorge; Kohler, Sigmund
2014-10-01
We investigate a tunnel contact coupled to a double quantum dot (DQD) and employed as a charge monitor for the latter. We consider both the classical limit and the quantum regime. In the classical case, we derive measurement correlations from conditional probabilities, yielding quantitative statements about the parameter regime in which the detection scheme works well. Moreover, we demonstrate that not only the DQD occupation but also the corresponding current may strongly correlate with the detector current. The quantum-mechanical solution, obtained with a Bloch-Redfield master equation, shows that the backaction of the measurement tends to localize the DQD electrons, and thus significantly reduces the DQD current. Moreover, it provides the effective parameters of the classical treatment. It turns out that already the classical description is adequate for most operating regimes.
Non-Markovian quantum Brownian motion of a harmonic oscillator
Tang, J.
1994-02-01
We apply the density-matrix method to the study of quantum Brownian motion of a harmonic oscillator coupled to a heat bath, a system investigated previously by Caldeira and Leggett using a different method. Unlike the earlier work, in our derivation of the master equation the non-Markovian terms are maintained. Although the same model of interaction is used, discrepancy is found between their results and our equation in the Markovian limit. We also point out that the particular interaction model used by both works cannot lead to the phenomenological generalized Langevin theory of Kubo.
Supersymmetric quantum spin chains and classical integrable systems
NASA Astrophysics Data System (ADS)
Tsuboi, Zengo; Zabrodin, Anton; Zotov, Andrei
2015-05-01
For integrable inhomogeneous supersymmetric spin chains (generalized graded magnets) constructed employing Y( gl( N| M))-invariant R-matrices in finite-dimensional representations we introduce the master T-operator which is a sort of generating function for the family of commuting quantum transfer matrices. Any eigenvalue of the master T-operator is the tau-function of the classical mKP hierarchy. It is a polynomial in the spectral parameter which is identified with the 0-th time of the hierarchy. This implies a remarkable relation between the quantum supersymmetric spin chains and classical many-body integrable systems of particles of the Ruijsenaars-Schneider type. As an outcome, we obtain a system of algebraic equations for the spectrum of the spin chain Hamiltonians.
Quantum logics and chemical kinetics
NASA Astrophysics Data System (ADS)
Ivanov, C. I.
1981-06-01
A statistical theory of chemical kinetics is presented based on the quantum logical concept of chemical observables. The apparatus of Boolean algebra B is applied for the construction of appropriate composition polynomials referring to any stipulated arrangement of the atomic constituents. A physically motivated probability measure μ( F) is introduced on the field B of chemical observables, which considers the occurrence of the yes response of a given F ɛ B. The equations for the time evolution of the species density operators and the master equations for the corresponding number densities are derived. The general treatment is applied to a superposition of elementary substitution reactions (AB) α + C ⇄ (AC) β + B. The expressions for the reaction rate coefficients are established.
Inequivalence between the Schroedinger equation and the Madelung hydrodynamic equations
Wallstrom, T.C.
1994-03-01
By differentiating the Schroedinger equation and separating the real amd imaginary parts, one obtains the Madelung hydrodynamic equations, which have inspired numerous classical interpretations of quantum mechanics. Such interpretations frequently assume that these equations are equivalent to the Schroedinger equation, and thus provide an alternative basis for quantum mechanics. This paper proves that this is incorrect: to recover the Schroedinger equation, one must add by hand a quantization condition, as in the old quantum theory. The implications for various alternative interpretations of quantum mechanics are discussed.
Continuous quantum measurement in spin environments
NASA Astrophysics Data System (ADS)
Xie, Dong; Wang, An Min
2015-08-01
We derive a stochastic master equation (SME) which describes the decoherence dynamics of a system in spin environments conditioned on the measurement record. Markovian and non-Markovian nature of environment can be revealed by a spectroscopy method based on weak continuous quantum measurement. On account of that correlated environments can lead to a non-local open system which exhibits strong non-Markovian effects although the local dynamics are Markovian, the spectroscopy method can be used to demonstrate that there is correlation between two environments.
NASA Astrophysics Data System (ADS)
Danel, J.-F.; Kazandjian, L.
2015-01-01
We test two isothermal-isobaric mixing rules, respectively based on excess-pressure and total-pressure equilibration, applied to the equation of state of a dense plasma. While the equation of state is generally known for pure species, that of arbitrary mixtures is not available so that the validation of accurate mixing rules, that implies resorting to first-principles simulations, is very useful. Here we consider the case of a plastic with composition C2H3 and we implement two complementary ab initio approaches adapted to the dense plasma domain: quantum molecular dynamics, limited to low temperature by its computational cost, and orbital-free molecular dynamics, that can be implemented at high temperature. The temperature and density range considered is 1-10 eV and 0.6-10 g/cm 3 for quantum molecular dynamics, and 5-1000 eV and 1-10 g/cm 3 for orbital-free molecular dynamics. Simulations for the full C2H3 mixture are the benchmark against which to assess the mixing rules, and both pressure and internal energy are compared. We find that the mixing rule based on excess-pressure equilibration is overall more accurate than that based on total-pressure equilibration; except for quantum molecular dynamics and a thermodynamic domain characterized by very low or negative excess pressures, it gives pressures which are generally within statistical error or within 1% of the exact ones. Besides, its superiority is amplified in the calculation of a principal Hugoniot.
ERIC Educational Resources Information Center
Clark, Kelly
2004-01-01
In painting and drawing classes, it is typical to ask students to work directly from a master. It is one way to study composition techniques, and to become familiar with classical style firsthand. In museums, easels are set up as artists work, not in an attempt to copy or plagiarize, but in an attempt to be part of history by participating in it.…
Non-stochastic matrix Schrödinger equation for open systems
Joubert-Doriol, Loïc; Ryabinkin, Ilya G.; Izmaylov, Artur F.
2014-12-21
We propose an extension of the Schrödinger equation for a quantum system interacting with environment. This extension describes dynamics of a collection of auxiliary wavefunctions organized as a matrix m, from which the system density matrix can be reconstructed as ρ{sup ^}=mm{sup †}. We formulate a compatibility condition, which ensures that the reconstructed density satisfies a given quantum master equation for the system density. The resulting non-stochastic evolution equation preserves positive-definiteness of the system density and is applicable to both Markovian and non-Markovian system-bath treatments. Our formalism also resolves a long-standing problem of energy loss in the time-dependent variational principle applied to mixed states of closed systems.
Quantum state transfer in optomechanical arrays
NASA Astrophysics Data System (ADS)
de Moraes Neto, G. D.; Andrade, F. M.; Montenegro, V.; Bose, S.
2016-06-01
Quantum state transfer between distant nodes is at the heart of quantum processing and quantum networking. Stimulated by this, we propose a scheme where one can achieve quantum state transfer with a high fidelity between sites in a cavity quantum optomechanical network. In our lattice, each individual site is composed of a localized mechanical mode which interacts with a laser-driven cavity mode via radiation pressure, while photons hop between neighboring sites. After diagonalization of the Hamiltonian of each cell, we show that the system can be reduced to an effective Hamiltonian of two decoupled bosonic chains, and therefore we can apply the well-known results in quantum state transfer together with an additional condition on the transfer times. In fact, we show that our transfer protocol works for any arbitrary joint quantum state of a mechanical and an optical mode. Finally, in order to analyze a more realistic scenario we take into account the effects of independent thermal reservoirs for each site. By solving the standard master equation within the Born-Markov approximation, we reassure both the effective model and the feasibility of our protocol.
Driven harmonic oscillator as a quantum simulator for open systems
Piilo, Jyrki; Maniscalco, Sabrina
2006-09-15
We show theoretically how a driven harmonic oscillator can be used as a quantum simulator for the non-Markovian damped harmonic oscillator. In the general framework, our results demonstrate the possibility to use a closed system as a simulator for open quantum systems. The quantum simulator is based on sets of controlled drives of the closed harmonic oscillator with appropriately tailored electric field pulses. The non-Markovian dynamics of the damped harmonic oscillator is obtained by using the information about the spectral density of the open system when averaging over the drives of the closed oscillator. We consider single trapped ions as a specific physical implementation of the simulator, and we show how the simulator approach reveals physical insight into the open system dynamics, e.g., the characteristic quantum mechanical non-Markovian oscillatory behavior of the energy of the damped oscillator, usually obtained by the non-Lindblad-type master equation, can have a simple semiclassical interpretation.
NASA Astrophysics Data System (ADS)
Marvian, Milad; Lidar, Daniel
We investigate the performance of error suppression schemes for adiabatic quantum computation. Assuming a Markovian environment and using an adiabatic master equation we compare the rate of excitation from the ground subspace of the encoded Hamiltonian during the evolution to that of the unprotected Hamiltonian. For different forms of Markovian environments -- such as sub-Ohmic, Ohmic and super-Ohmic -- we identify the parameter thresholds for which encoding starts exhibiting its benefits.
NASA Astrophysics Data System (ADS)
Moreland, J. Scott; Soltz, Ron A.
2016-04-01
Hydrodynamic calculations of ultrarelativistic heavy-ion collisions are performed using the iebe-vishnu 2+1-dimensional code with fluctuating initial conditions and three different parametrizations of the lattice QCD equations of state: continuum extrapolations for stout and HISQ/tree actions, as well as the s95p-v1 parametrization based upon calculations using the p4 action. All parametrizations are matched to a hadron resonance gas equation of state at T =155 MeV, at which point the calculations are continued using the urqmd hadronic cascade. Simulations of √{sN N}=200 GeV Au+Au collisions in three centrality classes are used to quantify anisotropic flow developed in the hydrodynamic phase of the collision as well as particle spectra and pion Hanbury-Brown-Twiss (HBT) radii after hadronic rescattering, which are compared with experimental data. Experimental observables for the stout and HISQ/tree equations of state are observed to differ by less than a few percent for all observables, while the s95p-v1 equation of state generates spectra and flow coefficients which differ by ˜10 -20 % . Calculations in which the HISQ/tree equation of state is sampled from the published error distribution are also observed to differ by less than a few percent.
Generalized Quantum Theory and Mathematical Foundations of Quantum Field Theory
NASA Astrophysics Data System (ADS)
Maroun, Michael Anthony
This dissertation is divided into two main topics. The first is the generalization of quantum dynamics when the Schrodinger partial differential equation is not defined even in the weak mathematical sense because the potential function itself is a distribution in the spatial variable, the same variable that is used to define the kinetic energy operator, i.e. the Laplace operator. The procedure is an extension and broadening of the distributional calculus and offers spectral results as an alternative to the only other two known methods to date, namely a) the functional calculi; and b) non-standard analysis. Furthermore, the generalizations of quantum dynamics presented within give a resolution to the time asymmetry paradox created by multi-particle quantum mechanics due to the time evolution still being unitary. A consequence is the randomization of phases needed for the fundamental justification Pauli master equation. The second topic is foundations of the quantum theory of fields. The title is phrased as ``foundations'' to emphasize that there is no claim of uniqueness but rather a proposal is put forth, which is markedly different than that of constructive or axiomatic field theory. In particular, the space of fields is defined as a space of generalized functions with involutive symmetry maps (the CPT invariance) that affect the topology of the field space. The space of quantum fields is then endowed the Frechet property and interactions change the topology in such a way as to cause some field spaces to be incompatible with others. This is seen in the consequences of the Haag theorem. Various examples and discussions are given that elucidate a new view of the quantum theory of fields and its (lack of) mathematical structure.
Escobar, M.; Meyerovich, A. E.
2014-12-15
We discuss transport of particles along random rough surfaces in quantum size effect conditions. As an intriguing application, we analyze gravitationally quantized ultracold neutrons in rough waveguides in conjunction with GRANIT experiments (ILL, Grenoble). We present a theoretical description of these experiments in the biased diffusion approximation for neutron mirrors with both one- and two-dimensional (1D and 2D) roughness. All system parameters collapse into a single constant which determines the depletion times for the gravitational quantum states and the exit neutron count. This constant is determined by a complicated integral of the correlation function (CF) of surface roughness. The reliable identification of this CF is always hindered by the presence of long fluctuation-driven correlation tails in finite-size samples. We report numerical experiments relevant for the identification of roughness of a new GRANIT waveguide and make predictions for ongoing experiments. We also propose a radically new design for the rough waveguide.
NASA Astrophysics Data System (ADS)
Escobar, M.; Meyerovich, A. E.
2014-12-01
We discuss transport of particles along random rough surfaces in quantum size effect conditions. As an intriguing application, we analyze gravitationally quantized ultracold neutrons in rough waveguides in conjunction with GRANIT experiments (ILL, Grenoble). We present a theoretical description of these experiments in the biased diffusion approximation for neutron mirrors with both one- and two-dimensional (1D and 2D) roughness. All system parameters collapse into a single constant which determines the depletion times for the gravitational quantum states and the exit neutron count. This constant is determined by a complicated integral of the correlation function (CF) of surface roughness. The reliable identification of this CF is always hindered by the presence of long fluctuation-driven correlation tails in finite-size samples. We report numerical experiments relevant for the identification of roughness of a new GRANIT waveguide and make predictions for ongoing experiments. We also propose a radically new design for the rough waveguide.
NASA Astrophysics Data System (ADS)
Wang, Mingliang; Wong, Chung F.; Liu, Jianhong; Zhang, Peixin
2007-07-01
We have successfully coupled the Kohn-Sham with Poisson-Boltzmann equations to predict the solvation free energy, where the Kohn-Sham equations were solved by implementing the flexible pseudo atomic orbitals as in S IESTA package. It was found that the calculated solvation free energy is in good agreement with experimental results for small neutral molecules, and its standard error is 1.33 kcal/mol, the correlation coefficient is 0.97. Due to its high efficiency and accuracy, the proposed model can be a promising tool for computing solvation free energies in computer aided drug design in future.