Quantum fields versus strings at finite temperature
Osorio, M.A.R. . Lyman Lab. of Physics)
19920720
In this paper, the authors study some aspects of the relationship between the oneloop free energy of closed superstrings computed as a sum over the free energies of the quantum field present in the string (the analog model) and the modular invariant expression of the same quantity. In particular, by getting a generalized duality relation for the integrand of the modular invariant expression for the free energy of closed superstrings and using a regularization procedure, the authors connect the contribution to the vacuum energy from the bosonic degrees of freedom in the analog model (one half of the total number) with the coefficient governing the high temperature behavior of the free energy. The authors also study the physical meaning of this regularization and the role played by the leftright constraint defining the physical fields in the lightcone gauge.
Finite fielddependent symmetries in perturbative quantum gravity
Upadhyay, Sudhaker
20140115
In this paper we discuss the absolutely anticommuting nilpotent symmetries for perturbative quantum gravity in general curved spacetime in linear and nonlinear gauges. Further, we analyze the finite fielddependent BRST (FFBRST) transformation for perturbative quantum gravity in general curved spacetime. The FFBRST transformation changes the gaugefixing and ghost parts of the perturbative quantum gravity within functional integration. However, the operation of such symmetry transformation on the generating functional of perturbative quantum gravity does not affect the theory on physical ground. The FFBRST transformation with appropriate choices of finite BRST parameter connects nonlinear Curci–Ferrari and Landau gauges of perturbative quantum gravity. The validity of the results is also established at quantum level using Batalin–Vilkovisky (BV) formulation.  Highlights: •The perturbative quantum gravity is treated as gauge theory. •BRST and antiBRST transformations are developed in linear and nonlinear gauges. •BRST transformation is generalized by making it finite and field dependent. •Connection between linear and nonlinear gauges is established. •Using BV formulation the results are established at quantum level also.
Quantum electronvibrational dynamics at finite temperature: Thermo field dynamics approach.
Borrelli, Raffaele; Gelin, Maxim F
20161214
Quantum electronvibrational dynamics in molecular systems at finite temperature is described using an approach based on the thermo field dynamics theory. This formulation treats temperature effects in the Hilbert space without introducing the Liouville space. A comparison with the theoretically equivalent density matrix formulation shows the key numerical advantages of the present approach. The solution of thermo field dynamics equations with a novel technique for the propagation of tensor trains (matrix product states) is discussed. Numerical applications to model spinboson systems show that the present approach is a promising tool for the description of quantum dynamics of complex molecular systems at finite temperature.
The Quantum Hall Effect in Finite Magnetic Fields
NASA Astrophysics Data System (ADS)
Sondhi, Shivaji Lal
In the theory of the Quantum Hall Effect it is often technically and conceptually convenient to ignore terms in the Hamiltonian that scatter electrons between different Landau levels. Physically, this is equivalent to assuming the presence of an infinite magnetic field. This dissertation consists of three studies which move beyond this approximation. The first study considers the effects of including Landau level mixing on the structure of the quasiparticles and on the ground state correlation functions. By means of perturbation theory in the interactions and by using the LandauGinzburg theory of the Hall Effect it is shown that for Coulomb (1/r) interactions the asymptotic long distance behavior of the charge and current profiles of the quasiparticles and of the correlation functions becomes algebraic when Landau level mixing is included and is therefore greatly altered from the exponential behavior in the infinite field limit. Among the consequences is that the quasiparticle charge in experimental geometries is not quantized as precisely as the Hall conductance. The long range of the quasiparticle current distribution makes the angular momentum of an isolated quasiparticle illdefined and thus appears to rule out a spinstatistics connection in the Hall Effect. The second study is concerned with the Quantum Hall Effect at odd integer filling factors, and at nu = 1/3 and 1/5, in a parameter space characterized by an arbitrary ratio of the Zeeman gap to the typical interaction energy. It is shown that the system is incompressible, even when the Zeeman gap vanishes. However the quasiparticles are very different in different regimes. When the Zeeman gap is large they are microscopic but in the limit of a vanishing Zeeman gap they are Skyrmionsspatially unbounded distortions of the spin density. Exact asymptotic results for the size, spin and energy of these excitations at small Zeeman energies are presented. The last study examines the problem of rigorously
The density of states approach for the simulation of finite density quantum field theories
NASA Astrophysics Data System (ADS)
Langfeld, K.; Lucini, B.; Rago, A.; Pellegrini, R.; Bongiovanni, L.
20150701
Finite density quantum field theories have evaded first principle MonteCarlo simulations due to the notorious signproblem. The partition function of such theories appears as the Fourier transform of the generalised densityofstates, which is the probability distribution of the imaginary part of the action. With the advent of WangLandau type simulation techniques and recent advances [1], the densityofstates can be calculated over many hundreds of orders of magnitude. Current research addresses the question whether the achieved precision is high enough to reliably extract the finite density partition function, which is exponentially suppressed with the volume. In my talk, I review the stateofplay for the high precision calculations of the densityofstates as well as the recent progress for obtaining reliable results from highly oscillating integrals. I will review recent progress for the Z3 quantum field theory for which results can be obtained from the simulation of the dual theory, which appears to free of a sign problem.
Finitefrequencydependent noise of a quantum dot in a magnetic field
NASA Astrophysics Data System (ADS)
Moca, C. P.; Simon, P.; Chung, ChungHou; Zaránd, G.
20140401
We present a detailed study for the finitefrequency current noise of a Kondo quantum dot in the presence of a magnetic field by using a recently developed realtime functional renormalization group approach [C. P. Moca, P. Simon, C. H. Chung, and G. Zaránd, Phys. Rev. B 83, 201303(R) (2011), 10.1103/PhysRevB.83.201303]. The scaling equations are modified in an external magnetic field; the couplings and nonlocal current vertices become strongly anisotropic, and develop new singularities. Consequently, in addition to the natural emission threshold frequency, ℏω =eV, a corresponding singular behavior is found to emerge in the noise spectrum at frequencies ℏω ≈eV±B. The predicted singularities are measurable with presentday experimental techniques.
NASA Astrophysics Data System (ADS)
Ban, Yue; Chen, Xi; Li, ChunFang
20070401
We investigate the controllable negative and positive group delay in transmission through a single quantum well at the finite longitudinal magnetic fields. It is shown that the magnetocoupling effect between the longitudinal motion component and the transverse Landau orbits plays an important role in the group delay. The group delay depends not only on the width of potential well and the incident energy, but also on the magneticfield strengthen and the Landau quantum number. The results show that the group delay can be changed from positive to negative by the modulation of the magnetic field. These interesting phenomena may lead to the tunable quantum mechanical delay line.
Quantum memories at finite temperature
NASA Astrophysics Data System (ADS)
Brown, Benjamin J.; Loss, Daniel; Pachos, Jiannis K.; Self, Chris N.; Wootton, James R.
20161001
To use quantum systems for technological applications one first needs to preserve their coherence for macroscopic time scales, even at finite temperature. Quantum error correction has made it possible to actively correct errors that affect a quantum memory. An attractive scenario is the construction of passive storage of quantum information with minimal active support. Indeed, passive protection is the basis of robust and scalable classical technology, physically realized in the form of the transistor and the ferromagnetic hard disk. The discovery of an analogous quantum system is a challenging open problem, plagued with a variety of nogo theorems. Several approaches have been devised to overcome these theorems by taking advantage of their loopholes. The stateoftheart developments in this field are reviewed in an informative and pedagogical way. The main principles of selfcorrecting quantum memories are given and several milestone examples from the literature of two, three and higherdimensional quantum memories are analyzed.
Brownian motion and finite approximations of quantum systems over local fields
NASA Astrophysics Data System (ADS)
Bakken, Erik Makino; Digernes, Trond; Weisbart, David
We give a stochastic proof of the finite approximability of a class of Schrödinger operators over a local field, thereby completing a program of establishing in a nonArchimedean setting corresponding results and methods from the Archimedean (real) setting. A key ingredient of our proof is to show that Brownian motion over a local field can be obtained as a limit of random walks over finite grids. Also, we prove a FeynmanKac formula for the finite systems, and show that the propagator at the finite level converges to the propagator at the infinite level.
Finitetemperature scaling at the quantum critical point of the Ising chain in a transverse field
NASA Astrophysics Data System (ADS)
Haelg, Manuel; Huvonen, Dan; Guidi, Tatiana; QuinteroCastro, Diana Lucia; Boehm, Martin; Regnault, LouisPierre; Zheludev, Andrey
20150301
Inelastic neutron scattering is used to study the finitetemperature scaling behavior of spin correlations at the quantum critical point in an experimental realization of the onedimensional Ising model in a transverse field. The target compound is the wellcharacterized, anisotropic and bondalternating Heisenberg spin1 chain material NTENP. The validity and the limitations of the dynamic structure factor scaling are tested, discussed and compared to theoretical predictions. For this purpose neutron data have been collected on the threeaxes spectrometers IN14 at ILL and FLEXX at HZB as well as on the time of flight multichopper spectrometer LET at ISIS. In addition to the general statement about quantum criticality and universality, present study also reveals new insight into the properties of the spin chain compound NTENP in particular.
NASA Astrophysics Data System (ADS)
Çakır, Bekir; Yakar, Yusuf; Özmen, Ayhan
20170901
The magnetic effects on the energy states and binding energies of the ground and higher excited states of the spherical quantum dot are studied theoretically for various potential depths. Also, Zeeman transition energies in the case of ΔM = 0, ±1 are carried out. The results show that the energy states and binding energies in small dot radii are insensitive to the increase of magnetic field. In the case of negative m, in the strong confinement region, the binding energy increases as the confinement potential decreases. In the case of positive m, the binding energy decreases with the decrease of the confinement potential.
Quantum dots with even number of electrons: kondo effect in a finite magnetic field
Pustilnik; Avishai; Kikoin
20000221
We show that the Kondo effect can be induced by an external magnetic field in quantum dots with an even number of electrons. If the Zeeman energy B is close to the singleparticle level spacing Delta in the dot, the scattering of the conduction electrons from the dot is dominated by an anisotropic exchange interaction. A Kondo resonance then occurs despite the fact that B exceeds by far the Kondo temperature T(K). As a result, at low temperatures T
Finite groups and quantum physics
Kornyak, V. V.
20130215
Concepts of quantum theory are considered from the constructive 'finite' point of view. The introduction of a continuum or other actual infinities in physics destroys constructiveness without any need for them in describing empirical observations. It is shown that quantum behavior is a natural consequence of symmetries of dynamical systems. The underlying reason is that it is impossible in principle to trace the identity of indistinguishable objects in their evolutiononly information about invariant statements and values concerning such objects is available. General mathematical arguments indicate that any quantum dynamics is reducible to a sequence of permutations. Quantum phenomena, such as interference, arise in invariant subspaces of permutation representations of the symmetry group of a dynamical system. Observable quantities can be expressed in terms of permutation invariants. It is shown that nonconstructive number systems, such as complex numbers, are not needed for describing quantum phenomena. It is sufficient to employ cyclotomic numbersa minimal extension of natural numbers that is appropriate for quantum mechanics. The use of finite groups in physics, which underlies the present approach, has an additional motivation. Numerous experiments and observations in the particle physics suggest the importance of finite groups of relatively small orders in some fundamental processes. The origin of these groups is unclear within the currently accepted theoriesin particular, within the Standard Model.
Quantum oneway permutation over the finite field of two elements
NASA Astrophysics Data System (ADS)
de Castro, Alexandre
20170601
In quantum cryptography, a oneway permutation is a bounded unitary operator U:{H} → {H} on a Hilbert space {H} that is easy to compute on every input, but hard to invert given the image of a random input. Levin (Probl Inf Transm 39(1):92103, 2003) has conjectured that the unitary transformation g(a,x)=(a,f(x)+ax), where f is any lengthpreserving function and a,x \\in {GF}_{{2}^{\\Vert x\\Vert }}, is an informationtheoretically secure operator within a polynomial factor. Here, we show that Levin's oneway permutation is provably secure because its output values are four maximally entangled twoqubit states, and whose probability of factoring them approaches zero faster than the multiplicative inverse of any positive polynomial poly( x) over the Boolean ring of all subsets of x. Our results demonstrate through wellknown theorems that existence of classical oneway functions implies existence of a universal quantum oneway permutation that cannot be inverted in subexponential time in the worst case.
Role of dissipation in biasing the vacuum selection in quantum field theory at finite temperature
Freire, F.; Achucarro, A.; Antunes, N.D.; Salmi, P.
20050815
We study the symmetry breaking pattern of an O(4) symmetric model of scalar fields, with both charged and neutral fields, interacting with a photon bath. Nagasawa and Brandenberger argued that in favorable circumstances the vacuum manifold would be reduced from S{sup 3} to S{sup 1}. Here it is shown that a selective condensation of the neutral fields, that are not directly coupled to photons, can be achieved in the presence of a minimal external dissipation, i.e. not related to interactions with a bath. This should be relevant in the early universe or in heavyion collisions where dissipation occurs due to expansion.
Finite quantum theory of the harmonic oscillator
NASA Astrophysics Data System (ADS)
ShiriGarakani, Mohsen
We apply the Segal process of group simplification to the linear harmonic oscillator. The result is a finite quantum theory with three quantum constants h, h', h″ instead of the usual one. We compare the classical (CLHO), quantum (QLHO), and finite (FLHO) linear harmonic oscillators and their canonical or unitary groups. The FLHO is isomorphic to a dipole rotator with N = l(l + 1) ˜ 1/(h ' h″) states and Hamiltonian H = A(Lx)2 + B(Ly)2, and the physically interesting case has N ≫ 1. The position and momentum variables are quantized with uniform finite spectra. For fixed quantum constants and large N ≫ 1 there are three broad classes of FLHO: soft, medium, and hard, with B/A ≪ 1, B/A ˜ 1, and B/A ≫ 1 respectively. The field oscillators responsible for infrared and ultraviolet divergences are soft and hard respectively. Medium oscillators have B/A ˜ 1 and approximate the QLHO. They have ˜ N lowlying states with nearly the same zeropoint energy and level spacing as the QLHO, and nearly obeying the Heisenberg uncertainty principle and the equipartition principle. The corresponding rotators are nearly polarized along the z axis with Lz ˜ +/l. The soft and hard FLHO's have infinitesimal 0point energy and grossly violate equipartition and the Heisenberg uncertainty principle. They do not resemble the QLHO at all. Their lowlying energy states correspond to rotators with Lx ˜ 0 or Ly ˜ 0 instead of Lz ˜ +/l. Soft oscillators have frozen momentum, because their maximum potential energy is too small to produce one quantum of momentum. Hard oscillators have frozen position, because their maximum kinetic energy is too small to excite one quantum of position.
Schuler, Michael; Whitsitt, Seth; Henry, LouisPaul; Sachdev, Subir; Läuchli, Andreas M
20161118
The lowenergy spectra of many body systems on a torus, of finite size L, are well understood in magnetically ordered and gapped topological phases. However, the spectra at quantum critical points separating such phases are largely unexplored for (2+1)D systems. Using a combination of analytical and numerical techniques, we accurately calculate and analyze the lowenergy torus spectrum at an Ising critical point which provides a universal fingerprint of the underlying quantum field theory, with the energy levels given by universal numbers times 1/L. We highlight the implications of a neighboring topological phase on the spectrum by studying the Ising* transition (i.e. the transition between a Z_{2} topological phase and a trivial paramagnet), in the example of the toric code in a longitudinal field, and advocate a phenomenological picture that provides qualitative insight into the operator content of the critical field theory.
NASA Astrophysics Data System (ADS)
Schuler, Michael; Whitsitt, Seth; Henry, LouisPaul; Sachdev, Subir; Läuchli, Andreas M.
20161101
The lowenergy spectra of many body systems on a torus, of finite size L , are well understood in magnetically ordered and gapped topological phases. However, the spectra at quantum critical points separating such phases are largely unexplored for (2 +1 )D systems. Using a combination of analytical and numerical techniques, we accurately calculate and analyze the lowenergy torus spectrum at an Ising critical point which provides a universal fingerprint of the underlying quantum field theory, with the energy levels given by universal numbers times 1 /L . We highlight the implications of a neighboring topological phase on the spectrum by studying the Ising* transition (i.e. the transition between a Z2 topological phase and a trivial paramagnet), in the example of the toric code in a longitudinal field, and advocate a phenomenological picture that provides qualitative insight into the operator content of the critical field theory.
Finitesize scaling at quantum transitions
NASA Astrophysics Data System (ADS)
Campostrini, Massimo; Pelissetto, Andrea; Vicari, Ettore
20140301
We develop the finitesize scaling (FSS) theory at quantum transitions. We consider various boundary conditions, such as open and periodic boundary conditions, and characterize the corrections to the leading FSS behavior. Using renormalizationgroup (RG) theory, we generalize the classical scaling ansatz to describe FSS in the quantum case, classifying the different sources of scaling corrections. We identify nonanalytic corrections due to irrelevant (bulk and boundary) RG perturbations and analytic contributions due to regular backgrounds and analytic expansions of the nonlinear scaling fields. To check the general predictions, we consider the quantum XY chain in a transverse field. For this model exact or numerically accurate results can be obtained by exploiting its fermionic quadratic representation. We study the FSS of several observables, such as the free energy, the energy differences between lowenergy levels, correlation functions of the order parameter, etc., confirming the general predictions in all cases. Moreover, we consider bipartite entanglement entropies, which are characterized by the presence of additional scaling corrections, as predicted by conformal field theory.
Electron Dynamics in Finite Quantum Systems
NASA Astrophysics Data System (ADS)
McDonald, Christopher R.
The multiconfiguration timedependent HartreeFock (MCTDHF) and multiconfiguration timedependent Hartree (MCTDH) methods are employed to investigate nonperturbative multielectron dynamics in finite quantum systems. MCTDHF is a powerful tool that allows for the investigation of multielectron dynamics in strongly perturbed quantum systems. We have developed an MCTDHF code that is capable of treating problems involving three dimensional (3D) atoms and molecules exposed to strong laser fields. This code will allow for the theoretical treatment of multielectron phenomena in attosecond science that were previously inaccessible. These problems include complex ionization processes in pumpprobe experiments on noble gas atoms, the nonlinear effects that have been observed in Ne atoms in the presence of an xray freeelectron laser (XFEL) and the molecular rearrangement of cations after ionization. An implementation of MCTDH that is optimized for two electrons, each moving in two dimensions (2D), is also presented. This implementation of MCTDH allows for the efficient treatment of 2D spinfree systems involving two electrons; however, it does not scale well to 3D or to systems containing more that two electrons. Both MCTDHF and MCTDH were used to treat 2D problems in nanophysics and attosecond science. MCTDHF is used to investigate plasmon dynamics and the quantum breathing mode for several electrons in finite lateral quantum dots. MCTDHF is also used to study the effects of manipulating the potential of a double lateral quantum dot containing two electrons; applications to quantum computing are discussed. MCTDH is used to examine a diatomic model molecular system exposed to a strong laser field; nonsequential double ionization and high harmonic generation are studied and new processes identified and explained. An implementation of MCTDHF is developed for nonuniform tensor product grids; this will allow for the full 3D implementation of MCTDHF and will provide a means to
Quantum coding with finite resources
Tomamichel, Marco; Berta, Mario; Renes, Joseph M.
20160101
The quantum capacity of a memoryless channel determines the maximal rate at which we can communicate reliably over asymptotically many uses of the channel. Here we illustrate that this asymptotic characterization is insufficient in practical scenarios where decoherence severely limits our ability to manipulate large quantum systems in the encoder and decoder. In practical settings, we should instead focus on the optimal tradeoff between three parameters: the rate of the code, the size of the quantum devices at the encoder and decoder, and the fidelity of the transmission. We find approximate and exact characterizations of this tradeoff for various channels of interest, including dephasing, depolarizing and erasure channels. In each case, the tradeoff is parameterized by the capacity and a second channel parameter, the quantum channel dispersion. In the process, we develop several bounds that are valid for general quantum channels and can be computed for small instances. PMID:27156995
NASA Astrophysics Data System (ADS)
Banks, Tom
20080901
1. Introduction; 2. Quantum theory of free scalar fields; 3. Interacting field theory; 4. Particles of spin one, and gauge invariance; 5. Spin 1/2 particles and Fermi statistics; 6. Massive quantum electrodynamics; 7. Symmetries, Ward identities and Nambu Goldstone bosons; 8. Nonabelian gauge theory; 9. Renormalization and effective field theory; 10. Instantons and solitons; 11. Concluding remarks; Appendices; References; Index.
Estimation of quantum finite mixtures
Vicente, J. I. de; Calsamiglia, J.; MunozTapia, R.; Bagan, E.
20100115
We consider the problem of determining the weights of a quantum ensemble. That is to say, given a quantum system that is in a set of possible known states according to an unknown probability law, we give strategies to estimate the individual probabilities, weights, or mixing proportions. Such strategies can be used to estimate the frequencies at which different independent signals are emitted by a source. They can also be used to estimate the weights of particular terms in a canonical decomposition of a quantum channel. The quality of these strategies is quantified by a covariancetype error matrix. According with this cost function, we give optimal strategies in both the singleshot and multiplecopy scenarios. The latter is also analyzed in the asymptotic limit of large number of copies. We give closed expressions of the error matrix for twocomponent quantum mixtures of qubit systems. The Fisher information plays an unusual role in the problem at hand, providing exact expressions of the minimum covariance matrix for any number of copies.
Finitesize scaling at the firstorder quantum transitions of quantum Potts chains.
Campostrini, Massimo; Nespolo, Jacopo; Pelissetto, Andrea; Vicari, Ettore
20150501
We investigate finitesize effects at firstorder quantum transitions. For this purpose we consider the onedimensional qstate quantum Potts chain, in particular with q=10, which undergoes a firstorder transition, separating the quantum disordered and ordered phases with a discontinuity in the energy density of the ground state. In agreement with the general theory, around the transition the lowenergy properties show finitesize scaling with respect to appropriate scaling variables. Their size dependence is particularly sensitive to boundary conditions, which is a specific feature of firstorder quantum transitions. Finally, we also discuss the finitesize behavior of the qstate Potts model (q≥2) at the firstorder transitions driven by a parallel magnetic field, occurring in the ferromagnetic phase.
Trapped modes in finite quantum waveguides
NASA Astrophysics Data System (ADS)
Delitsyn, A. L.; Nguyen, B. T.; Grebenkov, D. S.
20120601
The eigenstates of an electron in an infinite quantum waveguide (e.g., a bent strip or a twisted tube) are often trapped or localized in a bounded region that prohibits the electron transmission through the waveguide at the corresponding energies. We revisit this statement for resonators with long but finite branches that we call "finite waveguides". Although the Laplace operator in bounded domains has no continuous spectrum and all eigenfunctions have finite L2 norm, the trapping of an eigenfunction can be understood as its exponential decay inside the branches. We describe a general variational formalism for detecting trapped modes in such resonators. For finite waveguides with general cylindrical branches, we obtain a sufficient condition which determines the minimal length of branches for getting a trapped eigenmode. Varying the branch lengths may switch certain eigenmodes from nontrapped to trapped or, equivalently, the waveguide state from conducting to insulating. These concepts are illustrated for several typical waveguides (Lshape, bent strip, crossing of two strips, etc.). We conclude that the wellestablished theory of trapping in infinite waveguides may be incomplete and require further development for applications to finitesize microscopic quantum devices.
High resolution finite volume scheme for the quantum hydrodynamic equations
NASA Astrophysics Data System (ADS)
Lin, ChinTien; Yeh, JiaYi; Chen, JiunYeu
20090301
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 thirdorder modified OsherChakravarthy (MOC) upwindcentered finite volume scheme was constructed for conservation law to evaluate the convective terms, and a secondorder central finite volume scheme was used to map the quantum potential field. An explicit RungeKutta 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 twodimensional particle motions were
High resolution finite volume scheme for the quantum hydrodynamic equations
Lin, C.T. Yeh, J.Y. Chen, J.Y.
20090320
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 thirdorder modified OsherChakravarthy (MOC) upwindcentered finite volume scheme was constructed for conservation law to evaluate the convective terms, and a secondorder central finite volume scheme was used to map the quantum potential field. An explicit RungeKutta 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{sup 5} to 10{sup 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{sup 4}. To check the QFD finite difference numerical computations, one and twodimensional particle
NASA Astrophysics Data System (ADS)
TylanTyler, Anthony
The [special characters omitted] fractional quantum Hall effect (FQHE) is a unique and interesting experimental and theoretical state. A great deal of experimental, theoretical and numerical work suggests that this state may support quasihole excitations with nonAbelian statistics, where the order of particle exchange influences the final state of the system. Thus, the [special characters omitted] FQHE offers a system in which the properties of the particles may be explored experimentally and theoretically. Additionally, by controlling the exchange of such particles, it is possible to create a topologicallyprotected quantum computer. In order to make this possible, however, we must first understand the nature of the ground state. The two leading candidates, the MooreRead Pfaffian and the antiPfaffian, both support nonAbelian excitations, but there has not been a clear answer for which state is realized in experiment. In the present work, we present results of exact diagaonlization calculations which strive to answer this question using a disk geometry. What we find is that the ground state of the system is dependent upon device specific quantities and thus we may be able to engineer samples which will have specific ground state properties.
Finitesize scaling for quantum criticality using the finiteelement method.
Antillon, Edwin; WehefritzKaufmann, Birgit; Kais, Sabre
20120301
Finite size scaling for the Schrödinger equation is a systematic approach to calculate the quantum critical parameters for a given Hamiltonian. This approach has been shown to give very accurate results for critical parameters by using a systematic expansion with global basistype functions. Recently, the finiteelement method was shown to be a powerful numerical method for ab initio electronicstructure calculations with a variable realspace resolution. In this work, we demonstrate how to obtain quantum critical parameters by combining the finiteelement method (FEM) with finite size scaling (FSS) using different ab initio approximations and exact formulations. The critical parameters could be atomic nuclear charges, internuclear distances, electron density, disorder, lattice structure, and external fields for stability of atomic, molecular systems and quantum phase transitions of extended systems. To illustrate the effectiveness of this approach we provide detailed calculations of applying FEM to approximate solutions for the twoelectron atom with varying nuclear charge; these include HartreeFock, local density approximation, and an "exact" formulation using FEM. We then use the FSS approach to determine its critical nuclear charge for stability; here, the size of the system is related to the number of elements used in the calculations. Results prove to be in good agreement with previous Slaterbasis set calculations and demonstrate that it is possible to combine finite size scaling with the finiteelement method by using ab initio calculations to obtain quantum critical parameters. The combined approach provides a promising firstprinciples approach to describe quantum phase transitions for materials and extended systems.
Critical properties of dissipative quantum spin systems in finite dimensions
NASA Astrophysics Data System (ADS)
Takada, Kabuki; Nishimori, Hidetoshi
20161001
We study the critical properties of finitedimensional dissipative quantum spin systems with uniform ferromagnetic interactions. Starting from the transverse field Ising model coupled to a bath of harmonic oscillators with Ohmic spectral density, we generalize its classical representation to classical spin systems with O(n) symmetry and then take the largen limit to reduce the system to a spherical model. The exact solution to the resulting spherical model with longrange interactions along the imaginary time axis shows a phase transition with static critical exponents coinciding with those of the conventional shortrange spherical model in d+2 dimensions, where d is the spatial dimensionality of the original quantum system. This implies that the dynamical exponent is z = 2. These conclusions are consistent with the results of Monte Carlo simulations and renormalization group calculations for dissipative transverse field Ising and O(n) models in one and two dimensions. The present approach therefore serves as a useful tool for analytically investigating the properties of quantum phase transitions of the dissipative transverse field Ising and other related models. Our method may also offer a platform to study more complex phase transitions in dissipative finitedimensional quantum spin systems, which have recently received renewed interest in the context of quantum annealing in a noisy environment.
Finite Quantum Tomography and Semidefinite Programming
NASA Astrophysics Data System (ADS)
Mirzaee, M.; Rezaee, M.; Jafarizadeh, M. A.
20070601
Using the convex semidefinite programming method and superoperator formalism we obtain the finite quantum tomography of some mixed quantum states such as: truncated coherent states tomography, phase tomography and coherent spin state tomography, qudit tomography, Nqubit tomography, where that obtained results are in agreement with those of References (Buzek et al., Chaos, Solitons and Fractals 10 (1999) 981; Schack and Caves, Separable states of N quantum bits. In: Proceedings of the X. International Symposium on Theoretical Electrical Engineering, 73. W. Mathis and T. Schindler, eds. OttovonGuericke University of Magdeburg, Germany (1999); Pegg and Barnett Physical Review A 39 (1989) 1665; Barnett and Pegg Journal of Modern Optics 36 (1989) 7; St. Weigert Acta Physica Slov. 4 (1999) 613).
Quantum Monte Carlo finite temperature electronic structure of quantum dots
NASA Astrophysics Data System (ADS)
Leino, Markku; Rantala, Tapio T.
20020801
Quantum Monte Carlo methods allow a straightforward procedure for evaluation of electronic structures with a proper treatment of electronic correlations. This can be done even at finite temperatures [1]. We test the Path Integral Monte Carlo (PIMC) simulation method [2] for one and two electrons in one and three dimensional harmonic oscillator potentials and apply it in evaluation of finite temperature effects of single and coupled quantum dots. Our simulations show the correct finite temperature excited state populations including degeneracy in cases of one and three dimensional harmonic oscillators. The simulated one and two electron distributions of a single and coupled quantum dots are compared to those from experiments and other theoretical (0 K) methods [3]. Distributions are shown to agree and the finite temperature effects are discussed. Computational capacity is found to become the limiting factor in simulations with increasing accuracy. Other essential aspects of PIMC and its capability in this type of calculations are also discussed. [1] R.P. Feynman: Statistical Mechanics, Addison Wesley, 1972. [2] D.M. Ceperley, Rev.Mod.Phys. 67, 279 (1995). [3] M. Pi, A. Emperador and M. Barranco, Phys.Rev.B 63, 115316 (2001).
Quantum key distribution for composite dimensional finite systems
NASA Astrophysics Data System (ADS)
Shalaby, Mohamed; Kamal, Yasser
20170601
The application of quantum mechanics contributes to the field of cryptography with very important advantage as it offers a mechanism for detecting the eavesdropper. The pioneering work of quantum key distribution uses mutually unbiased bases (MUBs) to prepare and measure qubits (or qudits). Weak mutually unbiased bases (WMUBs) have weaker properties than MUBs properties, however, unlike MUBs, a complete set of WMUBs can be constructed for systems with composite dimensions. In this paper, we study the use of weak mutually unbiased bases (WMUBs) in quantum key distribution for composite dimensional finite systems. We prove that the security analysis of using a complete set of WMUBs to prepare and measure the quantum states in the generalized BB84 protocol, gives better results than using the maximum number of MUBs that can be constructed, when they are analyzed against the intercept and resend attack.
NASA Astrophysics Data System (ADS)
Steffens, A.; Riofrío, C. A.; Hübener, R.; Eisert, J.
20141201
We introduce the concept of quantum field tomography, the efficient and reliable reconstruction of unknown quantum fields based on data of correlation functions. At the basis of the analysis is the concept of continuous matrix product states (cMPS), a complete set of variational states grasping states in onedimensional quantum field theory. We innovate a practical method, making use of and developing tools in estimation theory used in the context of compressed sensing such as Prony methods and matrix pencils, allowing us to faithfully reconstruct quantum field states based on loworder correlation functions. In the absence of a phase reference, we highlight how specific higher order correlation functions can still be predicted. We exemplify the functioning of the approach by reconstructing randomized cMPS from their correlation data and study the robustness of the reconstruction for different noise models. Furthermore, we apply the method to data generated by simulations based on cMPS and using the timedependent variational principle. The presented approach is expected to open up a new window into experimentally studying continuous quantum systems, such as those encountered in experiments with ultracold atoms on top of atom chips. By virtue of the analogy with the inputoutput formalism in quantum optics, it also allows for studying open quantum systems.
Quantum cellular automata and free quantum field theory
NASA Astrophysics Data System (ADS)
D'Ariano, Giacomo Mauro; Perinotti, Paolo
20170201
In a series of recent papers [14] it has been shown how free quantum field theory can be derived without using mechanical primitives (including spacetime, special relativity, quantization rules, etc.), but only considering the easiest quantum algorithm encompassing a countable set of quantum systems whose network of interactions satisfies the simple principles of unitarity, homogeneity, locality, and isotropy. This has opened the route to extending the axiomatic informationtheoretic derivation of the quantum theory of abstract systems [5, 6] to include quantum field theory. The inherent discrete nature of the informational axiomatization leads to an extension of quantum field theory to a quantum cellular automata theory, where the usual field theory is recovered in a regime where the discrete structure of the automata cannot be probed. A simple heuristic argument sets the scale of discreteness to the Planck scale, and the customary physical regime where discreteness is not visible is the relativistic one of small wavevectors. In this paper we provide a thorough derivation from principles that in the most general case the graph of the quantum cellular automaton is the Cayley graph of a finitely presented group, and showing how for the case corresponding to Euclidean emergent space (where the group resorts to an Abelian one) the automata leads to Weyl, Dirac and Maxwell field dynamics in the relativistic limit. We conclude with some perspectives towards the more general scenario of nonlinear automata for interacting quantum field theory.
Leastsquares finite element methods for quantum chromodynamics
Ketelsen, Christian; Brannick, J; Manteuffel, T; Mccormick, S
20080101
A significant amount of the computational time in large Monte Carlo simulations of lattice quantum chromodynamics (QCD) is spent inverting the discrete Dirac operator. Unfortunately, traditional covariant finite difference discretizations of the Dirac operator present serious challenges for standard iterative methods. For interesting physical parameters, the discretized operator is large and illconditioned, and has random coefficients. More recently, adaptive algebraic multigrid (AMG) methods have been shown to be effective preconditioners for Wilson's discretization of the Dirac equation. This paper presents an alternate discretization of the Dirac operator based on leastsquares finite elements. The discretization is systematically developed and physical properties of the resulting matrix system are discussed. Finally, numerical experiments are presented that demonstrate the effectiveness of adaptive smoothed aggregation ({alpha}SA ) multigrid as a preconditioner for the discrete field equations resulting from applying the proposed leastsquares FE formulation to a simplified test problem, the 2d Schwinger model of quantum electrodynamics.
Diffeomorphisms of Quantum Fields
NASA Astrophysics Data System (ADS)
Kreimer, Dirk; Yeats, Karen
20170601
We study field diffeomorphisms φ (x)\\to F(φ (x))=a0φ (x)+a1φ 2(x)+\\ldots ={\\sum }_{j+0}^{\\infty } aj φ ^{j+1}, for free and interacting quantum fields Φ. We find that the theory is invariant under such diffeomorphisms if and only if kinematic renormalization schemes are used.
Reverse engineering quantum field theory
NASA Astrophysics Data System (ADS)
Oeckl, Robert
20121201
An approach to the foundations of quantum theory is advertised that proceeds by "reverse engineering" quantum field theory. As a concrete instance of this approach, the general boundary formulation of quantum theory is outlined.
Quantum emitters dynamically coupled to a quantum field
NASA Astrophysics Data System (ADS)
Acevedo, O. L.; Quiroga, L.; Rodríguez, F. J.; Johnson, N. F.
20131201
We study theoretically the dynamical response of a set of solidstate quantum emitters arbitrarily coupled to a singlemode microcavity system. Ramping the matterfield coupling strength in round trips, we quantify the hysteresis or irreversible quantum dynamics. The matterfield system is modeled as a finitesize Dicke model which has previously been used to describe equilibrium (including quantum phase transition) properties of systems such as quantum dots in a microcavity. Here we extend this model to address nonequilibrium situations. Analyzing the system's quantum fidelity, we find that the nearadiabatic regime exhibits the richest phenomena, with a strong asymmetry in the internal collective dynamics depending on which phase is chosen as the starting point. We also explore signatures of the crossing of the critical points on the radiation subsystem by monitoring its Wigner function; then, the subsystem can exhibit the emergence of nonclassicality and complexity.
Quantum emitters dynamically coupled to a quantum field
Acevedo, O. L.; Quiroga, L.; Rodríguez, F. J.; Johnson, N. F.
20131204
We study theoretically the dynamical response of a set of solidstate quantum emitters arbitrarily coupled to a singlemode microcavity system. Ramping the matterfield coupling strength in round trips, we quantify the hysteresis or irreversible quantum dynamics. The matterfield system is modeled as a finitesize Dicke model which has previously been used to describe equilibrium (including quantum phase transition) properties of systems such as quantum dots in a microcavity. Here we extend this model to address nonequilibrium situations. Analyzing the system’s quantum fidelity, we find that the nearadiabatic regime exhibits the richest phenomena, with a strong asymmetry in the internal collective dynamics depending on which phase is chosen as the starting point. We also explore signatures of the crossing of the critical points on the radiation subsystem by monitoring its Wigner function; then, the subsystem can exhibit the emergence of nonclassicality and complexity.
Finite particle number approach to quantum physics
Noyes, H.P.
19820401
Bridgman has contended that the inside of an electron cannot be given operational meaning. The basic reason for this is taken to be that when relativity is coupled to quantum mechanics the uncertainty principle in energy requires the existence of an indefinitely large number of particulate degrees of freedom corresponding to particles of finite mass when any system is examined at short distance, as was first pointed out by Wick. This principle is examined in the context of the nuclear force problem and shown to frustrate a precise theory of strong interactions using conventional approaches. However, once relativistic scattering theory is recast in the form of free particle wave functions and elementary scatterings, progress becomes possible. In particular, a unitary and covariant first approximation to the nuclear force problem using only two particles and one quantum can be formulated simply by postulating that particle (or antiparticle) can bind with the quantum to make a system of the same mass as the particle and physically indistinguishable from it.
Quantum field theory of fluids.
Gripaios, Ben; Sutherland, Dave
20150220
The quantum theory of fields is largely based on studying perturbations around noninteracting, or free, field theories, which correspond to a collection of quantummechanical harmonic oscillators. The quantum theory of an ordinary fluid is "freer", in the sense that the noninteracting theory also contains an infinite collection of quantummechanical free particles, corresponding to vortex modes. By computing a variety of correlation functions at tree and loop level, we give evidence that a quantum perfect fluid can be consistently formulated as a lowenergy, effective field theory. We speculate that the quantum behavior is radically different from both classical fluids and quantum fields.
Quantum algorithms for quantum field theories.
Jordan, Stephen P; Lee, Keith S M; Preskill, John
20120601
Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We developed a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic selfinteractions (φ(4) theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strongcoupling and highprecision regimes, our quantum algorithm achieves exponential speedup over the fastest known classical algorithm.
Lyapunov control of quantum systems with impulsive control fields.
Yang, Wei; Sun, Jitao
20130101
We investigate the Lyapunov control of finitedimensional quantum systems with impulsive control fields, where the studied quantum systems are governed by the Schrödinger equation. By three different Lyapunov functions and the invariant principle of impulsive systems, we study the convergence of quantum systems with impulsive control fields and propose new results for the mentioned quantum systems in the form of sufficient conditions. Two numerical simulations are presented to illustrate the effectiveness of the proposed control method.
Lyapunov Control of Quantum Systems with Impulsive Control Fields
Yang, Wei; Sun, Jitao
20130101
We investigate the Lyapunov control of finitedimensional quantum systems with impulsive control fields, where the studied quantum systems are governed by the Schrödinger equation. By three different Lyapunov functions and the invariant principle of impulsive systems, we study the convergence of quantum systems with impulsive control fields and propose new results for the mentioned quantum systems in the form of sufficient conditions. Two numerical simulations are presented to illustrate the effectiveness of the proposed control method. PMID:23766712
Finite quantum kinematics of the harmonic oscillatora)
NASA Astrophysics Data System (ADS)
ShiriGarakani, Mohsen; Finkelstein, David Ritz
20060301
Arbitrarily small changes in the commutation relations suffice to transform the usual singular quantum theories into regular quantum theories. This process is an extension of canonical quantization that we call general quantization. Here we apply general quantization to the timeindependent linear harmonic oscillator. The unstable Heisenberg group becomes the stable group SO(3). This freezes out the zeropoint energy of very soft or very hard oscillators, like those responsible for the infrared or ultraviolet divergencies of usual field theories, without much changing the medium oscillators. It produces pronounced violations of equipartition and of the usual uncertainty relations for soft or hard oscillators, and interactions between the previously uncoupled excitation quanta of the oscillator, weakly attractive for medium quanta, strongly repulsive for soft or hard quanta.
Finite quantum kinematics of the harmonic oscillator
ShiriGarakani, Mohsen; Finkelstein, David Ritz
20060315
Arbitrarily small changes in the commutation relations suffice to transform the usual singular quantum theories into regular quantum theories. This process is an extension of canonical quantization that we call general quantization. Here we apply general quantization to the timeindependent linear harmonic oscillator. The unstable Heisenberg group becomes the stable group SO(3). This freezes out the zeropoint energy of very soft or very hard oscillators, like those responsible for the infrared or ultraviolet divergencies of usual field theories, without much changing the medium oscillators. It produces pronounced violations of equipartition and of the usual uncertainty relations for soft or hard oscillators, and interactions between the previously uncoupled excitation quanta of the oscillator, weakly attractive for medium quanta, strongly repulsive for soft or hard quanta.
Quantum Mechanics and Quantum Field Theory
NASA Astrophysics Data System (ADS)
Dimock, Jonathan
20110201
Introduction; Part I. Nonrelativistic: 1. Mathematical prelude; 2. Classical mechanics; 3. Quantum mechanics; 4. Single particle; 5. Many particles; 6. Statistical mechanics; Part II. Relativistic: 7. Relativity; 8. Scalar particles and fields; 9. Electrons and photons; 10. Field theory on a manifold; Part III. Probabilistic Methods: 11. Path integrals; 12. Fields as random variables; 13. A nonlinear field theory; Appendices; References; Index.
A note on powers in finite fields
NASA Astrophysics Data System (ADS)
Aabrandt, Andreas; Lundsgaard Hansen, Vagn
20160801
The study of solutions to polynomial equations over finite fields has a long history in mathematics and is an interesting area of contemporary research. In recent years, the subject has found important applications in the modelling of problems from applied mathematical fields such as signal analysis, system theory, coding theory and cryptology. In this connection, it is of interest to know criteria for the existence of squares and other powers in arbitrary finite fields. Making good use of polynomial division in polynomial rings over finite fields, we have examined a classical criterion of Euler for squares in odd prime fields, giving it a formulation that is apt for generalization to arbitrary finite fields and powers. Our proof uses algebra rather than classical number theory, which makes it convenient when presenting basic methods of applied algebra in the classroom.
Quantum codes from linear codes over finite chain rings
NASA Astrophysics Data System (ADS)
Liu, Xiusheng; Liu, Hualu
20171001
In this paper, we provide two methods of constructing quantum codes from linear codes over finite chain rings. The first one is derived from the CalderbankShorSteane (CSS) construction applied to selfdual codes over finite chain rings. The second construction is derived from the CSS construction applied to Gray images of the linear codes over finite chain ring F_{p^{2m}}+u{F}_{p^{2m}}. The good parameters of quantum codes from cyclic codes over finite chain rings are obtained.
Observable measure of quantum coherence in finite dimensional systems.
Girolami, Davide
20141024
Quantum coherence is the key resource for quantum technology, with applications in quantum optics, information processing, metrology, and cryptography. Yet, there is no universally efficient method for quantifying coherence either in theoretical or in experimental practice. I introduce a framework for measuring quantum coherence in finite dimensional systems. I define a theoretical measure which satisfies the reliability criteria established in the context of quantum resource theories. Then, I present an experimental scheme implementable with current technology which evaluates the quantum coherence of an unknown state of a ddimensional system by performing two programmable measurements on an ancillary qubit, in place of the O(d2) direct measurements required by full state reconstruction. The result yields a benchmark for monitoring quantum effects in complex systems, e.g., certifying nonclassicality in quantum protocols and probing the quantum behavior of biological complexes.
del Campo, Adolfo; Rams, Marek M; Zurek, Wojciech H
20120914
The dynamics of a quantum phase transition is inextricably woven with the formation of excitations, as a result of critical slowing down in the neighborhood of the critical point. We design a transitionless quantum driving through a quantum critical point, allowing one to access the ground state of the brokensymmetry phase by a finiterate quench of the control parameter. The method is illustrated in the onedimensional quantum Ising model in a transverse field. Driving through the critical point is assisted by an auxiliary Hamiltonian, for which the interplay between the range of the interaction and the modes where excitations are suppressed is elucidated.
Langevin description of nonequilibrium quantum fields
NASA Astrophysics Data System (ADS)
Gautier, F.; Serreau, J.
20121201
We consider the nonequilibrium dynamics of a real quantum scalar field. We show the formal equivalence of the exact evolution equations for the statistical and spectral twopoint functions with a fictitious Langevin process and examine the conditions under which a local Markovian dynamics is a valid approximation. In quantum field theory, the memory kernel and the noise correlator typically exhibit long time power laws and are thus highly nonlocal, thereby questioning the possibility of a local description. We show that despite this fact, there is a finite time range during which a local description is accurate. This requires the theory to be (effectively) weakly coupled. We illustrate the use of such a local description for studies of decoherence and entropy production in quantum field theory.
Symmetry and Degeneracy in Quantum Mechanics. SelfDuality in Finite Spin Systems
ERIC Educational Resources Information Center
Osacar, C.; Pacheco, A. F.
20090101
The symmetry of selfduality (Savit 1980 "Rev. Mod. Phys. 52" 453) of some models of statistical mechanics and quantum field theory is discussed for finite spin blocks of the Ising chain in a transverse magnetic field. The existence of this symmetry in a specific type of these blocks, and not in others, is manifest by the degeneracy of their…
Symmetry and Degeneracy in Quantum Mechanics. SelfDuality in Finite Spin Systems
ERIC Educational Resources Information Center
Osacar, C.; Pacheco, A. F.
20090101
The symmetry of selfduality (Savit 1980 "Rev. Mod. Phys. 52" 453) of some models of statistical mechanics and quantum field theory is discussed for finite spin blocks of the Ising chain in a transverse magnetic field. The existence of this symmetry in a specific type of these blocks, and not in others, is manifest by the degeneracy of their…
Computational quantum field theory
NASA Astrophysics Data System (ADS)
Grobe, Rainer
20060501
I will give an overview on recent attempts to solve the timedependent Dirac equation for the electronpositron field operator. These numerical solutions permit a first temporally and spatially resolved insight into the mechanisms of how an electronpositron pair can be created from vacuum in a very strong force field. This approach has helped to illuminate a wide range of controversial questions. Some of these questions arise for complicated physical situations such as how an electron scatters off a supercritical potential barrier (Klein paradox). This requires the application of quantum field theory to study the combined effect of the pairproduction due to the supercriticality of the potential together with the scattering at the barrier involving the Pauliprinciple. Other phenomena include Schr"odinger's Zitterbewegung and the localization problem for a relativistic particle. This work has been supported by the NSF and Research Corporation. P. Krekora, K. Cooley, Q. Su and R. Grobe, Phys. Rev. Lett. 95, 070403 (2005). P. Krekora, Q. Su and R. Grobe, Phys. Rev. Lett. 93, 043004 (2004). P. Krekora, Q. Su and R. Grobe, Phys. Rev. Lett. 92, 040406 (2004).
A Note on Powers in Finite Fields
ERIC Educational Resources Information Center
Aabrandt, Andreas; Hansen, Vagn Lundsgaard
20160101
The study of solutions to polynomial equations over finite fields has a long history in mathematics and is an interesting area of contemporary research. In recent years, the subject has found important applications in the modelling of problems from applied mathematical fields such as signal analysis, system theory, coding theory and cryptology. In…
A Note on Powers in Finite Fields
ERIC Educational Resources Information Center
Aabrandt, Andreas; Hansen, Vagn Lundsgaard
20160101
The study of solutions to polynomial equations over finite fields has a long history in mathematics and is an interesting area of contemporary research. In recent years, the subject has found important applications in the modelling of problems from applied mathematical fields such as signal analysis, system theory, coding theory and cryptology. In…
Superrenormalizable or finite LeeWick quantum gravity
NASA Astrophysics Data System (ADS)
Modesto, Leonardo
20160801
We propose a class of multidimensional higher derivative theories of gravity without extra real degrees of freedom besides the graviton field. The propagator shows up the usual real graviton pole in k2 = 0 and extra complex conjugates poles that do not contribute to the absorptive part of the physical scattering amplitudes. Indeed, they may consistently be excluded from the asymptotic observable states of the theory making use of the LeeWick and Cutkosky, Landshoff, Olive and Polkinghorne prescription for the construction of a unitary Smatrix. Therefore, the spectrum consists of the graviton and short lived elementary unstable particles that we named ;antigravitons; because of their repulsive contribution to the gravitational potential at short distance. However, another interpretation of the complex conjugate pairs is proposed based on the Calmet's suggestion, i.e. they could be understood as black hole precursors long established in the classical theory. Since the theory is CPT invariant, the conjugate complex of the micro black hole precursor can be interpreted as a white hole precursor consistently with the 't Hooft complementarity principle. It is proved that the quantum theory is superrenormalizable in even dimension, i.e. only a finite number of divergent diagrams survive, and finite in odd dimension. Furthermore, turning on a local potential of the Riemann tensor we can make the theory finite in any dimension. The singularityfree Newtonian gravitational potential is explicitly computed for a range of higher derivative theories. Finally, we propose a new superrenormalizable or finite LeeWick standard model of particle physics.
On Quantum Estimation, Quantum Cloning and Finite Quantum de Finetti Theorems
NASA Astrophysics Data System (ADS)
Chiribella, Giulio
This paper presents a series of results on the interplay between quantum estimation, cloning and finite de Finetti theorems. First, we consider the measureandprepare channel that uses optimal estimation to convert M copies into k approximate copies of an unknown pure state and we show that this channel is equal to a random loss of all but s particles followed by cloning from s to k copies. When the number k of output copies is large with respect to the number M of input copies the measureandprepare channel converges in diamond norm to the optimal universal cloning. In the opposite case, when M is large compared to k, the estimation becomes almost perfect and the measureandprepare channel converges in diamond norm to the partial trace over all but k systems. This result is then used to derive de Finettitype results for quantum states and for symmetric broadcast channels, that is, channels that distribute quantum information to many receivers in a permutationally invariant fashion. Applications of the finite de Finetti theorem for symmetric broadcast channels include the derivation of diamondnorm bounds on the asymptotic convergence of quantum cloning to state estimation and the derivation of bounds on the amount of quantum information that can be jointly decoded by a group of k receivers at the output of a symmetric broadcast channel.
NASA Astrophysics Data System (ADS)
Malpetti, Daniele; Roscilde, Tommaso
20170201
The meanfield approximation is at the heart of our understanding of complex systems, despite its fundamental limitation of completely neglecting correlations between the elementary constituents. In a recent work [Phys. Rev. Lett. 117, 130401 (2016), 10.1103/PhysRevLett.117.130401], we have shown that in quantum manybody systems at finite temperature, twopoint correlations can be formally separated into a thermal part and a quantum part and that quantum correlations are generically found to decay exponentially at finite temperature, with a characteristic, temperaturedependent quantum coherence length. The existence of these two different forms of correlation in quantum manybody systems suggests the possibility of formulating an approximation, which affects quantum correlations only, without preventing the correct description of classical fluctuations at all length scales. Focusing on lattice boson and quantum Ising models, we make use of the pathintegral formulation of quantum statistical mechanics to introduce such an approximation, which we dub quantum meanfield (QMF) approach, and which can be readily generalized to a cluster form (cluster QMF or cQMF). The cQMF approximation reduces to cluster meanfield theory at T =0 , while at any finite temperature it produces a family of systematically improved, semiclassical approximations to the quantum statistical mechanics of the lattice theory at hand. Contrary to standard MF approximations, the correct nature of thermal critical phenomena is captured by any cluster size. In the two exemplary cases of the twodimensional quantum Ising model and of twodimensional quantum rotors, we study systematically the convergence of the cQMF approximation towards the exact result, and show that the convergence is typically linear or sublinear in the boundarytobulk ratio of the clusters as T →0 , while it becomes faster than linear as T grows. These results pave the way towards the development of semiclassical numerical
Nunes, Wagner A; de Sousa, J Ricardo; Viana, J Roberto; Richter, J
20100414
The ground state phase diagram of the quantum spin1/2 Heisenberg antiferromagnet in the presence of nearestneighbor (J(1)) and nextnearestneighbor (J(2)) interactions (J(1)J(2) model) on a stacked square lattice, where we introduce an interlayer coupling through nearestneighbor bonds of strength J(
Noncommutative Quantum Scalar Field Cosmology
Diaz Barron, L. R.; LopezDominguez, J. C.; Sabido, M.; Yee, C.
20100712
In this work we study noncommutative FriedmannRobertsonWalker (FRW) cosmology coupled to a scalar field endowed with an exponential potential. The quantum scenario is analyzed in the Bohmian formalism of quantum trajectories to investigate the effects of noncommutativity in the evolution of the universe.
Variational Equation for Quantum Number Projection at Finite Temperature
NASA Astrophysics Data System (ADS)
Tanabe, Kosai; Nakada, Hitoshi
20080401
To describe phase transitions in a finite system at finite temperature, we develop a formalism of the variationafterprojection (VAP) of quantum numbers based on the thermofield dynamics (TFD). We derive a new BardeenCooperSchrieffer (BCS)type equation by variating the free energy with approximate entropy without violating Peierls inequality. The solution to the new BCS equation describes the Sshape in the specific heat curve and the superfluidtonormal phase transition caused by the temperature effect. It simulates the exact quantum Monte Carlo results well.
Quantum linear Boltzmann equation with finite intercollision time
Diosi, Lajos
20091215
Inconsistencies are pointed out in the usual quantum versions of the classical linear Boltzmann equation constructed for a quantized test particle in a gas. These are related to the incorrect formal treatment of momentum decoherence. We prove that ideal collisions with the molecules would result in complete momentum decoherence, the persistence of coherence is only due to the finite intercollision time. A corresponding quantum linear Boltzmann equation is proposed.
Quantum Field Theory in (0 + 1) Dimensions
ERIC Educational Resources Information Center
Boozer, A. D.
20070101
We show that many of the key ideas of quantum field theory can be illustrated simply and straightforwardly by using toy models in (0 + 1) dimensions. Because quantum field theory in (0 + 1) dimensions is equivalent to quantum mechanics, these models allow us to use techniques from quantum mechanics to gain insight into quantum field theory. In…
Quantum Field Theory in (0 + 1) Dimensions
ERIC Educational Resources Information Center
Boozer, A. D.
20070101
We show that many of the key ideas of quantum field theory can be illustrated simply and straightforwardly by using toy models in (0 + 1) dimensions. Because quantum field theory in (0 + 1) dimensions is equivalent to quantum mechanics, these models allow us to use techniques from quantum mechanics to gain insight into quantum field theory. In…
Quantum spectral dimension in quantum field theory
NASA Astrophysics Data System (ADS)
Calcagni, Gianluca; Modesto, Leonardo; Nardelli, Giuseppe
20160301
We reinterpret the spectral dimension of spacetimes as the scaling of an effective selfenergy transition amplitude in quantum field theory (QFT), when the system is probed at a given resolution. This picture has four main advantages: (a) it dispenses with the usual interpretation (unsatisfactory in covariant approaches) where, instead of a transition amplitude, one has a probability density solving a nonrelativistic diffusion equation in an abstract diffusion time; (b) it solves the problem of negative probabilities known for higherorder and nonlocal dispersion relations in classical and quantum gravity; (c) it clarifies the concept of quantum spectral dimension as opposed to the classical one. We then consider a class of logarithmic dispersion relations associated with quantum particles and show that the spectral dimension dS of spacetime as felt by these quantum probes can deviate from its classical value, equal to the topological dimension D. In particular, in the presence of higher momentum powers it changes with the scale, dropping from D in the infrared (IR) to a value dSUV ≤ D in the ultraviolet (UV). We apply this general result to Stelle theory of renormalizable gravity, which attains the universal value dSUV = 2 for any dimension D.
Strong local passivity in finite quantum systems.
Frey, Michael; Funo, Ken; Hotta, Masahiro
20140701
Passive states of quantum systems are states from which no system energy can be extracted by any cyclic (unitary) process. Gibbs states of all temperatures are passive. Strong local (SL) passive states are defined to allow any general quantum operation, but the operation is required to be local, being applied only to a specific subsystem. Any mixture of eigenstates in a systemdependent neighborhood of a nondegenerate entangled ground state is found to be SL passive. In particular, Gibbs states are SL passive with respect to a subsystem only at or below a critical systemdependent temperature. SL passivity is associated in manybody systems with the presence of ground state entanglement in a way suggestive of collective quantum phenomena such as quantum phase transitions, superconductivity, and the quantum Hall effect. The presence of SL passivity is detailed for some simple spin systems where it is found that SL passivity is neither confined to systems of only a few particles nor limited to the near vicinity of the ground state.
Mean Field Theory for Collective Motion of Quantum Meson Fields
NASA Astrophysics Data System (ADS)
Tsue, Y.; Vautherin, D.; Matsui, T.
19990801
Mean field theory for the time evolution of quantum meson fields is studied in terms of the functional Schrödinger picture with a timedependent Gaussian variational wave functional. We first show that the equations of motion for the variational wavefunctional can be rewritten in a compact form similar to the HartreeBogoliubov equations in quantum manybody theory and this result is used to recover the covariance of the theory. We then apply this method to the O(N) model and present analytic solutions of the mean field evolution equations for an Ncomponent scalar field. These solutions correspond to quantum rotations in isospin space and represent generalizations of the classical solutions obtained earlier by Anselm and Ryskin. As compared to classical solutions new effects arise because of the coupling between the average value of the field and its quantum fluctuations. We show how to generalize these solutions to the case of mean field dynamics at finite temperature. The relevance of these solutions for the observation of a coherent collective state or a disoriented chiral condensate in ultrarelativistic nuclear collisions is discussed.
Electric fields and quantum wormholes
NASA Astrophysics Data System (ADS)
Engelhardt, Dalit; Freivogel, Ben; Iqbal, Nabil
20150901
Electric fields can thread a classical EinsteinRosen bridge. Maldacena and Susskind have recently suggested that in a theory of dynamical gravity the entanglement of ordinary perturbative quanta should be viewed as creating a quantum version of an EinsteinRosen bridge between the particles, or a "quantum wormhole." We demonstrate within lowenergy effective field theory that there is a precise sense in which electric fields can also thread such quantum wormholes. We define a nonperturbative "wormhole susceptibility" that measures the ease of passing an electric field through any sort of wormhole. The susceptibility of a quantum wormhole is suppressed by powers of the U (1 ) gauge coupling relative to that for a classical wormhole but can be made numerically equal with a sufficiently large amount of entangled matter.
Quantum electrodynamic effects in finite space
NASA Astrophysics Data System (ADS)
Dobiasch, P.; Walther, H.
The modifications of various quantum properties due to a discrete structure of the modes of the vacuum electromagnetic field are discussed. In contrast to the usual case of a continuous spectrum of the free space fluctuations, we consider physical systems in a resonator or in a wave guide. It is shown that the relaxation time of the system can be increased ot decreased, by increasing or decreasing the density of modes with respect to the case of unperturbed vacuum. On the other hand, we predict level shifts due to the reduced mass of the electron and deviations from the Lambshift for hydrogen in a wave guide, which can be detected with the presently feasible high resolution spectroscopy. We propose an experimental setup. Nous discutons les modifications de diverses propriétés quantiques sous l'influence d'une structure de modes discrets du champ électromagnétique dans le vide. En comparaison du cas habituel d'un spectre continu des fluctuations du vide dans l'espace libre, nous considérons ici des systèmes physiques dans un résonateur ou un guide d'ondes. Il est démontré que le temps de relaxation du système peut être prolongé ou raccourci, ceci en augmentant ou diminuant la densité des modes par rapport à sa valeur dans le vide nonperturbé. D'autre part, nous prédisons des déplacements de niveau dus à la masse réduite de l'électron et des déviations du Lamb shift pour des atomes d'hydrogène dans un guide d'ondes, qui peuvent être détectées grâce à la haute résolution accessible actuellement en spectroscopie. Nous présentons un dispositif expérimental.
Quantum Simulation of Quantum Field Theories in Trapped Ions
Casanova, J.; Lamata, L.; Egusquiza, I. L.; Gerritsma, R.; Roos, C. F.; GarciaRipoll, J. J.; Solano, E.
20111223
We propose the quantum simulation of fermion and antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.
Quantum simulation of quantum field theories in trapped ions.
Casanova, J; Lamata, L; Egusquiza, I L; Gerritsma, R; Roos, C F; GarcíaRipoll, J J; Solano, E
20111223
We propose the quantum simulation of fermion and antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.
Quantum phase transition of the transversefield quantum Ising model on scalefree networks.
Yi, Hangmo
20150101
I investigate the quantum phase transition of the transversefield quantum Ising model in which nearest neighbors are defined according to the connectivity of scalefree networks. Using a continuoustime quantum Monte Carlo simulation method and the finitesize scaling analysis, I identify the quantum critical point and study its scaling characteristics. For the degree exponent λ=6, I obtain results that are consistent with the meanfield theory. For λ=4.5 and 4, however, the results suggest that the quantum critical point belongs to a nonmeanfield universality class. Further simulations indicate that the quantum critical point remains meanfieldlike if λ>5, but it continuously deviates from the meanfield theory as λ becomes smaller.
NASA Astrophysics Data System (ADS)
Weinberg, Steven
19960801
In this second volume of The Quantum Theory of Fields, available for the first time in paperback, Nobel Laureate Steven Weinberg continues his masterly expoistion of quantum theory. Volume 2 provides an uptodate and selfcontained account of the methods of quantum field theory, and how they have led to an understanding of the weak, strong, and electromagnetic interactions of the elementary particles. The presentation of modern mathematical methods is throughout interwoven with accounts of the problems of elementary particle physics and condensed matter physics to which they have been applied. Exercises are included at the end of each chapter.
Finite hedging in field theory models of interest rates.
Baaquie, Belal E; Srikant, Marakani
20040301
We use path integrals to calculate hedge parameters and efficacy of hedging in a quantum field theory generalization of the Heath, Jarrow, and Morton [Robert Jarrow, David Heath, and Andrew Morton, Econometrica 60, 77 (1992)] term structure model, which parsimoniously describes the evolution of imperfectly correlated forward rates. We calculate, within the model specification, the effectiveness of hedging over finite periods of time, and obtain the limiting case of instantaneous hedging. We use empirical estimates for the parameters of the model to show that a lowdimensional hedge portfolio is quite effective.
Quantum oscillations without magnetic field
NASA Astrophysics Data System (ADS)
Liu, Tianyu; Pikulin, D. I.; Franz, M.
20170101
When the magnetic field B is applied to a metal, nearly all observable quantities exhibit oscillations periodic in 1 /B . Such quantum oscillations reflect the fundamental reorganization of electron states into Landau levels as a canonical response of the metal to the applied magnetic field. We predict here that, remarkably, in the recently discovered Dirac and Weyl semimetals, quantum oscillations can occur in the complete absence of magnetic field. These zerofield quantum oscillations are driven by elastic strain which, in the space of the lowenergy Dirac fermions, acts as a chiral gauge potential. We propose an experimental setup in which the strain in a thin film (or nanowire) can generate a pseudomagnetic field b as large as 15 T and demonstrate the resulting de Haasvan Alphen and Shubnikovde Haas oscillations periodic in 1 /b .
Finite key analysis for symmetric attacks in quantum key distribution
Meyer, Tim; Kampermann, Hermann; Kleinmann, Matthias; Bruss, Dagmar
20061015
We introduce a constructive method to calculate the achievable secret key rate for a generic class of quantum key distribution protocols, when only a finite number n of signals is given. Our approach is applicable to all scenarios in which the quantum state shared by Alice and Bob is known. In particular, we consider the six state protocol with symmetric eavesdropping attacks, and show that for a small number of signals, i.e., below n{approx}10{sup 4}, the finite key rate differs significantly from the asymptotic value for n{yields}{infinity}. However, for larger n, a good approximation of the asymptotic value is found. We also study secret key rates for protocols using higherdimensional quantum systems.
Most Efficient Quantum Thermoelectric at Finite Power Output
NASA Astrophysics Data System (ADS)
Whitney, Robert S.
20140401
Machines are only Carnot efficient if they are reversible, but then their power output is vanishingly small. Here we ask, what is the maximum efficiency of an irreversible device with finite power output? We use a nonlinear scattering theory to answer this question for thermoelectric quantum systems, heat engines or refrigerators consisting of nanostructures or molecules that exhibit a Peltier effect. We find that quantum mechanics places an upper bound on both power output and on the efficiency at any finite power. The upper bound on efficiency equals Carnot efficiency at zero power output but decays with increasing power output. It is intrinsically quantum (wavelength dependent), unlike Carnot efficiency. This maximum efficiency occurs when the system lets through all particles in a certain energy window, but none at other energies. A physical implementation of this is discussed, as is the suppression of efficiency by a phonon heat flow.
Eavesdropping on counterfactual quantum key distribution with finite resources
NASA Astrophysics Data System (ADS)
Liu, Xingtong; Zhang, Bo; Wang, Jian; Tang, Chaojing; Zhao, Jingjing; Zhang, Sheng
20140801
A striking scheme called "counterfactual quantum cryptography" gives a conceptually new approach to accomplish the task of key distribution. It allows two legitimate parties to share a secret even though a particle carrying secret information is not, in fact, transmitted through the quantum channel. Since an eavesdropper cannot directly access the entire quantum system of each signal particle, the protocol seems to provide practical security advantages. However, here we propose an eavesdropping method which works on the scheme in a finite key scenario. We show that, for practical systems only generating a finite number of keys, the eavesdropping can obtain all of the secret information without being detected. We also present a improved protocol as a countermeasure against this attack.
Bounding the Set of Finite Dimensional Quantum Correlations.
Navascués, Miguel; Vértesi, Tamás
20150710
We describe a simple method to derive high performance semidefinite programing relaxations for optimizations over complex and real operator algebras in finite dimensional Hilbert spaces. The method is very flexible, easy to program, and allows the user to assess the behavior of finite dimensional quantum systems in a number of interesting setups. We use this method to bound the strength of quantum nonlocality in Bell scenarios where the dimension of the parties is bounded from above. We derive new results in quantum communication complexity and prove the soundness of the prepareandmeasure dimension witnesses introduced in Gallego et al., Phys. Rev. Lett. 105, 230501 (2010). Finally, we propose a new dimension witness that can distinguish between classical, real, and complex twolevel systems.
Finite fieldenergy and interparticle potential in logarithmic electrodynamics
NASA Astrophysics Data System (ADS)
Gaete, Patricio; HelayëlNeto, José
20140301
We pursue an investigation of logarithmic electrodynamics, for which the field energy of a pointlike charge is finite, as happens in the case of the usual BornInfeld electrodynamics. We also show that, contrary to the latter, logarithmic electrodynamics exhibits the feature of birefringence. Next, we analyze the lowestorder modifications for both logarithmic electrodynamics and for its noncommutative version, within the framework of the gaugeinvariant pathdependent variables formalism. The calculation shows a longrange correction (type) to the Coulomb potential for logarithmic electrodynamics. Interestingly enough, for its noncommutative version, the interaction energy is ultraviolet finite. We highlight the role played by the new quantum of length in our analysis.
(Studies in quantum field theory)
Not Available
19900101
During the period 4/1/893/31/90 the theoretical physics group supported by Department of Energy Contract No. AC0278ER04915.A015 and consisting of Professors Bender and Shrauner, Associate Professor Papanicolaou, Assistant Professor Ogilvie, and Senior Research Associate Visser has made progress in many areas of theoretical and mathematical physics. Professors Bender and Shrauner, Associate Professor Papanicolaou, Assistant Professor Ogilvie, and Research Associate Visser are currently conducting research in many areas of high energy theoretical and mathematical physics. These areas include: strongcoupling approximation; classical solutions of nonAbelian gauge theories; meanfield approximation in quantum field theory; path integral and coherent state representations in quantum field theory; lattice gauge calculations; the nature of perturbation theory in large order; quark condensation in QCD; chiral symmetry breaking; the 1/N expansion in quantum field theory; effective potential and action in quantum field theories, including OCD; studies of the early universe and inflation, and quantum gravity.
Extracting signatures of quantum criticality in the finitetemperature behavior of manybody systems
NASA Astrophysics Data System (ADS)
Cuccoli, Alessandro; Taiti, Alessio; Vaia, Ruggero; Verrucchi, Paola
20070801
We face the problem of detecting and featuring footprints of quantum criticality in the finitetemperature behavior of quantum manybody systems. Our strategy is that of comparing the phase diagram of a system displaying a T=0 quantum phase transition with that of its classical limit, in order to single out the genuinely quantum effects. To this aim, we consider the onedimensional Ising model in a transverse field: while the quantum S=1/2 Ising chain is exactly solvable and extensively studied, results for the classical limit (S→∞) of such model are lacking, and we supply them here. They are obtained numerically, via the transfermatrix method, and their asymptotic lowtemperature behavior is also derived analytically by selfconsistent spinwave theory. We draw the classical phase diagram according to the same procedure followed in the quantum analysis, and the two phase diagrams are found unexpectedly similar: Three regimes are detected also in the classical case, each characterized by a functional dependence of the correlation length on temperature and field analogous to that of the quantum model. What discriminates the classical from the quantum case are the different values of the exponents entering such dependencies, a consequence of the different nature of zerotemperature quantum fluctuations with respect to the thermal ones.
Quantum and semiclassical Cooperpair tunneling in finite systems
NASA Astrophysics Data System (ADS)
Kleber, M.
20161201
We derive analytic solutions for the tunneling dynamics of two weakly coupled finite BCScondensates. Pairing interaction between the finitesize condensates is taken into account. Using particlenumber dependent chemical potentials the timedependent transfer of Cooper pairs is obtained from a phenomenological calculation. The results of this theory are compared to a microscopic calculation within the quasispin formulation in its semiclassical limit. In both cases the tunneling current can be mapped onto the motion of a simple pendulum: The results are analogous to the Josephson current between two superconductors and can be used as a starting point to include quantum fluctuations and Josephson radiation.
Informationally complete joint measurements on finite quantum systems
NASA Astrophysics Data System (ADS)
Carmeli, Claudio; Heinosaari, Teiko; Toigo, Alessandro
20120101
We show that there are informationally complete joint measurements of two conjugated observables on a finite quantum system, meaning that they enable the identification of all quantum states from their measurement outcome statistics. We further demonstrate that it is possible to implement a joint observable as a sequential measurement. If we require minimal noise in the joint measurement, then the joint observable is unique. If d is odd, then this observable is informationally complete. But if d is even, then the joint observable is not informationally complete, and one has to allow more noise in order to obtain informational completeness.
Realization schemes for quantum instruments in finite dimensions
Chiribella, Giulio; Perinotti, Paolo; D'Ariano, Giacomo Mauro
20090415
We present a general dilation scheme for quantum instruments with continuous outcome space in finite dimensions, in terms of a measurement on a finitedimensional ancilla, described by a positive operator valued measure (POVM). The general result is then applied to a large class of instruments generated by operator frames, which contains groupcovariant instruments as a particular case and allows one to construct dilation schemes based on a measurement on the ancilla followed by a conditional feedforward operation on the output. In the case of tight operator frames, our construction generalizes quantum teleportation and telecloning, producing a whole family of generalized teleportation schemes in which the instrument is realized via a joint POVM at the sender combined with a conditional feedforward operation at the receiver.
The quantum Ising model: finite sums and hyperbolic functions.
Damski, Bogdan
20151030
We derive exact closedform expressions for several sums leading to hyperbolic functions and discuss their applicability for studies of finitesize Ising spin chains. We show how they immediately lead to closedform expressions for both fidelity susceptibility characterizing the quantum critical point and the coefficients of the counterdiabatic Hamiltonian enabling arbitrarily quick adiabatic driving of the system. Our results generalize and extend the sums presented in the popular Gradshteyn and Ryzhik Table of Integrals, Series, and Products.
The quantum Ising model: finite sums and hyperbolic functions
NASA Astrophysics Data System (ADS)
Damski, Bogdan
20151001
We derive exact closedform expressions for several sums leading to hyperbolic functions and discuss their applicability for studies of finitesize Ising spin chains. We show how they immediately lead to closedform expressions for both fidelity susceptibility characterizing the quantum critical point and the coefficients of the counterdiabatic Hamiltonian enabling arbitrarily quick adiabatic driving of the system. Our results generalize and extend the sums presented in the popular Gradshteyn and Ryzhik Table of Integrals, Series, and Products.
Finitekey security analysis for multilevel quantum key distribution
NASA Astrophysics Data System (ADS)
Brádler, Kamil; Mirhosseini, Mohammad; Fickler, Robert; Broadbent, Anne; Boyd, Robert
20160701
We present a detailed security analysis of a ddimensional quantum key distribution protocol based on two and three mutually unbiased bases (MUBs) both in an asymptotic and finitekeylength scenario. The finite secret key rates (in bits per detected photon) are calculated as a function of the length of the sifted key by (i) generalizing the uncertainly relationbased insight from BB84 to any dlevel 2MUB QKD protocol and (ii) by adopting recent advances in the secondorder asymptotics for finite block length quantum coding (for both dlevel 2 and 3MUB QKD protocols). Since the finite and asymptotic secret key rates increase with d and the number of MUBs (together with the tolerable threshold) such QKD schemes could in principle offer an important advantage over BB84. We discuss the possibility of an experimental realization of the 3MUB QKD protocol with the orbital angular momentum degrees of freedom of photons.
On space of integrable quantum field theories
NASA Astrophysics Data System (ADS)
Smirnov, F. A.; Zamolodchikov, A. B.
20170201
We study deformations of 2D Integrable Quantum Field Theories (IQFT) which preserve integrability (the existence of infinitely many local integrals of motion). The IQFT are understood as "effective field theories", with finite ultraviolet cutoff. We show that for any such IQFT there are infinitely many integrable deformations generated by scalar local fields Xs, which are in onetoone correspondence with the local integrals of motion; moreover, the scalars Xs are built from the components of the associated conserved currents in a universal way. The first of these scalars, X1, coincides with the composite field (T T bar) built from the components of the energymomentum tensor. The deformations of quantum field theories generated by X1 are "solvable" in a certain sense, even if the original theory is not integrable. In a massive IQFT the deformations Xs are identified with the deformations of the corresponding factorizable Smatrix via the CDD factor. The situation is illustrated by explicit construction of the form factors of the operators Xs in sineGordon theory. We also make some remarks on the problem of UV completeness of such integrable deformations.
On space of integrable quantum field theories
Smirnov, F. A.; Zamolodchikov, A. B.
20161221
Here, we study deformations of 2D Integrable Quantum Field Theories (IQFT) which preserve integrability (the existence of infinitely many local integrals of motion). The IQFT are understood as “effective field theories”, with finite ultraviolet cutoff. We show that for any such IQFT there are infinitely many integrable deformations generated by scalar local fields Xs, which are in onetoone correspondence with the local integrals of motion; moreover, the scalars Xs are built from the components of the associated conserved currents in a universal way. The first of these scalars, X1, coincides with the composite field View the MathML source(TT¯) built frommore » the components of the energy–momentum tensor. The deformations of quantum field theories generated by X1 are “solvable” in a certain sense, even if the original theory is not integrable. In a massive IQFT the deformations Xs are identified with the deformations of the corresponding factorizable Smatrix via the CDD factor. The situation is illustrated by explicit construction of the form factors of the operators Xs in sineGordon theory. Lastly, we also make some remarks on the problem of UV completeness of such integrable deformations.« less
Topological order, entanglement, and quantum memory at finite temperature
Mazac, Dalimil Hamma, Alioscia
20120915
We compute the topological entropy of the toric code models in arbitrary dimension at finite temperature. We find that the critical temperatures for the existence of full quantum (classical) topological entropy correspond to the confinementdeconfinement transitions in the corresponding Z{sub 2} gauge theories. This implies that the thermal stability of topological entropy corresponds to the stability of quantum (classical) memory. The implications for the understanding of ergodicity breaking in topological phases are discussed.  Highlights: BlackRightPointingPointer We calculate the topological entropy of a general toric code in any dimension. BlackRightPointingPointer We find phase transitions in the topological entropy. BlackRightPointingPointer The phase transitions coincide with the appearance of quantum/classical memory.
Quantum coherence of spinboson model at finite temperature
NASA Astrophysics Data System (ADS)
Wu, Wei; Xu, JingBo
20170201
We investigate the dynamical behavior of quantum coherence in spinboson model, which consists of a qubit coupled to a finitetemperature bosonic bath with powerlaw spectral density beyond rotating wave approximation, by employing l1norm as well as quantum relative entropy. It is shown that the temperature of bosonic bath and counterrotating terms significantly affect the decoherence rate in subOhmic, Ohmic and superOhmic baths. At high temperature, we find the counterrotating terms of spinboson model are able to increase the decoherence rate for subOhmic baths, however, for Ohmic and superOhmic baths, the counterrotating terms tend to decrease the value of decoherence rate. At low temperature, we find the counterrotating terms always play a positive role in preserving the qubit's quantum coherence regardless of subOhmic, Ohmic and superOhmic baths.
Quantum Theory of a StronglyDissipative Scalar Field
NASA Astrophysics Data System (ADS)
Jafari, Marjan; Kheirandish, Fardin
20170401
The properties of a quantum dissipative scalar field is analyzed by CaldeiraLeggett model in strongcoupling regime. The Lagrangian of the total system is canonically quantized and the full Hamiltonian is diagonalized using Fano technique. A modedependent probability density is introduced. The steady state energy and correlation functions at finite temperature are calculated in terms of the probability density.
NASA Astrophysics Data System (ADS)
Lev, Felix M.
20170101
Classical mathematics (involving such notions as infinitely small/large and continuity) is usually treated as fundamental while finite mathematics is treated as inferior which is used only in special applications. We first argue that the situation is the opposite: classical mathematics is only a degenerate special case of finite one and finite mathematics is more pertinent for describing nature than standard one. Then we describe results of a quantum theory based on finite mathematics. Implications for foundation of mathematics are discussed.
Bohmian mechanics and quantum field theory.
Dürr, Detlef; Goldstein, Sheldon; Tumulka, Roderich; Zanghì, Nino
20040827
We discuss a recently proposed extension of Bohmian mechanics to quantum field theory. For more or less any regularized quantum field theory there is a corresponding theory of particle motion, which, in particular, ascribes trajectories to the electrons or whatever sort of particles the quantum field theory is about. Corresponding to the nonconservation of the particle number operator in the quantum field theory, the theory describes explicit creation and annihilation events: the world lines for the particles can begin and end.
Quantum Field Theory, Revised Edition
NASA Astrophysics Data System (ADS)
Mandl, F.; Shaw, G.
19940101
Quantum Field Theory Revised Edition F. Mandl and G. Shaw, Department of Theoretical Physics, The Schuster Laboratory, The University, Manchester, UK When this book first appeared in 1984, only a handful of W± and Z° bosons had been observed and the experimental investigation of high energy electroweak interactions was in its infancy. Nowadays, W± bosons and especially Z° bosons can be produced by the thousand and the study of their properties is a precise science. We have revised the text of the later chapters to incorporate these developments and discuss their implications. We have also taken this opportunity to update the references throughout and to make some improvements in the treatment of dimensional regularization. Finally, we have corrected some minor errors and are grateful to various people for pointing these out. This book is designed as a short and simple introduction to quantum field theory for students beginning research in theoretical and experimental physics. The three main objectives are to explain the basic physics and formalism of quantum field theory, to make the reader fully proficient in theory calculations using Feynman diagrams, and to introduce the reader to gauge theories, which play such a central role in elementary particle physics. The theory is applied to quantum electrodynamics (QED), where quantum field theory had its early triumphs, and to weak interactions where the standard electroweak theory has had many impressive successes. The treatment is based on the canonical quantization method, because readers will be familiar with this, because it brings out lucidly the connection between invariance and conservation laws, and because it leads directly to the Feynman diagram techniques which are so important in many branches of physics. In order to help inexperienced research students grasp the meaning of the theory and learn to handle it confidently, the mathematical formalism is developed from first principles, its physical
Algebraic complexities and algebraic curves over finite fields
Chudnovsky, D. V.; Chudnovsky, G. V.
19870101
We consider the problem of minimal (multiplicative) complexity of polynomial multiplication and multiplication in finite extensions of fields. For infinite fields minimal complexities are known [Winograd, S. (1977) Math. Syst. Theory 10, 169180]. We prove lower and upper bounds on minimal complexities over finite fields, both linear in the number of inputs, using the relationship with linear coding theory and algebraic curves over finite fields. PMID:16593816
Quantum field theory on a cosmological, quantum spacetime
Ashtekar, Abhay; Kaminski, Wojciech; Lewandowski, Jerzy
20090315
In loop quantum cosmology, FriedmannLeMaitreRobertsonWalker spacetimes arise as welldefined approximations to specific quantum geometries. We initiate the development of a quantum theory of test scalar fields on these quantum geometries. Emphasis is on the new conceptual ingredients required in the transition from classical spacetime backgrounds to quantum spacetimes. These include a ''relational time''a la Leibniz, the emergence of the Hamiltonian operator of the test field from the quantum constraint equation, and ramifications of the quantum fluctuations of the background geometry on the resulting dynamics. The familiar quantum field theory on classical FriedmannLeMaitreRobertsonWalker models arises as a welldefined reduction of this more fundamental theory.
Quantum perceptron over a field and neural network architecture selection in a quantum computer.
da Silva, Adenilton José; Ludermir, Teresa Bernarda; de Oliveira, Wilson Rosa
20160401
In this work, we propose a quantum neural network named quantum perceptron over a field (QPF). Quantum computers are not yet a reality and the models and algorithms proposed in this work cannot be simulated in actual (or classical) computers. QPF is a direct generalization of a classical perceptron and solves some drawbacks found in previous models of quantum perceptrons. We also present a learning algorithm named Superposition based Architecture Learning algorithm (SAL) that optimizes the neural network weights and architectures. SAL searches for the best architecture in a finite set of neural network architectures with linear time over the number of patterns in the training set. SAL is the first learning algorithm to determine neural network architectures in polynomial time. This speedup is obtained by the use of quantum parallelism and a nonlinear quantum operator. Copyright © 2016 Elsevier Ltd. All rights reserved.
Aspects of renormalization in finitedensity field theory
Fitzpatrick, A. Liam; Torroba, Gonzalo; Wang, Huajia
20150526
We study the renormalization of the Fermi surface coupled to a massless boson near three spatial dimensions. For this, we set up a Wilsonian RG with independent decimation procedures for bosons and fermions, where the fourfermion interaction “Landau parameters” run already at tree level. Our explicit oneloop analysis resolves previously found obstacles in the renormalization of finitedensity field theory, including logarithmic divergences in nonlocal interactions and the appearance of multilogarithms. The key aspects of the RG are the above treelevel running, and a UVIR mixing between virtual bosons and fermions at the quantum level, which is responsible for the renormalization of the Fermi velocity. We apply this approach to the renormalization of 2 k F singularities, and to Fermi surface instabilities in a companion paper, showing how multilogarithms are properly renormalized. We end with some comments on the renormalization of finitedensity field theory with the inclusion of Landau damping of the boson.
Deriving the Jordan structure of finitedimensional quantum theory
NASA Astrophysics Data System (ADS)
Wilce, Alexander; Barnum, Howard
20120201
The KoecherVinberg theorem tells us that formally real Jordan algebras are equivalent to finitedimensional orderunit spaces having homogeneous, selfdual cones. Recent work by the authors and others has identified various conditions that imply the homogeneity and selfduality of the cones generated by the states and effects of a generalized probabilistic model. This talk highlights two results: one shows that a certain package of conditions, relating the the symmetries of a system and the existence of certain correlations between systems, is sufficient to ground a model's selfduality. Another shows that any daggermonoidal category of homogeneous, selfdual probabilistic theories having locally tomographic composites and containing a system with the structure of a qubit, must consist of selfadjoint parts of complex matrix algebras  must, in other words, be a standard finitedimensional quantum theory.
Formulation and numerical solution of finitelevel quantum optimal control problems
NASA Astrophysics Data System (ADS)
Borzi`, A.; Salomon, J.; Volkwein, S.
20080601
Optimal control of finitelevel quantum systems is investigated, and iterative solution schemes for the optimization of a control representing laser pulses are developed. The purpose of this external field is to channel the system's wavefunction between given states in its most efficient way. Physically motivated constraints, such as limited laser resources or population suppression of certain states, are accounted for through an appropriately chosen cost functional. Firstorder necessary optimality conditions and secondorder sufficient optimality conditions are investigated. For solving the optimal control problems, a cascadic nonlinear conjugate gradient scheme and a monotonic scheme are discussed. Results of numerical experiments with a representative finitelevel quantum system demonstrate the effectiveness of the optimal control formulation and efficiency and robustness of the proposed approaches.
Finite temperature static charge screening in quantum plasmas
NASA Astrophysics Data System (ADS)
Eliasson, B.; AkbariMoghanjoughi, M.
20160701
The shielding potential around a test charge is calculated, using the linearized quantum hydrodynamic formulation with the statistical pressure and Bohm potential derived from finite temperature kinetic theory, and the temperature effects on the force between ions is assessed. The derived screening potential covers the full range of electron degeneracy in the equation of state of the plasma electrons. An attractive force between shielded ions in an arbitrary degenerate plasma exists below a critical temperature and density. The effect of the temperature on the screening potential profile qualitatively describes the ionion bound interaction strength and length variations. This may be used to investigate physical properties of plasmas and in moleculardynamics simulations of fermion plasma. It is further shown that the Bohm potential including the kinetic corrections has a profound effect on the Thomson scattering cross section in quantum plasmas with arbitrary degeneracy.
Finitesize behavior of quantum collective spin systems
Liberti, Giuseppe; Piperno, Franco; Plastina, Francesco
20100115
We discuss the finite size behavior of the adiabatic Dicke model, describing the collective coupling of a set of N twolevel atoms (qubits) to a faster (electromagnetic) oscillator mode. The energy eigenstates of this system are shown to be directly related to those of another widely studied collective spin model, the uniaxial one. By employing an approximate continuum approach, we obtain a complete characterization of the properties of the latter, which we then use to evaluate the scaling properties of various observables for the original Dicke model near its quantum phase transition.
A finite Zitterbewegung model for relativistic quantum mechanics
Noyes, H.P.
19900219
Starting from steps of length h/mc and time intervals h/mc{sup 2}, which imply a quasilocal Zitterbewegung with velocity steps {plus minus}c, we employ discrimination between bitstrings of finite length to construct a necessary 3+1 dimensional eventspace for relativistic quantum mechanics. By using the combinatorial hierarchy to label the strings, we provide a successful start on constructing the coupling constants and mass ratios implied by the scheme. Agreement with experiments is surprisingly accurate. 22 refs., 1 fig.
Error Rate Estimation in Quantum Key Distribution with Finite Resources
NASA Astrophysics Data System (ADS)
Lu, Zhao; Shi, JianHong; Li, FengGuang
20170401
The goal of quantum key distribution (QKD) is to generate secret key shared between two distant players, Alice and Bob. We present the connection between sampling rate and erroneous judgment probability when estimating error rate with random sampling method, and propose a method to compute optimal sampling rate, which can maximize final secure key generation rate. These results can be applied to choose the optimal sampling rate and improve the performance of QKD system with finite resources. Supported by the National Natural Science Foundation of China under Grant Nos. U1304613 and 11204379
Quantum mechanics of Proca fields
NASA Astrophysics Data System (ADS)
Zamani, Farhad; Mostafazadeh, Ali
20090501
We construct the most general physically admissible positivedefinite inner product on the space of Proca fields. Up to a trivial scaling this defines a fiveparameter family of Lorentz invariant inner products that we use to construct a genuine Hilbert space for the quantum mechanics of Proca fields. If we identify the generator of time translations with the Hamiltonian, we obtain a unitary quantum system that describes firstquantized Proca fields and does not involve the conventional restriction to the positivefrequency fields. We provide a rather comprehensive analysis of this system. In particular, we examine the conserved current density responsible for the conservation of the probabilities, explore the global gauge symmetry underlying the conservation of the probabilities, obtain a probability current density, construct position, momentum, helicity, spin, and angular momentum operators, and determine the localized Proca fields. We also compute the generalized parity (P), generalized timereversal (T), and generalized charge or chirality (C) operators for this system and offer a physical interpretation for its PT, C, and CPTsymmetries.
Infinite finitely generated fields are biinterpretable with {{N}}
NASA Astrophysics Data System (ADS)
Scanlon, Thomas
20080701
Using the work of several other mathematicians, principally the results of Poonen refining the work of Pop that algebraic independence is definable within the class of finitely generated fields and of Rumely that the ring of rational integers is uniformly interpreted in global fields, and a theorem on the definability of valuations on function fields of curves, we show that each infinite finitely generated field considered in the ring language is parametrically biinterpretable with {N} . As a consequence, for any finitely generated field there is a firstorder sentence in the language of rings which is true in that field but false in every other finitely generated field and, hence, Pop's conjecture that elementarily equivalent finitely generated fields are isomorphic is true.
Externally controlled local magnetic field in a conducting mesoscopic ring coupled to a quantum wire
Maiti, Santanu K.
20150114
In the present work, the possibility of regulating local magnetic field in a quantum ring is investigated theoretically. The ring is coupled to a quantum wire and subjected to an inplane electric field. Under a finite bias voltage across the wire a net circulating current is established in the ring which produces a strong magnetic field at its centre. This magnetic field can be tuned externally in a wide range by regulating the inplane electric field, and thus, our present system can be utilized to control magnetic field at a specific region. The feasibility of this quantum system in designing spinbased quantum devices is also analyzed.
Quantum Monte Carlo calculations of two neutrons in finite volume
Klos, P.; Lynn, J. E.; Tews, I.; Gandolfi, Stefano; Gezerlis, A.; Hammer, H. W.; Hoferichter, M.; Schwenk, A.
20161118
Ab initio calculations provide direct access to the properties of pure neutron systems that are challenging to study experimentally. In addition to their importance for fundamental physics, their properties are required as input for effective field theories of the strong interaction. In this work, we perform auxiliaryfield diffusion Monte Carlo calculations of the ground state and first excited state of two neutrons in a finite box, considering a simple contact potential as well as chiral effective field theory interactions. We compare the results against exact diagonalizations and present a detailed analysis of the finitevolume effects, whose understanding is crucial for determining observables from the calculated energies. Finally, using the Lüscher formula, we extract the lowenergy Swave scattering parameters from ground and excitedstate energies for different box sizes.
Quantum Monte Carlo calculations of two neutrons in finite volume
Klos, P.; Lynn, J. E.; Tews, I.; ...
20161118
Ab initio calculations provide direct access to the properties of pure neutron systems that are challenging to study experimentally. In addition to their importance for fundamental physics, their properties are required as input for effective field theories of the strong interaction. In this work, we perform auxiliaryfield diffusion Monte Carlo calculations of the ground state and first excited state of two neutrons in a finite box, considering a simple contact potential as well as chiral effective field theory interactions. We compare the results against exact diagonalizations and present a detailed analysis of the finitevolume effects, whose understanding is crucial formore » determining observables from the calculated energies. Finally, using the Lüscher formula, we extract the lowenergy Swave scattering parameters from ground and excitedstate energies for different box sizes.« less
Double quantum dot Cooperpair splitter at finite couplings
NASA Astrophysics Data System (ADS)
Hussein, Robert; Jaurigue, Lina; Governale, Michele; Braggio, Alessandro
20161201
We consider the subgap physics of a hybrid doublequantum dot Cooperpair splitter with large singlelevel spacings, in the presence of tunneling between the dots and finite Coulomb intra and interdot Coulomb repulsion. In the limit of a large superconducting gap, we treat the coupling of the dots to the superconductor exactly. We employ a generalized masterequation method, which easily yields currents, noise, and crosscorrelators. In particular, for finite inter and intradot Coulomb interaction, we investigate how the transport properties are determined by the interplay between local and nonlocal tunneling processes between the superconductor and the dots. We examine the effect of interdot tunneling on the particlehole symmetry of the currents with and without spinorbit interaction. We show that spinorbit interaction in combination with finite Coulomb energy opens the possibility to control the nonlocal entanglement and its symmetry (singlet/triplet). We demonstrate that the generation of nonlocal entanglement can be achieved even without any direct nonlocal coupling to the superconducting lead.
3D quantum gravity and effective noncommutative quantum field theory.
Freidel, Laurent; Livine, Etera R
20060609
We show that the effective dynamics of matter fields coupled to 3D quantum gravity is described after integration over the gravitational degrees of freedom by a braided noncommutative quantum field theory symmetric under a kappa deformation of the Poincaré group.
Improved Algorithm For FiniteField NormalBasis Multipliers
NASA Technical Reports Server (NTRS)
Wang, C. C.
19890101
Improved algorithm reduces complexity of calculations that must precede design of MasseyOmura finitefield normalbasis multipliers, used in errorcorrectingcode equipment and cryptographic devices. Algorithm represents an extension of development reported in "Algorithm To Design FiniteField NormalBasis Multipliers" (NPO17109), NASA Tech Briefs, Vol. 12, No. 5, page 82.
Quantum dynamics at finite temperature: Timedependent quantum Monte Carlo study
Christov, Ivan P.
20160815
In this work we investigate the ground state and the dissipative quantum dynamics of interacting charged particles in an external potential at finite temperature. The recently devised timedependent quantum Monte Carlo (TDQMC) method allows a selfconsistent treatment of the system of particles together with bath oscillators first for imaginarytime propagation of Schrödinger type of equations where both the system and the bath converge to their finite temperature ground state, and next for real time calculation where the dissipative dynamics is demonstrated. In that context the application of TDQMC appears as promising alternative to the pathintegral related techniques where the real time propagation can be a challenge.
Haag's theorem in noncommutative quantum field theory
Antipin, K. V.; Mnatsakanova, M. N.; Vernov, Yu. S.
20130815
Haag's theorem was extended to the general case of noncommutative quantum field theory when time does not commute with spatial variables. It was proven that if S matrix is equal to unity in one of two theories related by unitary transformation, then the corresponding one in the other theory is equal to unity as well. In fact, this result is valid in any SO(1, 1)invariant quantum field theory, an important example of which is noncommutative quantum field theory.
NASA Astrophysics Data System (ADS)
Krovi, Hari; Russell, Alexander
20150301
Knot and link invariants naturally arise from any braided Hopf algebra. We consider the computational complexity of the invariants arising from an elementary family of finitedimensional Hopf algebras: quantum doubles of finite groups [denoted , for a group G]. These induce a rich family of knot invariants and, additionally, are directly related to topological quantum computation. Regarding algorithms for these invariants, we develop quantum circuits for the quantum Fourier transform over ; in general, we show that when one can uniformly and efficiently carry out the quantum Fourier transform over the centralizers Z( g) of the elements of G, one can efficiently carry out the quantum Fourier transform over . We apply these results to the symmetric groups to yield efficient circuits for the quantum Fourier transform over . With such a Fourier transform, it is straightforward to obtain additive approximation algorithms for the related link invariant. As for hardness results, first we note that in contrast to those concerning the Jones polynomial—where the images of the braid group representations are dense in the unitary group—the images of the representations arising from are finite. This important difference appears to be directly reflected in the complexity of these invariants. While additively approximating "dense" invariants is complete and multiplicatively approximating them is complete, we show that certain invariants (such as invariants) are hard to additively approximate, hard to multiplicatively approximate, and hard to exactly evaluate. To show this, we prove that, for groups (such as A n ) which satisfy certain properties, the probability of success of any randomized computation can be approximated to within any by the plat closure. Finally, we make partial progress on the question of simulating anyonic computation in groups uniformly as a function of the group size. In this direction, we provide efficient quantum circuits for the Clebsch
Entanglement of a quantum field with a dispersive medium.
Klich, Israel
20120810
In this Letter we study the entanglement of a quantum radiation field interacting with a dielectric medium. In particular, we describe the quantum mixed state of a field interacting with a dielectric through plasma and Drude models and show that these generate very different entanglement behavior, as manifested in the entanglement entropy of the field. We also present a formula for a "Casimir" entanglement entropy, i.e., the distance dependence of the field entropy. Finally, we study a toy model of the interaction between two plates. In this model, the field entanglement entropy is divergent; however, as in the Casimir effect, its distancedependent part is finite, and the field matter entanglement is reduced when the objects are far.
NASA Astrophysics Data System (ADS)
Kumar, D. Sanjeev; Mukhopadhyay, Soma; Chatterjee, Ashok
20161101
The magnetization and susceptibility of a twoelectron parabolic quantum dot are studied in the presence of electronelectron and spinorbit interactions as a function of magnetic field and temperature. The spinorbit interactions are treated by a unitary transformation and an exactly soluble parabolic interaction model is considered to mimic the electronelectron interaction. The theory is finally applied to an InAs quantum dot. Magnetization and susceptibility are calculated using canonical ensemble approach. Our results show that Temperature has no effect on magnetization and susceptibility in the diamagnetic regime whereas electronelectron interaction reduces them. The temperature however reduces the height of the paramagnetic peak. The Rashba spinorbit interaction is shown to shift the paramagnetic peak towards higher magnetic fields whereas the Dresselhaus spinorbit interaction shifts it to the lower magnetic field side. Spinorbit interaction has no effect on magnetization and susceptibility at larger temperatures.
Measuring finite quantum geometries via quasicoherent states
NASA Astrophysics Data System (ADS)
Schneiderbauer, Lukas; Steinacker, Harold C.
20160701
We develop a systematic approach to determine and measure numerically the geometry of generic quantum or ‘fuzzy’ geometries realized by a set of finitedimensional Hermitian matrices. The method is designed to recover the semiclassical limit of quantized symplectic spaces embedded in {{{R}}}d including the wellknown examples of fuzzy spaces, but it applies much more generally. The central tool is provided by quasicoherent states, which are defined as ground states of Laplace or Dirac operators corresponding to localized point branes in target space. The displacement energy of these quasicoherent states is used to extract the local dimension and tangent space of the semiclassical geometry, and provides a measure for the quality and selfconsistency of the semiclassical approximation. The method is discussed and tested with various examples, and implemented in an opensource Mathematica package.
Quantum de Finetti theorems and meanfield theory from quantum phase space representations
NASA Astrophysics Data System (ADS)
Trimborn, F.; Werner, R. F.; Witthaut, D.
20160401
We introduce the numberconserving quantum phase space description as a versatile tool to address fundamental aspects of quantum manybody systems. Using phase space methods we prove two alternative versions of the quantum de Finetti theorem for finitedimensional bosonic quantum systems, which states that a reduced density matrix of a manybody quantum state can be approximated by a convex combination of product states where the error is proportional to the inverse particle number. This theorem provides a formal justification for the meanfield description of manybody quantum systems, as it shows that quantum correlations can be neglected for the calculation of fewbody observables when the particle number is large. Furthermore we discuss methods to derive the exact evolution equations for quantum phase space distribution functions as well as upper and lower bounds for the ground state energy. As an important example, we consider the BoseHubbard model and show that the meanfield dynamics is given by a classical phase space flow equivalent to the discrete GrossPitaevskii equation.
Integrand Reduction Reloaded: Algebraic Geometry and Finite Fields
NASA Astrophysics Data System (ADS)
Sameshima, Ray D.; Ferroglia, Andrea; Ossola, Giovanni
20170101
The evaluation of scattering amplitudes in quantum field theory allows us to compare the phenomenological prediction of particle theory with the measurement at collider experiments. The study of scattering amplitudes, in terms of their symmetries and analytic properties, provides a theoretical framework to develop techniques and efficient algorithms for the evaluation of physical cross sections and differential distributions. Treelevel calculations have been known for a long time. Loop amplitudes, which are needed to reduce the theoretical uncertainty, are more challenging since they involve a large number of Feynman diagrams, expressed as integrals of rational functions. At oneloop, the problem has been solved thanks to the combined effect of integrand reduction, such as the OPP method, and unitarity. However, plenty of work is still needed at higher orders, starting with the twoloop case. Recently, integrand reduction has been revisited using algebraic geometry. In this presentation, we review the salient features of integrand reduction for dimensionally regulated Feynman integrals, and describe an interesting technique for their reduction based on multivariate polynomial division. We also show a novel approach to improve its efficiency by introducing finite fields. Supported in part by the National Science Foundation under Grant PHY1417354.
Dynamical meanfield theory for quantum chemistry.
Lin, Nan; Marianetti, C A; Millis, Andrew J; Reichman, David R
20110304
The dynamical meanfield concept of approximating an unsolvable manybody problem in terms of the solution of an auxiliary quantum impurity problem, introduced to study bulk materials with a continuous energy spectrum, is here extended to molecules, i.e., finite systems with a discrete energy spectrum. The application to small clusters of hydrogen atoms yields ground state energies which are competitive with leading quantum chemical approaches at intermediate and large interatomic distances as well as good approximations to the excitation spectrum.
Sifting attacks in finitesize quantum key distribution
NASA Astrophysics Data System (ADS)
Pfister, Corsin; Lütkenhaus, Norbert; Wehner, Stephanie; Coles, Patrick J.
20160501
A central assumption in quantum key distribution (QKD) is that Eve has no knowledge about which rounds will be used for parameter estimation or key distillation. Here we show that this assumption is violated for iterative sifting, a sifting procedure that has been employed in some (but not all) of the recently suggested QKD protocols in order to increase their efficiency. We show that iterative sifting leads to two security issues: (1) some rounds are more likely to be key rounds than others, (2) the public communication of past measurement choices changes this bias round by round. We analyze these two previously unnoticed problems, present eavesdropping strategies that exploit them, and find that the two problems are independent. We discuss some sifting protocols in the literature that are immune to these problems. While some of these would be inefficient replacements for iterative sifting, we find that the sifting subroutine of an asymptotically secure protocol suggested by Lo et al (2005 J. Cryptol. 18 13365), which we call LCA sifting, has an efficiency on par with that of iterative sifting. One of our main results is to show that LCA sifting can be adapted to achieve secure sifting in the finitekey regime. More precisely, we combine LCA sifting with a certain parameter estimation protocol, and we prove the finitekey security of this combination. Hence we propose that LCA sifting should replace iterative sifting in future QKD implementations. More generally, we present two formal criteria for a sifting protocol that guarantee its finitekey security. Our criteria may guide the design of future protocols and inspire a more rigorous QKD analysis, which has neglected siftingrelated attacks so far.
Global Existence of Finite Energy Weak Solutions of Quantum NavierStokes Equations
NASA Astrophysics Data System (ADS)
Antonelli, Paolo; Spirito, Stefano
20170901
In this paper we consider the Quantum NavierStokes system both in two and in three space dimensions and prove the global existence of finite energy weak solutions for large initial data. In particular, the notion of weak solutions is the standard one. This means that the vacuum region is included in the weak formulation. In particular, no extra terms like damping or cold pressure are added to the system in order to define the velocity field in the vacuum region. The main contribution of this paper is the construction of a regular approximating system consistent with the effective velocity transformation needed to get the necessary a priori estimates.
Unusual signs in quantum field theory
NASA Astrophysics Data System (ADS)
O'Connell, Donal
Quantum field theory is by now a mature field. Nevertheless, certain physical phenomena remain difficult to understand. This occurs in some cases because wellestablished quantum field theories are strongly coupled and therefore difficult to solve; in other cases, our current understanding of quantum field theory seems to be inadequate. In this thesis, we will discuss various modifications of quantum field theory which can help to alleviate certain of these problems, either in their own right or as a component of a greater computational scheme. The modified theories we will consider all include unusual signs in some aspect of the theory. We will also discuss limitations on what we might expect to see in experiments, imposed by sign constraints in the customary formulation of quantum field theory.
Quantum field theory in spaces with closed timelike curves
NASA Astrophysics Data System (ADS)
Boulware, David G.
19921101
Gott spacetime has closed timelike curves, but no locally anomalous stress energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 2π. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, onshell, particles in the noncausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the noncausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.
Renormalization group for a continuoustime quantum search in finite dimensions
NASA Astrophysics Data System (ADS)
Li, Shanshan; Boettcher, Stefan
20170301
We consider the quantum search problem with a continuoustime quantum walk for networks characterized by a finite spectral dimension ds of the network Laplacian. For general networks of fractal (integer or noninteger) dimension df, for which in general df≠ds , it suggests that it is ds that determines the computational complexity of the quantum search. Our results continue those of A. M. Childs and J. Goldstone [Phys. Rev. A 70, 022314 (2004), 10.1103/PhysRevA.70.022314] for lattices of integer dimension, where d =df=ds . Thus, we find for general fractals that the Grover limit of quantum search can be obtained whenever ds>4 . This complements the recent discussion of meanfield (i.e., ds→∞ ) networks by S. Chakraborty et al. [Phys. Rev. Lett. 116, 100501 (2016), 10.1103/PhysRevLett.116.100501] showing that for all those networks, spatial search by quantum walk is optimal.
Finite anticanonical transformations in fieldantifield formalism
NASA Astrophysics Data System (ADS)
Batalin, Igor A.; Lavrov, Peter M.; Tyutin, Igor V.
20150601
We study the role of arbitrary (finite) anticanonical transformations in the fieldantifield formalism and the gaugefixing procedure based on the use of these transformations. The properties of the generating functionals of the Green functions subjected to finite anticanonical transformations are considered.
Exact integrability in quantum field theory
Thacker, H.B.
19800801
The treatment of exactly integrable systems in various branches of twodimensional classical and quantum physics has recently been placed in a unified framework by the development of the quantum inverse method. This method consolidates a broad range of developments in classical nonlinear wave (soliton) physics, statistical mechanics, and quantum field theory. The essential technique for analyzing exactly integrable quantum systems was invested by Bethe in 1931. The quantummechanical extension of the inverse scattering method and its relationship to the methods associated with Bethe's ansatz are examined here. (RWR)
Finitesize version of the excitonic instability in graphene quantum dots
Paananen, Tomi; Egger, Reinhold
20111015
By a combination of HartreeFock simulations, exact diagonalization, and perturbative calculations, we investigate the groundstate properties of disorderfree circular quantum dots formed in a graphene monolayer. Taking the reference chemical potential at the Dirac point, we study N{<=}15 interacting particles, where the fine structure constant {alpha} parametrizes the Coulomb interaction. We explore three different models: (i) Sucher's positive projection (''nopair'') approach, (ii) a more general Hamiltonian conserving both N and the number of additional electronhole pairs, and (iii) the full quantum electrodynamics problem, where only N is conserved. We find that electronhole pair production is important for {alpha} > or approx. 1. This corresponds to a reconstruction of the filled Dirac sea and is a finitesize version of the bulk excitonic instability. We also address the effects of an orbital magnetic field.
Holographic geometry of cMERA for quantum quenches and finite temperature
NASA Astrophysics Data System (ADS)
Mollabashi, Ali; Naozaki, Masahiro; Ryu, Shinsei; Takayanagi, Tadashi
20140301
We study the time evolution of cMERA (continuous MERA) under quantum quenches in free field theories. We calculate the corresponding holographic metric using the proposal in arXiv:1208.3469 and confirm that it qualitatively agrees with its gravity dual given by a half of the AdS black hole spacetime, argued by Hartman and Maldacena in arXiv:1303.1080. By doubling the cMERA for the quantum quench, we give an explicit construction of finite temperature cMERA. We also study cMERA in the presence of chemical potential and show that there is an enhancement of metric in the infrared region corresponding to the Fermi energy.
Quantum simulation of quantum field theory using continuous variables
Marshall, Kevin; Pooser, Raphael C.; Siopsis, George; Weedbrook, Christian
20151214
Much progress has been made in the field of quantum computing using continuous variables over the last couple of years. This includes the generation of extremely large entangled cluster states (10,000 modes, in fact) as well as a fault tolerant architecture. This has lead to the point that continuousvariable quantum computing can indeed be thought of as a viable alternative for universal quantum computing. With that in mind, we present a new algorithm for continuousvariable quantum computers which gives an exponential speedup over the best known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonic quantum field theory, a problem that is known to be hard using a classical computer. Thus, we give an experimental implementation based on cluster states that is feasible with today's technology.
Quantum simulation of quantum field theory using continuous variables
Marshall, Kevin; Pooser, Raphael C.; Siopsis, George; ...
20151214
Much progress has been made in the field of quantum computing using continuous variables over the last couple of years. This includes the generation of extremely large entangled cluster states (10,000 modes, in fact) as well as a fault tolerant architecture. This has lead to the point that continuousvariable quantum computing can indeed be thought of as a viable alternative for universal quantum computing. With that in mind, we present a new algorithm for continuousvariable quantum computers which gives an exponential speedup over the best known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonicmore » quantum field theory, a problem that is known to be hard using a classical computer. Thus, we give an experimental implementation based on cluster states that is feasible with today's technology.« less
Simulating quantum fields with cavity QED.
Barrett, Sean; Hammerer, Klemens; Harrison, Sarah; Northup, Tracy E; Osborne, Tobias J
20130301
As the realization of a fully operational quantum computer remains distant, quantum simulation, whereby one quantum system is engineered to simulate another, becomes a key goal of great practical importance. Here we report on a variational method exploiting the natural physics of cavity QED architectures to simulate strongly interacting quantum fields. Our scheme is broadly applicable to any architecture involving tunable and strongly nonlinear interactions with light; as an example, we demonstrate that existing cavity devices could simulate models of strongly interacting bosons. The scheme can be extended to simulate systems of entangled multicomponent fields, beyond the reach of existing classical simulation methods.
QuantumShell Corrections to the FiniteTemperature ThomasFermiDirac Statistical Model of the Atom
Ritchie, A B
20030722
Quantumshell corrections are made directly to the finitetemperature ThomasFermiDirac statistical model of the atom by a partition of the electronic density into bound and free components. The bound component is calculated using analytic basis functions whose parameters are chosen to minimize the energy. Poisson's equation is solved for the modified density, thereby avoiding the need to solve Schroedinger's equation for a selfconsistent field. The shock Hugoniot is calculated for aluminum: shell effects characteristic of quantum selfconsistent field models are fully captures by the present model.
Free Quantum Field Theory from Quantum Cellular Automata
NASA Astrophysics Data System (ADS)
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo; Tosini, Alessandro
20151001
After leading to a new axiomatic derivation of quantum theory (see D'Ariano et al. in Found Phys, 2015), the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field theory to including an hypothetical Planck scale, and with the usual quantum field theory recovered in the relativistic limit of small wavevectors. Being derived from simple principles (linearity, unitarity, locality, homogeneity, isotropy, and minimality of dimension), the automata theory is quantum abinitio, and does not assume Lorentz covariance and mechanical notions. Being discrete it can describe localized states and measurements (unmanageable by quantum field theory), solving all the issues plaguing field theory originated from the continuum. These features make the theory an ideal framework for quantum gravity, with relativistic covariance and spacetime emergent solely from the interactions, and not assumed a priori. The paper presents a synthetic derivation of the automata theory, showing how the principles lead to a description in terms of a quantum automaton over a Cayley graph of a group. Restricting to Abelian groups we show how the automata recover the Weyl, Dirac and Maxwell dynamics in the relativistic limit. We conclude with some new routes about the more general scenario of nonAbelian Cayley graphs. The phenomenology arising from the automata theory in the ultrarelativistic domain and the analysis of corresponding distorted Lorentz covariance is reviewed in Bisio et al. (Found Phys 2015, in this same issue).
Finitetime measurement of quantum particle's mean position
NASA Astrophysics Data System (ADS)
Liu, Y.; Sokolovski, D.
20010101
We analyze nonrelativistic quantum measurement of the time average of the particle's coordinate, X≡t 1∫t0x(t')dt'. The measurement amplitude is constructed by restricting the Feynman path integral to paths with the required value of X. The resulting decomposition of the Schrödinger wave function determines the type of meter needed to measure X. We show that such meter can be realized as a magnetic moment traveling with the particle in a magnetic field whose magnitude linearly changes with x. Weak and strong measurement regimes are discussed.
Classical field approach to quantum weak measurements.
Dressel, Justin; Bliokh, Konstantin Y; Nori, Franco
20140321
By generalizing the quantum weak measurement protocol to the case of quantum fields, we show that weak measurements probe an effective classical background field that describes the average field configuration in the spacetime region between pre and postselection boundary conditions. The classical field is itself a weak value of the corresponding quantum field operator and satisfies equations of motion that extremize an effective action. Weak measurements perturb this effective action, producing measurable changes to the classical field dynamics. As such, weakly measured effects always correspond to an effective classical field. This general result explains why these effects appear to be robust for pre and postselected ensembles, and why they can also be measured using classical field techniques that are not weak for individual excitations of the field.
Finiterange multiplexing enhances quantum key distribution via quantum repeaters
NASA Astrophysics Data System (ADS)
Abruzzo, Silvestre; Kampermann, Hermann; Bruß, Dagmar
20140101
Quantum repeaters represent one possible way to achieve longdistance quantum key distribution. Collins et al. [O. A. Collins, S. D. Jenkins, A. Kuzmich, and T. A. B. Kennedy, Phys. Rev. Lett. 98, 060502 (2007), 10.1103/PhysRevLett.98.060502] proposed multiplexing as a method to increase the repeater rate and to decrease the requirement of memory coherence time. Motivated by the experimental fact that longrange connections are practically demanding, in this paper we extend the original quantum repeater multiplexing protocol to the case of shortrange connection. We derive analytical formulas for the repeater rate and we show that for short connection lengths it is possible to have most of the benefits of a fullrange multiplexing protocol. Then we incorporate decoherence of quantum memories and we study the optimal matching for the Bellstate measurement protocol permitting us to minimize the memory requirements. Finally, we calculate the secret key rate and we show that the improvement via finiterange multiplexing is of the same order of magnitude as that via fullrange multiplexing.
Dynamics of quantum coherence in twodimensional quantum walk on finite lattices
NASA Astrophysics Data System (ADS)
He, Zhimin; Huang, Zhiming; Situ, Haozhen
20170701
We study the dynamics of the l1 norm coherence in a twodimensional quantum walk on finite lattices with fourdimensional (4D) and twodimensional (2D) coins. It is observed that the boundaries suppress the growth of coherence of both the whole system and the position subsystem. The coherence of the quantum walk with a 2D coin is larger than that of the quantum walk with a 4D coin when it stabilizes after a number of steps. We also analyze the influence of two kinds of noise, i.e., broken links and lattice congestion, on the coherence of a bounded quantum walk. Experimental results show that both the broken links and the lattice congestion with low probability slightly increase the coherence of the whole system and the position subsystem. However, a high noise level significantly suppresses the growth of coherence, especially for static noise. The coherence of the coin subsystem is also analyzed and we find that the boundaries result in a large fluctuation of coherence of the coin subsystem.
Pilotwave theory and quantum fields
NASA Astrophysics Data System (ADS)
Struyve, Ward
20101001
Pilotwave theories provide possible solutions to the measurement problem. In such theories, quantum systems are not only described by the state vector but also by some additional variables. These additional variables, also called beables, can be particle positions, field configurations, strings, etc. In this paper we focus our attention on pilotwave theories in which the additional variables are field configurations. The first such theory was proposed by Bohm for the free electromagnetic field. Since Bohm, similar pilotwave theories have been proposed for other quantum fields. The purpose of this paper is to present an overview and further development of these proposals. We discuss various bosonic quantum field theories such as the Schrödinger field, the free electromagnetic field, scalar quantum electrodynamics and the Abelian Higgs model. In particular, we compare the pilotwave theories proposed by Bohm and by Valentini for the electromagnetic field, finding that they are equivalent. We further discuss the proposals for fermionic fields by Holland and Valentini. In the case of Holland's model we indicate that further work is required in order to show that the model is capable of reproducing the standard quantum predictions. We also consider a similar model, which does not seem to reproduce the standard quantum predictions. In the case of Valentini's model we point out a problem that seems hard to overcome.
Neoclassical Radial Electric Field and Transport with Finite Orbits
Wang, W. X.; Hinton, F. L.; Wong, S. K.
20010730
Neoclassical transport in a toroidal plasma with finite ion orbits is studied, including for the first time the selfconsistent radial electric field. Using a lownoise {delta}f particle simulation, we demonstrate that a deep electricfield well develops in a region with a steep density gradient, because of the selfcollisiondriven ion flux. We find that the electric field agrees with the standard neoclassical expression, when the toroidal rotation is zero, even for a steep density gradient. Ion thermal transport is modified by the electricfield well in a way which is consistent with the orbit squeezing effect, but smoothed by the finite orbits.
Continuum regularization of quantum field theory
Bern, Z.
19860401
Possible nonperturbative continuum regularization schemes for quantum field theory are discussed which are based upon the Langevin equation of Parisi and Wu. Breit, Gupta and Zaks made the first proposal for new gauge invariant nonperturbative regularization. The scheme is based on smearing in the ''fifthtime'' of the Langevin equation. An analysis of their stochastic regularization scheme for the case of scalar electrodynamics with the standard covariant gauge fixing is given. Their scheme is shown to preserve the masslessness of the photon and the tensor structure of the photon vacuum polarization at the oneloop level. Although stochastic regularization is viable in oneloop electrodynamics, two difficulties arise which, in general, ruins the scheme. One problem is that the superficial quadratic divergences force a bottomless action for the noise. Another difficulty is that stochastic regularization by fifthtime smearing is incompatible with Zwanziger's gauge fixing, which is the only known nonperturbaive covariant gauge fixing for nonabelian gauge theories. Finally, a successful covariant derivative scheme is discussed which avoids the difficulties encountered with the earlier stochastic regularization by fifthtime smearing. For QCD the regularized formulation is manifestly Lorentz invariant, gauge invariant, ghost free and finite to all orders. A vanishing gluon mass is explicitly verified at one loop. The method is designed to respect relevant symmetries, and is expected to provide suitable regularization for any theory of interest. Hopefully, the scheme will lend itself to nonperturbative analysis. 44 refs., 16 figs.
Quantum simulation of quantum field theory using continuous variables
NASA Astrophysics Data System (ADS)
Marshall, Kevin; Pooser, Raphael; Siopsis, George; Weedbrook, Christian
20151201
The year 1982 is often credited as the year that theoretical quantum computing was started with a keynote speech by Richard Feynman, who proposed a universal quantum simulator, the idea being that if you had such a machine you could in principle "imitate any quantum system, including the physical world." With that in mind, we present an algorithm for a continuousvariable quantum computing architecture which gives an exponential speedup over the bestknown classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonic quantum field theory, a problem that is believed to be hard using a classical computer. Building on this, we give an experimental implementation based on continuousvariable states that is feasible with today's technology.
Continuous Time Finite State Mean Field Games
Gomes, Diogo A.; Mohr, Joana Souza, Rafael Rigao
20130801
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initialterminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1player problem, which the mean field model attempts to approximate. Our main result is the convergence as N{yields}{infinity} of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games.
A generalized algorithm to design finite field normal basis multipliers
NASA Technical Reports Server (NTRS)
Wang, C. C.
19860101
Finite field arithmetic logic is central in the implementation of some errorcorrecting coders and some cryptographic devices. There is a need for good multiplication algorithms which can be easily realized. Massey and Omura recently developed a new multiplication algorithm for finite fields based on a normal basis representation. Using the normal basis representation, the design of the finite field multiplier is simple and regular. The fundamental design of the MasseyOmura multiplier is based on a design of a product function. In this article, a generalized algorithm to locate a normal basis in a field is first presented. Using this normal basis, an algorithm to construct the product function is then developed. This design does not depend on particular characteristics of the generator polynomial of the field.
Quantum entanglement of local operators in conformal field theories.
Nozaki, Masahiro; Numasawa, Tokiro; Takayanagi, Tadashi
20140321
We introduce a series of quantities which characterize a given local operator in any conformal field theory from the viewpoint of quantum entanglement. It is defined by the increased amount of (Rényi) entanglement entropy at late time for an excited state defined by acting the local operator on the vacuum. We consider a conformal field theory on an infinite space and take the subsystem in the definition of the entanglement entropy to be its half. We calculate these quantities for a free massless scalar field theory in two, four and six dimensions. We find that these results are interpreted in terms of quantum entanglement of a finite number of states, including EinsteinPodolskyRosen states. They agree with a heuristic picture of propagations of entangled particles.
Quantum Entanglement of Local Operators in Conformal Field Theories
NASA Astrophysics Data System (ADS)
Nozaki, Masahiro; Numasawa, Tokiro; Takayanagi, Tadashi
20140301
We introduce a series of quantities which characterize a given local operator in any conformal field theory from the viewpoint of quantum entanglement. It is defined by the increased amount of (Rényi) entanglement entropy at late time for an excited state defined by acting the local operator on the vacuum. We consider a conformal field theory on an infinite space and take the subsystem in the definition of the entanglement entropy to be its half. We calculate these quantities for a free massless scalar field theory in two, four and six dimensions. We find that these results are interpreted in terms of quantum entanglement of a finite number of states, including EinsteinPodolskyRosen states. They agree with a heuristic picture of propagations of entangled particles.
Exact quantum field mappings between different experiments on quantum gases
NASA Astrophysics Data System (ADS)
Wamba, Etienne; Pelster, Axel; Anglin, James R.
20161001
Experiments on trapped quantum gases can probe challenging regimes of quantum manybody dynamics, where strong interactions or nonequilibrium states prevent exact solutions. Here we present a different kind of exact result, which applies even in the absence of actual solutions: a class of spacetime mappings of different experiments onto each other. Since our result is an identity relating secondquantized field operators in the Heisenberg picture of quantum mechanics, it is extremely general; it applies to arbitrary measurements on any mixtures of Bose or Fermi gases, in arbitrary initial states. It represents a strong prediction of quantum field theory which can be tested in current laboratories, and whose practical applications include perfect simulation of interesting experiments with other experiments which may be easier to perform.
NASA Astrophysics Data System (ADS)
Rajabpour, M. A.
20161201
We calculate formation probabilities of the ground state of the finite size quantum critical chains using conformal field theory (CFT) techniques. In particular, we calculate the formation probability of one interval in the finite open chain and also formation probability of two disjoint intervals in a finite periodic system. The presented formulas can be also interpreted as the Casimir energy of needles in particular geometries. We numerically check the validity of the exact CFT results in the case of the transverse field Ising chain.
Fields and Laplacians on Quantum Geometries
NASA Astrophysics Data System (ADS)
Thürigen, Johannes
20150101
In fundamentally discrete approaches to quantum gravity such as loop quantum gravity, spinfoam models, group field theories or Regge calculus observables are functions on discrete geometries. We present a braket formalism of function spaces and discrete calculus on abstract simplicial complexes equipped with geometry and apply it to the mentioned theories of quantum gravity. In particular we focus on the quantum geometric Laplacian and discuss as an example the expectation value of the heat kernel trace from which the spectral dimension follows.
Fractional Talbot field and of finite gratings: compact analytical formulation.
Arrizón, V; RojoVelázquez, G
20010601
We present a compact analytical formulation for the fractional Talbot effect at the paraxial domain of a finite grating. Our results show that laterally shifted distorted images of the grating basic cell form the Fresnel field at a fractional Talbot plane of the grating. Our formulas give the positions of those images and show that they are given by the convolution of the nondistorted cells (modulated by a quadratic phase factor) with the Fourier transform of the finitegrating pupil.
Quantum equivalence of dual field theories
NASA Astrophysics Data System (ADS)
Fradkin, E. S.; Tseytlin, A. A.
19850601
Motivated by the study of ultraviolet properties of different versions of supergravities duality transformations at the quantum level are discussed. Using the background field method it is proven on shell quantum equivalence for several pairs of dual field theories known to be classically equivalent. The examples considered include duality in chiral model, duality of scalars and second rank antisymmetric gauge tensors, vector duality and duality of the Einstein theory with cosmological term and the EddingtonSchrödinger theory.
Geometric continuum regularization of quantum field theory
Halpern, M.B. . Dept. of Physics)
19891108
An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinateinvariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs.
Electromagnetic field at finite temperature: A first order approach
NASA Astrophysics Data System (ADS)
Casana, R.; Pimentel, B. M.; Valverde, J. S.
20061001
In this work we study the electromagnetic field at finite temperature via the massless DKP formalism. The constraint analysis is performed and the partition function for the theory is constructed and computed. When it is specialized to the spin 1 sector we obtain the wellknown result for the thermodynamic equilibrium of the electromagnetic field.
Spinor field theory at finite temperature in the early Universe
NASA Astrophysics Data System (ADS)
Banerjee, N.; Mallik, S.
19920101
We consider the Dirac field on a spatially flat RobertsonWalker spacetime. We find the exact expression for the Dirac propagator for an arbitrary scale factor in the realtime formulation of finitetemperature field theory. The mode functions used in the construction satisfy uncoupled ordinary differential equations.
Finite temperature quantum critical transport near the Mott transition
NASA Astrophysics Data System (ADS)
Terletska, Hanna; Dobrosavljevic, Vladimir
20100301
We use Dynamical MeanField Theory to study incoherent transport above the critical endpoint temperature Tc of the single band Hubbard model at halffilling. By employing an eigenvalue analysis for the free energy functional, we are able to precisely identify the crossover temperature T*(U) separating the Fermi liquid and the Mott insulating regimes. Our calculations demonstrate that a broad parameter range exist around the crossover line, where the family of resistivity curves displays simple scaling behavior. This is interpreted as a manifestation of quantum criticality controlled by the T=0 Mott transition, which is ``interrupted'' by the emergence of the coexistence dome at T < Tc . We argue that in situations where the critical temperature Tc is significantly reduced, so that the coexistence region is reduced or even absent (as in twoband, particlehole asymmetric models, where this is found even in the clean d>∞ limit [1, 2]), similar critical scaling properties should persist down to much lower temperatures, resembling quantum critical transport similar to that found in a number of experiments [2]. [1] A. Amaricci, G. Sordi, and M. J. Rosenberg, Phys. Rev. Lett. 101, 146403 (2008) [2] A. Camjayi, K. Haule, V. Dobrosavljevic, and G. Kotliar, Nature Physics, 4, 932 (2008)
Dynamical meanfield theory from a quantum chemical perspective.
Zgid, Dominika; Chan, Garnet KinLic
20110307
We investigate the dynamical meanfield theory (DMFT) from a quantum chemical perspective. Dynamical meanfield theory offers a formalism to extend quantum chemical methods for finite systems to infinite periodic problems within a local correlation approximation. In addition, quantum chemical techniques can be used to construct new ab initio Hamiltonians and impurity solvers for DMFT. Here, we explore some ways in which these things may be achieved. First, we present an informal overview of dynamical meanfield theory to connect to quantum chemical language. Next, we describe an implementation of dynamical meanfield theory where we start from an ab initio HartreeFock Hamiltonian that avoids double counting issues present in many applications of DMFT. We then explore the use of the configuration interaction hierarchy in DMFT as an approximate solver for the impurity problem. We also investigate some numerical issues of convergence within DMFT. Our studies are carried out in the context of the cubic hydrogen model, a simple but challenging test for correlation methods. Finally, we finish with some conclusions for future directions.
Quantum field theory on toroidal topology: Algebraic structure and applications
NASA Astrophysics Data System (ADS)
Khanna, F. C.; Malbouisson, A. P. C.; Malbouisson, J. M. C.; Santana, A. E.
20140501
The development of quantum theory on a torus has a long history, and can be traced back to the 1920s, with the attempts by Nordström, Kaluza and Klein to define a fourth spatial dimension with a finite size, being curved in the form of a torus, such that Einstein and Maxwell equations would be unified. Many developments were carried out considering cosmological problems in association with particle physics, leading to methods that are useful for areas of physics, in which size effects play an important role. This interest in finite size effect systems has been increasing rapidly over the last decades, due principally to experimental improvements. In this review, the foundations of compactified quantum field theory on a torus are presented in a unified way, in order to consider applications in particle and condensed matter physics. The theory on a torus ΓDd=(S1)d×RDd is developed from a Liegroup representation and c*c*algebra formalisms. As a first application, the quantum field theory at finite temperature, in its real and imaginarytime versions, is addressed by focusing on its topological structure, the torus Γ41. The toroidal quantumfield theory provides the basis for a consistent approach of spontaneous symmetry breaking driven by both temperature and spatial boundaries. Then the superconductivity in films, wires and grains are analyzed, leading to some results that are comparable with experiments. The Casimir effect is studied taking the electromagnetic and Dirac fields on a torus. In this case, the method of analysis is based on a generalized Bogoliubov transformation, that separates the Green function into two parts: one is associated with the empty spacetime, while the other describes the impact of compactification. This provides a natural procedure for calculating the renormalized energymomentum tensor. Self interacting fourfermion systems, described by the GrossNeveu and NambuJonaLasinio models, are considered. Then finite size effects on
Arrival time in quantum field theory
NASA Astrophysics Data System (ADS)
Wang, ZhiYong; Xiong, CaiDong; He, Bing
20080901
Via the propertime eigenstates (event states) instead of the propermass eigenstates (particle states), freemotion timeofarrival theory for massive spin1/2 particles is developed at the level of quantum field theory. The approach is based on a positionmomentum dual formalism. Within the framework of field quantization, the total timeofarrival is the sum of the single eventofarrival contributions, and contains zeropoint quantum fluctuations because the clocks under consideration follow the laws of quantum mechanics.
Quantum Hall Physics Equals Noncommutive Field Theory
Rammsdonk , Mark van
20010809
In this note, we study a matrixregularized version of noncommutative U(1) ChernSimons theory proposed recently by Polychronakos. We determine a complete minimal basis of exact wavefunctions for the theory at arbitrary level k and rank N and show that these are in onetoone correspondence with Laughlintype wavefunctions describing excitations of a quantum Hall droplet composed of N electrons at filling fraction 1/k. The finite matrix ChernSimons theory is shown to be precisely equivalent to the theory of composite fermions in the lowest Landau level, believed to provide an accurate description of the filling fraction 1/k fractional quantum Hall state. In the large N limit, this implies that level k noncommutative U(1) ChernSimons theory is equivalent to the Laughlin theory of the filling fraction 1k quantum Hall fluid, as conjectured recently by Susskind.
The quantum compass chain in a transverse magnetic field
NASA Astrophysics Data System (ADS)
Motamedifar, M.; Mahdavifar, S.; Farjami Shayesteh, S.
20110901
We study the magnetic behaviors of a spin1/2 quantum compass chain (QCC) in a transverse magnetic field, by means of the analytical spinless fermion approach and numerical Lanczos method. In the absence of the magnetic field, the phase diagram is divided into four gapped regions. To determine what happens by applying a transverse magnetic field, using the spinless fermion approach, critical fields are obtained as a function of exchanges. Our analytical results show, the fieldinduced effects depend on in which one of the four regions the system is. In two regions of the phase diagram, the Isingtype phase transition happens in a finite field. In another region, we have identified two quantum phase transitions (QPT)s in the ground state magnetic phase diagram. These quantum phase transitions belong to the universality class of the commensurateincommensurate phase transition. We also present a detailed numerical analysis of the low energy spectrum and the ground state magnetic phase diagram. In particular, we show that the intermediate state (hc1 < h < hc2) is gapful, describing the spinflop phase.
Nearfield magnetoabsorption of quantum dots
NASA Astrophysics Data System (ADS)
Simserides, Constantinos; Zora, Anna; Triberis, Georgios
20060401
We investigate the effect of an external magnetic field of variable orientation and magnitude (up to 20T ) on the linear nearfield optical absorption spectra of single and coupled IIIV semiconductor quantum dots. We focus on the spatial as well as on the magnetic confinement, varying the dimensions of the quantum dots and the magnetic field. We show that the groundstate exciton binding energy can be manipulated utilizing the spatial and magnetic confinement. The effect of the magnetic field on the absorption spectra, increasing the nearfield illumination spot, is also investigated. The zeromagneticfield “structural” symmetry can be destroyed varying the magnetic field orientation and this affects the nearfield spectra. The asymmetry induced (except for specific orientations along symmetry axes) by the magnetic field can be revealed in the nearfield but not in the farfield spectra. We predict that nearfield magnetoabsorption experiments, of realistic spatial resolution, will be in the position to bring to light the quantum dot symmetry. This exceptional symmetryresolving power of the nearfield magnetoabsorption is lost in the far field. The influence of the Coulomb interactions on the absorption spectra is also discussed. Finally, we show that certain modifications of the magnetoexcitonic structure can be uncovered using a realistically acute nearfield probe of ≈20nm .
Spinpolarized electronhole quantum bilayers: finite layer width and massasymmetric effects
NASA Astrophysics Data System (ADS)
Gangadhar Nayak, Mukesh; Saini, Lalit Kumar
20130301
The influence of massasymmetry and finite layer width in phasetransition from the liquidstate to the densitymodulated groundstate of the spinpolarized electronhole quantum bilayers (EHBL) is explored within the Singwi, Tosi, Land and Sjölander (qSTLS) approach. At the same number density of electrons and holes, in addition to the stronger interlayer correlations, the massasymmetry also shows stronger intralayer correlations in the hole layer than that of the electron layer. This change in the behaviour of correlations affects the groundstate of the spinpolarized EHBL system. Interestingly, we notice the enhancement of critical density for the onset of Wigner crystallization as compared to the recent results of spinpolarized masssymmetric EHBL system. Paircorrelation function and localfield correction factor show a strong inphase oscillations at the instability region. Further, we find that the inclusion of finite layer width weakens the intralayer correlations. As a result, the critical density for Wigner crystallization is lowered. The present results are compared with the recent results of spinpolarized (and unpolarized) masssymmetric EHBL with zero (finite) layer width. Contribution to the Topical Issue "Excitonic Processes in Condensed Matter, Nanostructured and Molecular Materials", edited by Maria Antonietta Loi, Jasper Knoester and Paul H. M. van Loosdrecht.
Universal shorttime quantum critical dynamics of finitesize systems
NASA Astrophysics Data System (ADS)
Shu, YuRong; Yin, Shuai; Yao, DaoXin
20170901
We investigate the shorttime quantum critical dynamics in the imaginarytime relaxation processes of finitesize systems. Universal scaling behaviors exist in the imaginarytime evolution. In particular, the system undergoes a critical initial slip stage characterized by an exponent θ , in which an initial powerlaw increase emerges in the imaginarytime correlation function when the initial state has a zero order parameter and a vanishing correlation length. Under different initial conditions, the quantum critical point and critical exponents can be determined from the universal scaling behaviors. We apply the method to the one and twodimensional transverse field Ising models using quantum Monte Carlo (QMC) simulations. In the onedimensional case, we locate the quantum critical point at (h/J ) c=1.000 03 (8 ) in the thermodynamic limit, and we estimate the critical initial slip exponent θ =0.3734 (2 ) and the static exponent β /ν =0.1251 (2 ) by analyzing data on chains of length L =32 256 and 48256, respectively. For the twodimensional squarelattice system, the critical coupling ratio is given by 3.044 51 (7 ) in the thermodynamic limit, while the critical exponents are θ =0.209 (4 ) and β /ν =0.518 (1 ) estimated by data on systems of size L =24 64 and 3264, respectively. Remarkably, the critical initial slip exponents obtained in both models are notably distinct from their classical counterparts due to the essential differences between classical and quantum dynamics. The shorttime critical dynamics and the imaginarytime relaxation QMC approach can be readily adapted to various models.
Quantum processes: A Whiteheadian interpretation of quantum field theory
NASA Astrophysics Data System (ADS)
Bain, Jonathan
Quantum processes: A Whiteheadian interpretation of quantum field theory is an ambitious and thoughtprovoking exercise in physics and metaphysics, combining an erudite study of the very complex metaphysics of A.N. Whitehead with a wellinformed discussion of contemporary issues in the philosophy of algebraic quantum field theory. Hättich's overall goal is to construct an interpretation of quantum field theory. He does this by translating key concepts in Whitehead's metaphysics into the language of algebraic quantum field theory. In brief, this HättichWhitehead (HW, hereafter) interpretation takes "actual occasions" as the fundamental ontological entities of quantum field theory. An actual occasion is the result of two types of processes: a "transition process" in which a set of initial possiblypossessed properties for the occasion (in the form of "eternal objects") is localized to a spacetime region; and a "concrescence process" in which a subset of these initial possiblypossessed properties is selected and actualized to produce the occasion. Essential to these processes is the "underlying activity", which conditions the way in which properties are initially selected and subsequently actualized. In short, under the HW interpretation of quantum field theory, an initial set of possiblypossessed eternal objects is represented by a Boolean sublattice of the lattice of projection operators determined by a von Neumann algebra R (O) associated with a region O of Minkowski spacetime, and the underlying activity is represented by a state on R (O) obtained by conditionalizing off of the vacuum state. The details associated with the HW interpretation involve imposing constraints on these representations motivated by principles found in Whitehead's metaphysics. These details are spelled out in the three sections of the book. The first section is a summary and critique of Whitehead's metaphysics, the second section introduces the formalism of algebraic quantum field
Quantum Coherence and Random Fields at Mesoscopic Scales
Rosenbaum, Thomas F.
20160301
We seek to explore and exploit model, disordered and geometrically frustrated magnets where coherent spin clusters stably detach themselves from their surroundings, leading to extreme sensitivity to finite frequency excitations and the ability to encode information. Global changes in either the spin concentration or the quantum tunneling probability via the application of an external magnetic field can tune the relative weights of quantum entanglement and random field effects on the mesoscopic scale. These same parameters can be harnessed to manipulate domain wall dynamics in the ferromagnetic state, with technological possibilities for magnetic information storage. Finally, extensions from quantum ferromagnets to antiferromagnets promise new insights into the physics of quantum fluctuations and effective dimensional reduction. A combination of ac susceptometry, dc magnetometry, noise measurements, hole burning, nonlinear Fano experiments, and neutron diffraction as functions of temperature, magnetic field, frequency, excitation amplitude, dipole concentration, and disorder address issues of stability, overlap, coherence, and control. We have been especially interested in probing the evolution of the local order in the progression from spin liquid to spin glass to longrangeordered magnet.
New quantum codes from dualcontaining cyclic codes over finite rings
NASA Astrophysics Data System (ADS)
Tang, Yongsheng; Zhu, Shixin; Kai, Xiaoshan; Ding, Jian
20161101
Let R=F_{2m}+uF_{2m}+\\cdots +ukF_{2m}, where F_{2m} is the finite field with 2m elements, m is a positive integer, and u is an indeterminate with u^{k+1}=0. In this paper, we propose the constructions of two new families of quantum codes obtained from dualcontaining cyclic codes of odd length over R. A new Gray map over R is defined, and a sufficient and necessary condition for the existence of dualcontaining cyclic codes over R is given. A new family of 2mary quantum codes is obtained via the Gray map and the CalderbankShorSteane construction from dualcontaining cyclic codes over R. In particular, a new family of binary quantum codes is obtained via the Gray map, the trace map and the CalderbankShorSteane construction from dualcontaining cyclic codes over R.
Socioeconomic applications of finite state mean field games.
Gomes, Diogo; Velho, Roberto M; Wolfram, MarieTherese
20141113
In this paper, we present different applications of finite state mean field games to socioeconomic sciences. Examples include paradigm shifts in the scientific community or consumer choice behaviour in the free market. The corresponding finite state mean field game models are hyperbolic systems of partial differential equations, for which we present and validate different numerical methods. We illustrate the behaviour of solutions with various numerical experiments, which show interesting phenomena such as shock formation. Hence, we conclude with an investigation of the shock structure in the case of twostate problems.
NASA Astrophysics Data System (ADS)
de Vega, Sandra; Cox, Joel D.; de Abajo, F. Javier García
20160801
We study the potential of highly doped finite carbon nanotubes to serve as plasmonic elements that mediate the interaction between quantum emitters. Similar to graphene, nanotubes support intense plasmons that can be modulated by varying their level of electrical doping. These excitations exhibit large interaction with light and electron beams, as revealed upon examination of the corresponding light extinction crosssection and electron energyloss spectra. We show that quantum emitters experience recordhigh Purcell factors, while they undergo strong mutual interaction mediated by their coupling to the tube plasmons. Our results show the potential of doped finite nanotubes as tunable plasmonic materials for quantum optics applications.
Quantum jump model for a system with a finitesize environment.
Suomela, S; Kutvonen, A; AlaNissila, T
20160601
Measuring the thermodynamic properties of open quantum systems poses a major challenge. A calorimetric detection has been proposed as a feasible experimental scheme to measure work and fluctuation relations in open quantum systems. However, the detection requires a finite size for the environment, which influences the system dynamics. This process cannot be modeled with the standard stochastic approaches. We develop a quantum jump model suitable for systems coupled to a finitesize environment. We use the method to study the common fluctuation relations and prove that they are satisfied.
Regaining quantum incoherence for matter fields
GonzalezDriaaaz, P.F. )
19920115
The possible quantum state of wormholes or little baby universes should be described by a nonfactorizable density matrix given by the path integral over the class of asymptotically flat fourgeometries and asymptotically vanishing matterfield configurations which suitably match the prescribed data on threesurfaces which do not divide the manifold on the inner boundary. An instanton is here obtained which can represent such a nonsimply connected wormhole manifold, and is used to evaluate the asymptotic effective interaction of the resulting correlated baby universes with ordinary quantum fields at low energies in the Fock representation. It is argued that the demand of locality on the interacting quantum field commutators is no longer valid for correlated baby universes, and it is therefore concluded that quantum coherence in the matterfield sector is lost as a consequence of the interaction with nonsimply connected wormholes. A proposal is advanced that wormholes may provide us with a complementary quantum state sector that would induce the collapse of the state vector in the quantum measurement of any observable for ordinary microscopic matter systems.
Singularities in a scalar field quantum cosmology
NASA Astrophysics Data System (ADS)
Lemos, Nivaldo A.
19960401
The quantum theory of a spatially flat FriedmannRobertsonWalker universe with a massless scalar field as the source is further investigated. The classical model is singular and in the framework of a genuine canonical quantization (ArnowittDeserMisner formalism) a discussion is made of the cosmic evolution, particularly of the quantum gravitational collapse problem. It is shown that in a mattertime gauge such that time is identified with the scalar field the classical model is singular either at t=∞ or at t=+∞, but the quantum model is nonsingular. The latter behavior disproves a conjecture according to which quantum cosmological singularities are predetermined on the classical level by the choice of time.
Classical simulation of quantum fields I
NASA Astrophysics Data System (ADS)
Hirayama, T.; Holdom, B.
20061001
We study classical field theories in a background field configuration where all modes of the theory are excited, matching the zeropoint energy spectrum of quantum field theory. Our construction involves elements of a theory of classical electrodynamics by WheelerFeynman and the theory of stochastic electrodynamics of Boyer. The nonperturbative effects of interactions in these theories can be very efficiently studied on the lattice. In lambda phi(4) theory in 1 + 1 dimensions, we find results, in particular, for mass renormalization and the critical coupling for symmetry breaking that are in agreement with their quantum counterparts. We then study the perturbative expansion of the npoint Green's functions and find a loop expansion very similar to that of quantum field theory. When compared to the usual Feynman rules, we find some differences associated with particular combinations of internal lines going onshell simultaneously.
The facets of relativistic quantum field theory
NASA Astrophysics Data System (ADS)
Dosch, H. G.; Müller, V. F.
20110401
Relativistic quantum field theory is generally recognized to form the adequate theoretical frame for subatomic physics, with the Standard Model of Particle Physics as a major achievement. We point out that quantum field theory in its present form is not a monolithic theory, but rather consists of distinct facets, which aim at a common ideal goal. We give a short overview of the strengths and limitations of these facets. We emphasize the theorydependent relation between the quantum fields, and the basic objects in the empirical domain, the particles. Given the marked conceptual differences between the facets, we argue to view these, and therefore also the Standard Model, as symbolic constructions. We finally note that this view of physical theories originated in the 19th century and is related to the emergence of the classical field as an autonomous concept.
Universal order parameters and quantum phase transitions: a finitesize approach.
Shi, QianQian; Zhou, HuanQiang; Batchelor, Murray T
20150108
We propose a method to construct universal order parameters for quantum phase transitions in manybody lattice systems. The method exploits the Horthogonality of a few neardegenerate lowest states of the Hamiltonian describing a given finitesize system, which makes it possible to perform finitesize scaling and take full advantage of currently available numerical algorithms. An explicit connection is established between the fidelity per site between two Horthogonal states and the energy gap between the ground state and lowlying excited states in the finitesize system. The physical information encoded in this gap arising from finitesize fluctuations clarifies the origin of the universal order parameter. We demonstrate the procedure for the onedimensional quantum formulation of the qstate Potts model, for q = 2, 3, 4 and 5, as prototypical examples, using finitesize data obtained from the density matrix renormalization group algorithm.
Quantum Enhanced Estimation of a Multidimensional Field.
Baumgratz, Tillmann; Datta, Animesh
20160122
We present a framework for the quantum enhanced estimation of multiple parameters corresponding to noncommuting unitary generators. Our formalism provides a recipe for the simultaneous estimation of all three components of a magnetic field. We propose a probe state that surpasses the precision of estimating the three components individually, and we discuss measurements that come close to attaining the quantum limit. Our study also reveals that too much quantum entanglement may be detrimental to attaining the Heisenberg scaling in the estimation of unitarily generated parameters.
Quantum switches and nonlocal microwave fields
NASA Astrophysics Data System (ADS)
Davidovich, L.; Maali, A.; Brune, M.; Raimond, J. M.; Haroche, S.
19931001
A scheme to realize an optical switch with quantum coherence between its ``open'' and ``closed'' states is presented. It involves a single atom in a superposition of circular Rydberg states crossing a high Q cavity. A combination of switches could be used to prepare a quantum superposition of coherent microwave field states located simultaneously in two cavities. Such nonclassical states and their decoherence due to cavity dissipation could be studied by performing atom correlation experiments.
Self field electromagnetism and quantum phenomena
NASA Astrophysics Data System (ADS)
Schatten, Kenneth H.
19940701
Quantum Electrodynamics (QED) has been extremely successful inits predictive capability for atomic phenomena. Thus the greatest hope for any alternative view is solely to mimic the predictive capability of quantum mechanics (QM), and perhaps its usefulness will lie in gaining a better understanding of microscopic phenomena. Many ?paradoxes? and problematic situations emerge in QED. To combat the QED problems, the field of Stochastics Electrodynamics (SE) emerged, wherein a random ?zero point radiation? is assumed to fill all of space in an attmept to explain quantum phenomena, without some of the paradoxical concerns. SE, however, has greater failings. One is that the electromagnetic field energy must be infinit eto work. We have examined a deterministic side branch of SE, ?self field? electrodynamics, which may overcome the probelms of SE. Self field electrodynamics (SFE) utilizes the chaotic nature of electromagnetic emissions, as charges lose energy near atomic dimensions, to try to understand and mimic quantum phenomena. These fields and charges can ?interact with themselves? in a nonlinear fashion, and may thereby explain many quantum phenomena from a semiclassical viewpoint. Referred to as self fields, they have gone by other names in the literature: ?evanesccent radiation?, ?virtual photons?, and ?vacuum fluctuations?. Using self fields, we discuss the uncertainty principles, the Casimir effects, and the blackbody radiation spectrum, diffraction and interference effects, Schrodinger's equation, Planck's constant, and the nature of the electron and how they might be understood in the present framework. No new theory could ever replace QED. The self field view (if correct) would, at best, only serve to provide some understanding of the processes by which strange quantum phenomena occur at the atomic level. We discuss possible areas where experiments might be employed to test SFE, and areas where future work may lie.
Efficiency, Power and Period of a model quantum heat engine working in a finite time
NASA Astrophysics Data System (ADS)
Bekele, Mulugeta; Dima, Tolasa A.; Alemye, Mekuannent; Chegeno, Warga
We take a spinhalf quantum particle undergoing Carnot type cyclic process in a finite time assisted by two heat reservoirs and an external magnetic field. We find that the power of the heat engine is maximum at a particular period of the cyclic process and efficiency at the maximum power is at least half of the Carnot efficiency. We further apply the Omegacriterion for a figure of merit representing a compromise between useful power and lost power determining the corresponding efficiency for the optimization criterion to be at least three fourth of the Carnot efficiency. The authers are thankful to the International Science programme, IPS, Uppsala, Sweden for their support to our research lab.
Quantum Otto cycle with inner friction: finitetime and disorder effects
NASA Astrophysics Data System (ADS)
Alecce, A.; Galve, F.; Lo Gullo, N.; Dell'Anna, L.; Plastina, F.; Zambrini, R.
20150701
The concept of inner friction, by which a quantum heat engine is unable to follow adiabatically its strokes and thus dissipates useful energy, is illustrated in an exact physical model where the working substance consists of an ensemble of misaligned spins interacting with a magnetic field and performing the Otto cycle. The effect of this static disorder under a finitetime cycle gives a new perspective of the concept of inner friction under realistic settings. We investigate the efficiency and power of this engine and relate its performance to the amount of friction from misalignment and to the temperature difference between heat baths. Finally we propose an alternative experimental implementation of the cycle where the spin is encoded in the degree of polarization of photons.
Quantum contextual finite geometries from dessins d'enfants
NASA Astrophysics Data System (ADS)
Planat, Michel; Giorgetti, Alain; Holweck, Frédéric; Saniga, Metod
20150401
We point out an explicit connection between graphs drawn on compact Riemann surfaces defined over the field \\bar Q of algebraic numbers — the socalled Grothendieck's dessins d'enfants — and a wealth of distinguished pointline configurations. These include simplices, crosspolytopes, several notable projective configurations, a number of multipartite graphs and some "exotic" geometries. Among them, remarkably, we find not only those underlying Mermin's magic square and magic pentagram, but also those related to the geometry of two and threequbit Pauli groups. Of particular interest is the occurrence of all the three types of slim generalized quadrangles, namely GQ(2, 1), GQ(2, 2) and GQ(2, 4), and a couple of closely related graphs, namely the Schläfli and Clebsch ones. These findings seem to indicate that dessins d'enfants may provide us with a new powerful tool for gaining deeper insight into the nature of finitedimensional Hilbert spaces and their associated groups, with a special emphasis on contextuality.
TwoElement Generation of Unitary Groups Over Finite Fields
20130131
like to praise my Lord and Savior, Jesus Christ , for allowing me this opportunity to work on a Ph.D in mathematics, and for His sustaining grace...Ishibashi’s original result. The paper’s main theorem will show that all unitary groups over finite fields of odd characteristic are generated by only two
Finiteelementanalysis of fields radiated from ICRF antenna
NASA Astrophysics Data System (ADS)
Yamanaka, K.; Sugihara, R.
19840401
In several simple geometries, electromagnetic fields radiated from a loop antennas, on which a current oscillately flows across the static magnetic field are calculated by the finite element method (FEM) as well as by analytic methods in a cross section of a plasma cylinder. A finite wave number along the static magnetic field is assumed. Good agreement between FEM and the analytic solutions is obtained, which indicates the accuracy of FEM solutions. The method is applied to calculations of fields from a half turn antenna and reasonable results are obtained. It is found that a straightforward application of FEM to problems in an anisotropic medium may bring about erroneous results and that an appropriate coordinate transformation is needed for FEM become applicable.
Quantum transport in topological semimetals under magnetic fields
NASA Astrophysics Data System (ADS)
Lu, HaiZhou; Shen, ShunQing
20170601
Topological semimetals are threedimensional topological states of matter, in which the conduction and valence bands touch at a finite number of points, i.e., the Weyl nodes. Topological semimetals host paired monopoles and antimonopoles of Berry curvature at the Weyl nodes and topologically protected Fermi arcs at certain surfaces. We review our recent works on quantum transport in topological semimetals, according to the strength of the magnetic field. At weak magnetic fields, there are competitions between the positive magnetoresistivity induced by the weak antilocalization effect and negative magnetoresistivity related to the nontrivial Berry curvature. We propose a fitting formula for the magnetoconductivity of the weak antilocalization. We expect that the weak localization may be induced by intervalley effects and interaction effect, and occur in doubleWeyl semimetals. For the negative magnetoresistance induced by the nontrivial Berry curvature in topological semimetals, we show the dependence of the negative magnetoresistance on the carrier density. At strong magnetic fields, specifically, in the quantum limit, the magnetoconductivity depends on the type and range of the scattering potential of disorder. The highfield positive magnetoconductivity may not be a compelling signature of the chiral anomaly. For longrange Gaussian scattering potential and half filling, the magnetoconductivity can be linear in the quantum limit. A minimal conductivity is found at the Weyl nodes although the density of states vanishes there.
A quantum relaxationtime approximation for finite fermion systems
Reinhard, P.G.; Suraud, E.
20150315
We propose a relaxation time approximation for the description of the dynamics of strongly excited fermion systems. Our approach is based on timedependent density functional theory at the level of the local density approximation. This meanfield picture is augmented by collisional correlations handled in relaxation time approximation which is inspired from the corresponding semiclassical picture. The method involves the estimate of microscopic relaxation rates/times which is presently taken from the well established semiclassical experience. The relaxation time approximation implies evaluation of the instantaneous equilibrium state towards which the dynamical state is progressively driven at the pace of the microscopic relaxation time. As test case, we consider Na clusters of various sizes excited either by a swift ion projectile or by a short and intense laser pulse, driven in various dynamical regimes ranging from linear to strongly nonlinear reactions. We observe a strong effect of dissipation on sensitive observables such as net ionization and angular distributions of emitted electrons. The effect is especially large for moderate excitations where typical relaxation/dissipation time scales efficiently compete with ionization for dissipating the available excitation energy. Technical details on the actual procedure to implement a working recipe of such a quantum relaxation approximation are given in appendices for completeness.
A finite different field solver for dipole modes
Nelson, E.M.
19920801
A finite element field solver for dipole modes in axisymmetric structures has been written. The secondorder elements used in this formulation yield accurate mode frequencies with no spurious modes. Quasiperiodic boundaries are included to allow travelling waves in periodic structures. The solver is useful in applications requiring precise frequency calculations such as detuned accelerator structures for linear colliders. Comparisons are made with measurements and with the popular but less accurate field solver URMEL.
Dual field theories of quantum computation
NASA Astrophysics Data System (ADS)
Vanchurin, Vitaly
20160601
Given two quantum states of N qbits we are interested to find the shortest quantum circuit consisting of only one and two qbit gates that would transfer one state into another. We call it the quantum maze problem for the reasons described in the paper. We argue that in a large N limit the quantum maze problem is equivalent to the problem of finding a semiclassical trajectory of some lattice field theory (the dual theory) on an N +1 dimensional spacetime with geometrically flat, but topologically compact spatial slices. The spatial fundamental domain is an N dimensional hyperrhombohedron, and the temporal direction describes transitions from an arbitrary initial state to an arbitrary target state and so the initial and final dual field theory conditions are described by these two quantum computational states. We first consider a complex KleinGordon field theory and argue that it can only be used to study the shortest quantum circuits which do not involve generators composed of tensor products of multiple Pauli Z matrices. Since such situation is not generic we call it the Zproblem. On the dual field theory side the Zproblem corresponds to massless excitations of the phase (Goldstone modes) that we attempt to fix using Higgs mechanism. The simplest dual theory which does not suffer from the massless excitation (or from the Zproblem) is the AbelianHiggs model which we argue can be used for finding the shortest quantum circuits. Since every trajectory of the field theory is mapped directly to a quantum circuit, the shortest quantum circuits are identified with semiclassical trajectories. We also discuss the complexity of an actual algorithm that uses a dual theory prospective for solving the quantum maze problem and compare it with a geometric approach. We argue that it might be possible to solve the problem in subexponential time in 2 N , but for that we must consider the KleinGordon theory on curved spatial geometry and/or more complicated (than N torus
Normal basis of finite field GF(2 super m)
NASA Technical Reports Server (NTRS)
Pei, D. Y.; Wang, C. C.; Omura, J. K.
19860101
Massey and Omura (1981) recently developed a new multiplication algorithm for Galois fields based on the normal basis representation. This algorithm shows a much simpler way to perform multiplication in finite field than the conventional method. The necessary and sufficient conditions are presented for an element to generate a normal basis in the field GF(2 super m), where m = 2 super k p super n and p super n has two as a primitive root. This result provides a way to find a normal basis in the field.
Entanglement detection in a coupled atomfield system via quantum Fisher information
NASA Astrophysics Data System (ADS)
Mirkhalaf, Safoura Sadat; Smerzi, Augusto
20170201
We consider a system of finite number of particles collectively interacting with a singlemode coherent field inside a cavity. Depending on the strength of the initial field compared to the number of atoms, we consider three regimes of weak, intermediate, and strongfield interaction. The dynamics of multiparticle entanglement detected by quantum Fisher information and spin squeezing are studied in each regime. It is seen that in the weakfield regime, spin squeezing and quantum Fisher information coincide. However, by increasing the initial field population toward the strongfield regime, quantum Fisher information is more effective in detecting entanglement compared to spin squeezing. In addition, in the twoatom system, we also study concurrence. In this case, the quantum Fisher information as a function of time is in good agreement with concurrence in predicting entanglement peaks.
Quantum phenomena and the zeropoint radiation field
NASA Astrophysics Data System (ADS)
de La Peña, L.; Cetto, A. M.
19940601
The stationary solutions for a bound electron immersed in the random zeropoint radiation field of stochastic electrodynamics are studied, under the assumption that the characteristic Fourier frequencies of these solutions are not random. Under this assumption, the response of the particle to the field is linear and does not mix frequencies, irrespectively of the form of the binding force; the fluctuations of the random field fix the scale of the response. The effective radiation field that supports the stationary states of motion is no longer the free vacuum field, but a modified form of it with new statistical properties. The theory is expressed naturally in terms of matrices (or operators), and it leads to the Heisenberg equations and the Hilbert space formalism of quantum mechanics in the radiationless approximation. The connection with the poissonian formulation of stochastic electrodynamics is also established. At the end we briefly discuss a few important aspects of quantum mechanics which the present theory helps to clarify.
Tomograms for open quantum systems: In(finite) dimensional optical and spin systems
Thapliyal, Kishore; Banerjee, Subhashish; Pathak, Anirban
20160315
Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In realistic experimental conditions, quantum states are exposed to the ambient environment and hence subject to effects like decoherence and dissipation, which are dealt with here, consistently, using the formalism of open quantum systems. This is extremely relevant from the perspective of experimental implementation and issues related to state reconstruction in quantum computation and communication. These considerations are also expected to affect the quasiprobability distribution obtained from experimentally generated tomograms and nonclassicality observed from them.  Highlights: •Tomograms are constructed for open quantum systems. •Finite and infinite dimensional quantum systems are studied. •Finite dimensional systems (phase states, single & two qubit spin states) are studied. •A dissipative harmonic oscillator is considered as an infinite dimensional system. •Both pure dephasing as well as dissipation effects are studied.
Mean Field Analysis of Quantum Annealing Correction.
Matsuura, Shunji; Nishimori, Hidetoshi; Albash, Tameem; Lidar, Daniel A
20160603
Quantum annealing correction (QAC) is a method that combines encoding with energy penalties and decoding to suppress and correct errors that degrade the performance of quantum annealers in solving optimization problems. While QAC has been experimentally demonstrated to successfully error correct a range of optimization problems, a clear understanding of its operating mechanism has been lacking. Here we bridge this gap using tools from quantum statistical mechanics. We study analytically tractable models using a meanfield analysis, specifically the pbody ferromagnetic infiniterange transversefield Ising model as well as the quantum Hopfield model. We demonstrate that for p=2, where the phase transition is of second order, QAC pushes the transition to increasingly larger transverse field strengths. For p≥3, where the phase transition is of first order, QAC softens the closing of the gap for small energy penalty values and prevents its closure for sufficiently large energy penalty values. Thus QAC provides protection from excitations that occur near the quantum critical point. We find similar results for the Hopfield model, thus demonstrating that our conclusions hold in the presence of disorder.
Noncommutative Common Cause Principles in algebraic quantum field theory
HoferSzabo, Gabor; Vecsernyes, Peter
20130415
States in algebraic quantum field theory 'typically' establish correlation between spacelike separated events. Reichenbach's Common Cause Principle, generalized to the quantum field theoretical setting, offers an apt tool to causally account for these superluminal correlations. In the paper we motivate first why commutativity between the common cause and the correlating events should be abandoned in the definition of the common cause. Then we show that the Noncommutative Weak Common Cause Principle holds in algebraic quantum field theory with locally finite degrees of freedom. Namely, for any pair of projections A, B supported in spacelike separated regions V{sub A} and V{sub B}, respectively, there is a local projection C not necessarily commuting with A and B such that C is supported within the union of the backward light cones of V{sub A} and V{sub B} and the set {l_brace}C, C{sup UpTack }{r_brace} screens off the correlation between A and B.
Physical properties of quantum field theory measures
NASA Astrophysics Data System (ADS)
Mourão, J. M.; Thiemann, T.; Velhinho, J. M.
19990501
Well known methods of measure theory on infinite dimensional spaces are used to study physical properties of measures relevant to quantum field theory. The difference of typical configurations of free massive scalar field theories with different masses is studied. We apply the same methods to study the AshtekarLewandowski (AL) measure on spaces of connections. In particular we prove that the diffeomorphism group acts ergodically, with respect to the AL measure, on the AshtekarIsham space of quantum connections modulo gauge transformations. We also prove that a typical, with respect to the AL measure, quantum connection restricted to a (piecewise analytic) curve leads to a parallel transport discontinuous at every point of the curve.
Deterministic strongfield quantum control
NASA Astrophysics Data System (ADS)
Cavaletto, Stefano M.; Harman, Zoltán; Pfeifer, Thomas; Keitel, Christoph H.
20170401
Strongfield quantumstate control is investigated, taking advantage of the full—amplitude and phase—characterization of the interaction between matter and intense ultrashort pulses via transientabsorption spectroscopy. As an example, we apply the method to a nondegenerate V type threelevel system modeling atomic Rb, and use a sequence of intense delayed pulses, whose parameters are tailored to steer the system into a desired quantum state. We show how to experimentally enable this optimization by retrieving all quantum features of the lightmatter interaction from observable spectra. This provides a full characterization of the action of strong fields on the atomic system, including the dependence upon possibly unknown pulse properties and atomic structures. Precision and robustness of the scheme are tested, in the presence of surrounding atomic levels influencing the system's dynamics.
Quantum fields near phantomenergy ''sudden'' singularities
Calderon, Hector H.
20080815
This paper is committed to calculations near a type of future singularity driven by phantom energy. At the singularities considered, the scale factor remains finite but its derivative diverges. The general behavior of barotropic phantom energy producing this singularity is calculated under the assumption that near the singularity such fluid is the dominant contributor. We use the semiclassical formula for renormalized stress tensors of conformally invariant fields in conformally flat spacetimes and analyze the softening/enhancing of the singularity due to quantum vacuum contributions. This dynamical analysis is then compared to results from thermodynamical considerations. In both cases, the vacuum states of quantized scalar and spinor fields strengthen the accelerating expansion near the singularity whereas the vacuum states of vector fields weaken it.
NASA Astrophysics Data System (ADS)
Liu, XiJing; Hu, BingQuan; Cho, Sam Young; Zhou, HuanQiang; Shi, QianQian
20161001
Recently, the finitesize corrections to the geometrical entanglement per lattice site in the spin1/2 chain have been numerically shown to scale inversely with system size, and its prefactor b has been suggested to be possibly universal [QQ. Shi et al., New J. Phys. 12, 025008 (2010)]. As possible evidence of its universality, the numerical values of the prefactors have been confirmed analytically by using the AffleckLudwig boundary entropy with a Neumann boundary condition for a free compactified field [JM. Stephan et al., Phys. Rev. B 82, 180406(R) (2010)]. However, the AffleckLudwig boundary entropy is not unique and does depend on conformally invariant boundary conditions. Here, we show that a unique AffleckLudwig boundary entropy corresponding to a finitesize correction to the geometrical entanglement per lattice site exists and show that the ratio of the prefactor b to the corresponding minimum groundstate degeneracy gmin for the Affleck Ludwig boundary entropy is a constant for any critical region of the spin1 XXZ system with the singleion anisotropy, i.e., b/(2 log2 g min ) = 1. Previously studied spin1/2 systems, including the quantum threestate Potts model, have verified the universal ratio. Hence, the inverse finitesize correction to the geometrical entanglement per lattice site and its prefactor b are universal for onedimensional critical systems.
Distance and coupling dependence of entanglement in the presence of a quantum field
NASA Astrophysics Data System (ADS)
Hsiang, J.T.; Hu, B. L.
20151201
We study the entanglement between two coupled detectors, the internal degrees of freedom of which are modeled by harmonic oscillators, interacting with a common quantum field, paying special attention to two less studied yet important features: finite separation and direct coupling. Distance dependence is essential in quantum teleportation and relativistic quantum information considerations. The presence of a quantum field as the environment accords an indirect interaction between the two oscillators at finite separation of a nonMarkovian nature which competes with the direct coupling between them. The interplay between these two factors results in a rich variety of interesting entanglement behaviors at late times. We show that the entanglement behavior reported in prior work assuming no separation between the detectors can at best be a transient effect at very short times and claims that such behaviors represent latetime entanglement are misplaced. Entanglement between the detectors with direct coupling enters in the consideration of macroscopic quantum phenomena and other frontline issues. We find that with direct coupling entanglement between the two detectors can sustain over a finite distance, in contrast to the no direct coupling case reported before, where entanglement cannot survive at a separation more than a few inverse highfrequency cutoff scales. This work provides a functional platform for systematic investigations into the entanglement behavior of continuous variable quantum systems, such as used in quantum electro and optomechanics.
OpenSystem Quantum Annealing in MeanField Models with Exponential Degeneracy*
NASA Astrophysics Data System (ADS)
Kechedzhi, Kostyantyn; Smelyanskiy, Vadim N.
20160401
Reallife quantum computers are inevitably affected by intrinsic noise resulting in dissipative nonunitary dynamics realized by these devices. We consider an opensystem quantum annealing algorithm optimized for such a realistic analog quantum device which takes advantage of noiseinduced thermalization and relies on incoherent quantum tunneling at finite temperature. We theoretically analyze the performance of this algorithm considering a p spin model that allows for a meanfield quasiclassical solution and, at the same time, demonstrates the firstorder phase transition and exponential degeneracy of states, typical characteristics of spin glasses. We demonstrate that finitetemperature effects introduced by the noise are particularly important for the dynamics in the presence of the exponential degeneracy of metastable states. We determine the optimal regime of the opensystem quantum annealing algorithm for this model and find that it can outperform simulated annealing in a range of parameters. Largescale multiqubit quantum tunneling is instrumental for the quantum speedup in this model, which is possible because of the unusual nonmonotonous temperature dependence of the quantumtunneling action in this model, where the most efficient transition rate corresponds to zero temperature. This model calculation is the first analytically tractable example where opensystem quantum annealing algorithm outperforms simulated annealing, which can, in principle, be realized using an analog quantum computer.
Computing Gravitational Fields of FiniteSized Bodies
NASA Technical Reports Server (NTRS)
Quadrelli, Marco
20050101
A computer program utilizes the classical theory of gravitation, implemented by means of the finiteelement method, to calculate the near gravitational fields of bodies of arbitrary size, shape, and mass distribution. The program was developed for application to a spacecraft and to floating proof masses and associated equipment carried by the spacecraft for detecting gravitational waves. The program can calculate steady or timedependent gravitational forces, moments, and gradients thereof. Bodies external to a proof mass can be moving around the proof mass and/or deformed under thermoelastic loads. An arbitrarily shaped proof mass is represented by a collection of parallelepiped elements. The gravitational force and moment acting on each parallelepiped element of a proof mass, including those attributable to the selfgravitational field of the proof mass, are computed exactly from the closedform equation for the gravitational potential of a parallelepiped. The gravitational field of an arbitrary distribution of mass external to a proof mass can be calculated either by summing the fields of suitably many point masses or by higherorder GaussLegendre integration over all elements surrounding the proof mass that are part of a finiteelement mesh. This computer program is compatible with more general finiteelement codes, such as NASTRAN, because it is configured to read a generic input data file, containing the detailed description of the finiteelement mesh.
Finiteblocklength analysis in classical and quantum information theory
HAYASHI, Masahito
20170101
Coding technology is used in several information processing tasks. In particular, when noise during transmission disturbs communications, coding technology is employed to protect the information. However, there are two types of coding technology: coding in classical information theory and coding in quantum information theory. Although the physical media used to transmit information ultimately obey quantum mechanics, we need to choose the type of coding depending on the kind of information device, classical or quantum, that is being used. In both branches of information theory, there are many elegant theoretical results under the ideal assumption that an infinitely large system is available. In a realistic situation, we need to account for finite size effects. The present paper reviews finite size effects in classical and quantum information theory with respect to various topics, including applied aspects. PMID:28302962
Theory of finiteentanglement scaling at onedimensional quantum critical points.
Pollmann, Frank; Mukerjee, Subroto; Turner, Ari M; Moore, Joel E
20090626
Studies of entanglement in manyparticle systems suggest that most quantum critical ground states have infinitely more entanglement than noncritical states. Standard algorithms for onedimensional systems construct model states with limited entanglement, which are a worse approximation to quantum critical states than to others. We give a quantitative theory of previously observed scaling behavior resulting from finite entanglement at quantum criticality. Finiteentanglement scaling in onedimensional systems is governed not by the scaling dimension of an operator but by the "central charge" of the critical point. An important ingredient is the universal distribution of densitymatrix eigenvalues at a critical point [P. Calabrese and A. Lefevre, Phys. Rev. A 78, 032329 (2008)10.1103/PhysRevA.78.032329]. The parameterfree theory is checked against numerical scaling at several quantum critical points.
Finiteblocklength analysis in classical and quantum information theory.
Hayashi, Masahito
20170101
Coding technology is used in several information processing tasks. In particular, when noise during transmission disturbs communications, coding technology is employed to protect the information. However, there are two types of coding technology: coding in classical information theory and coding in quantum information theory. Although the physical media used to transmit information ultimately obey quantum mechanics, we need to choose the type of coding depending on the kind of information device, classical or quantum, that is being used. In both branches of information theory, there are many elegant theoretical results under the ideal assumption that an infinitely large system is available. In a realistic situation, we need to account for finite size effects. The present paper reviews finite size effects in classical and quantum information theory with respect to various topics, including applied aspects.
The role of type III factors in quantum field theory
NASA Astrophysics Data System (ADS)
Yngvason, Jakob
20050201
One of von Neumann's motivations for developing the theory of operator algebras and his and Murray's 1936 classification of factors was the question of possible decompositions of quantum systems into independent parts. For quantum systems with a finite number of degrees of freedom the simplest possibility, i.e. factors of type I in the terminology of Murray and von Neumann, are perfectly adequate. In relativistic quantum field theory (RQFT), on the other hand, factors of type III occur naturally. The same holds true in quantum statistical mechanics of infinite systems. In this brief review some physical consequences of the type III property of the von Neumann algebras corresponding to localized observables in RQFT and their difference from the type I case will be discussed. The cumulative effort of many people over more than 30 years has established a remarkable uniqueness result: The local algebras in RQFT are generically isomorphic to the unique, hyperfinite type III, factor in Connes' classification of 1973. Specific theories are characterized by the net structure of the collection of these isomorphic algebras for different spacetime regions, i.e. the way they are embedded into each other
Consistency restrictions on maximal electricfield strength in quantum field theory.
Gavrilov, S P; Gitman, D M
20080926
Quantum field theory with an external background can be considered as a consistent model only if backreaction is relatively small with respect to the background. To find the corresponding consistency restrictions on an external electric field and its duration in QED and QCD, we analyze the meanenergy density of quantized fields for an arbitrary constant electric field E, acting during a large but finite time T. Using the corresponding asymptotics with respect to the dimensionless parameter eET2, one can see that the leading contributions to the energy are due to the creation of particles by the electric field. Assuming that these contributions are small in comparison with the energy density of the electric background, we establish the abovementioned restrictions, which determine, in fact, the time scales from above of depletion of an electric field due to the backreaction.
Quantum dynamics in strong fluctuating fields
NASA Astrophysics Data System (ADS)
Goychuk, Igor; Hänggi, Peter
A large number of multifaceted quantum transport processes in molecular systems and physical nanosystems, such as e.g. nonadiabatic electron transfer in proteins, can be treated in terms of quantum relaxation processes which couple to one or several fluctuating environments. A thermal equilibrium environment can conveniently be modelled by a thermal bath of harmonic oscillators. An archetype situation provides a twostate dissipative quantum dynamics, commonly known under the label of a spinboson dynamics. An interesting and nontrivial physical situation emerges, however, when the quantum dynamics evolves far away from thermal equilibrium. This occurs, for example, when a charge transferring medium possesses nonequilibrium degrees of freedom, or when a strong timedependent control field is applied externally. Accordingly, certain parameters of underlying quantum subsystem acquire stochastic character. This may occur, for example, for the tunnelling coupling between the donor and acceptor states of the transferring electron, or for the corresponding energy difference between electronic states which assume via the coupling to the fluctuating environment an explicit stochastic or deterministic timedependence. Here, we review the general theoretical framework which is based on the method of projector operators, yielding the quantum master equations for systems that are exposed to strong external fields. This allows one to investigate on a common basis, the influence of nonequilibrium fluctuations and periodic electrical fields on those already mentioned dynamics and related quantum transport processes. Most importantly, such strong fluctuating fields induce a whole variety of nonlinear and nonequilibrium phenomena. A characteristic feature of such dynamics is the absence of thermal (quantum) detailed balance.ContentsPAGE1. Introduction5262. Quantum dynamics in stochastic fields531 2.1. Stochastic Liouville equation531 2.2. NonMarkovian vs. Markovian discrete
Phantom field dynamics in loop quantum cosmology
Samart, Daris; Gumjudpai, Burin
20070815
We consider a dynamical system of phantom scalar field under exponential potential in the background of loop quantum cosmology. In our analysis, there is neither stable node nor repeller unstable node but only two saddle points, hence no big rip singularity. Physical solutions always possess potential energy greater than the magnitude of the negative kinetic energy. We found that the universe bounces after accelerating even in the domination of the phantom field. After bouncing, the universe finally enters the oscillatory regime.
Changing Views of Quantum Field Theory
NASA Astrophysics Data System (ADS)
Weinberg, Steven
20100301
The first part of this talk reviews changes in our views regarding quantum field theory since its beginnings, leading eventually to the modern view that our most successful field theories may in fact be effective field theories, valid only as low energy approximations to an underlying theory that may not be a field theory at all. In the second part, I reminisce about the early development of effective field theories of the strong interactions, comment briefly on some other applications of effective field theories, then take up the idea that the Standard Model and General Relativity are the leading terms in an effective field theory, and finally cite recent calculations that suggest that the effective field theory of gravitation and matter is asymptotically safe. The second part is substantially the same as a talk given a month earlier at the 6th International Workshop on Chiral Dynamics, at the University of Bern, which is reproduced here.
Finite temperature scalar field theory in the early universe
Leutwyler, H.; Mallik, S. )
19910101
The authors study a scalar Higgs field in an expanding RobertsonWalker geometry, using the real time formulation of Semenoff and Weiss. It is shown that the density matrix associated with the Hamiltonian at a sharp time describes a state for which perturbation theory is not renormalizable and an alternative, renormalizable characterization of thermal equilibrium is given. They calculate the thermal quantum fluctuations surrounding a classical field and discuss the characteristic time scales occurring in the evolution of a scalar field from an initial radiation dominated phase of thermal equilibrium to an unstable, inflationary de Sitter phase.
Comparative analysis of finite fielddependent BRST transformations
NASA Astrophysics Data System (ADS)
Moshin, P. Yu.; Reshetnyak, A. A.
20170301
We review our recent study [16], introducing the concept of finite fielddependent BRST and BRSTantiBRST transformations for gauge theories and investigating their properties. An algorithm of exact calculation for the Jacobian of a respective change of variables in the path integral is presented. Applications to the YangMills theory, in view of infrared (Gribov) peculiarities, are discussed.
The sound field in a finite cylindrical shell
NASA Technical Reports Server (NTRS)
Junger, M. C.
19850101
The sound field excited by vibrating boundaries in a finite cylindrical space, e.g., in a cylindrical shell, differs from the pressure distribution in an infinite cylindrical shell of comparable structural wavelength by the pressure diffracted by the end caps. The latter pressure component is comparable in magnitude to the pressure generated by the vibrating cylindrical boundary, but does not introduce additional resonances or antiresonances. Finally, a third pressure component associated with end cap vibrations is formulated.
A stabilized finite element method for finitestrain threefield poroelasticity
NASA Astrophysics Data System (ADS)
Berger, Lorenz; Bordas, Rafel; Kay, David; Tavener, Simon
20170701
We construct a stabilized finiteelement method to compute flow and finitestrain deformations in an incompressible poroelastic medium. We employ a threefield mixed formulation to calculate displacement, fluid flux and pressure directly and introduce a Lagrange multiplier to enforce flux boundary conditions. We use a low order approximation, namely, continuous piecewiselinear approximation for the displacements and fluid flux, and piecewiseconstant approximation for the pressure. This results in a simple matrix structure with low bandwidth. The method is stable in both the limiting cases of small and large permeability. Moreover, the discontinuous pressure space enables efficient approximation of steep gradients such as those occurring due to rapidly changing material coefficients or boundary conditions, both of which are commonly seen in physical and biological applications.
Scattering amplitudes over finite fields and multivariate functional reconstruction
NASA Astrophysics Data System (ADS)
Peraro, Tiziano
20161201
Several problems in computer algebra can be efficiently solved by reducing them to calculations over finite fields. In this paper, we describe an algorithm for the reconstruction of multivariate polynomials and rational functions from their evaluation over finite fields. Calculations over finite fields can in turn be efficiently performed using machinesize integers in staticallytyped languages. We then discuss the application of the algorithm to several techniques related to the computation of scattering amplitudes, such as the four and sixdimensional spinorhelicity formalism, treelevel recursion relations, and multiloop integrand reduction via generalized unitarity. The method has good efficiency and scales well with the number of variables and the complexity of the problem. As an example combining these techniques, we present the calculation of full analytic expressions for the twoloop fivepoint onshell integrands of the maximal cuts of the planar pentabox and the nonplanar doublepentagon topologies in YangMills theory, for a complete set of independent helicity configurations.
Integrable structures in quantum field theory
NASA Astrophysics Data System (ADS)
Negro, Stefano
20160801
This review was born as notes for a lecture given at the Young Researchers Integrability School (YRIS) school on integrability in Durham, in the summer of 2015. It deals with a beautiful method, developed in the midnineties by Bazhanov, Lukyanov and Zamolodchikov and, as such, called BLZ. This method can be interpreted as a field theory version of the quantum inverse scattering, also known as the algebraic Bethe ansatz. Starting with the case of conformal field theories (CFTs) we show how to build the field theory analogues of commuting transfer T matrices and Baxter Qoperators of integrable lattice models. These objects contain the complete information of the integrable structure of the theory, viz. the integrals of motion, and can be used, as we will show, to derive the thermodynamic Bethe ansatz and nonlinear integral equations. This same method can be easily extended to the description of integrable structures of certain particular massive deformations of CFTs; these, in turn, can be described as quantum group reductions of the quantum sineGordon model and it is an easy step to include this last theory in the framework of BLZ approach. Finally we show an interesting and surprising connection of the BLZ structures with classical objects emerging from the study of classical integrable models via the inverse scattering transform method. This connection goes under the name of ODE/IM correspondence and we will present it for the specific case of quantum sineGordon model only.
Quantum signatures of breathers in a finite Heisenberg spin chain.
Djoufack, Z I; KenfackJiotsa, A; Nguenang, J P; Domngang, S
20100526
A map of a quantum Heisenberg spin chain into an extended BoseHubbardlike Hamiltonian is set up. Within this framework, the spectrum of the corresponding BoseHubbard chain, on a periodic onedimensional lattice containing two, four, and six bosons shows interesting detailed band structures. These fine structures are studied using numerical diagonalization, and nondegenerate and degenerate perturbation theory. We also focus our attention on the effect of the anisotropy and Heisenberg exchange energy on the detailed band structures. The signature of the quantum breather is also set up by the square of the amplitudes of the corresponding eigenvectors in real space.
Nishimura, Kohji; Nishimori, Hidetoshi; Ochoa, Andrew J; Katzgraber, Helmut G
20160901
We study the problem to infer the ground state of a spinglass Hamiltonian using data from another Hamiltonian with interactions disturbed by noise from the original Hamiltonian, motivated by the groundstate inference in quantum annealing on a noisy device. It is shown that the average Hamming distance between the inferred spin configuration and the true ground state is minimized when the temperature of the noisy system is kept at a finite value, and not at zero temperature. We present a spinglass generalization of a wellestablished result that the ground state of a purely ferromagnetic Hamiltonian is best inferred at a finite temperature in the sense of smallest Hamming distance when the original ferromagnetic interactions are disturbed by noise. We use the numerical transfermatrix method to establish the existence of an optimal finite temperature in one and twodimensional systems. Our numerical results are supported by meanfield calculations, which give an explicit expression of the optimal temperature to infer the spinglass ground state as a function of variances of the distributions of the original interactions and the noise. The meanfield prediction is in qualitative agreement with numerical data. Implications on postprocessing of quantum annealing on a noisy device are discussed.
NASA Astrophysics Data System (ADS)
Nishimura, Kohji; Nishimori, Hidetoshi; Ochoa, Andrew J.; Katzgraber, Helmut G.
20160901
We study the problem to infer the ground state of a spinglass Hamiltonian using data from another Hamiltonian with interactions disturbed by noise from the original Hamiltonian, motivated by the groundstate inference in quantum annealing on a noisy device. It is shown that the average Hamming distance between the inferred spin configuration and the true ground state is minimized when the temperature of the noisy system is kept at a finite value, and not at zero temperature. We present a spinglass generalization of a wellestablished result that the ground state of a purely ferromagnetic Hamiltonian is best inferred at a finite temperature in the sense of smallest Hamming distance when the original ferromagnetic interactions are disturbed by noise. We use the numerical transfermatrix method to establish the existence of an optimal finite temperature in one and twodimensional systems. Our numerical results are supported by meanfield calculations, which give an explicit expression of the optimal temperature to infer the spinglass ground state as a function of variances of the distributions of the original interactions and the noise. The meanfield prediction is in qualitative agreement with numerical data. Implications on postprocessing of quantum annealing on a noisy device are discussed.
Exact stabilization of entangled states in finite time by dissipative quantum circuits
NASA Astrophysics Data System (ADS)
Johnson, Peter D.; Ticozzi, Francesco; Viola, Lorenza
20170701
Open quantum systems evolving according to discretetime dynamics are capable, unlike continuoustime counterparts, to converge to a stable equilibrium in finite time with zero error. We consider dissipative quantum circuits consisting of sequences of quantum channels subject to specified quasilocality constraints, and determine conditions under which stabilization of a pure multipartite entangled state of interest may be exactly achieved in finite time. Special emphasis is devoted to characterizing scenarios where finitetime stabilization may be achieved robustly with respect to the order of the applied quantum maps, as suitable for unsupervised control architectures. We show that if a decomposition of the physical Hilbert space into virtual subsystems is found, which is compatible with the locality constraint and relative to which the target state factorizes, then robust stabilization may be achieved by independently cooling each component. We further show that if the same condition holds for a scalable class of pure states, a continuoustime quasilocal Markov semigroup ensuring rapid mixing can be obtained. Somewhat surprisingly, we find that the commutativity of the canonical parent Hamiltonian one may associate to the target state does not directly relate to its finitetime stabilizability properties, although in all cases where we can guarantee robust stabilization, a (possibly noncanonical) commuting parent Hamiltonian may be found. Aside from graph states, quantum states amenable to finitetime robust stabilization include a class of universal resource states displaying twodimensional symmetryprotected topological order, along with tensor network states obtained by generalizing a construction due to Bravyi and Vyalyi [Quantum Inf. Comput. 5, 187 (2005)]. Extensions to representative classes of mixed graphproduct and thermal states are also discussed.
Matterenhanced transition probabilities in quantum field theory
Ishikawa, Kenzo Tobita, Yutaka
20140515
The relativistic quantum field theory is the unique theory that combines the relativity and quantum theory and is invariant under the Poincaré transformation. The ground state, vacuum, is singlet and one particle states are transformed as elements of irreducible representation of the group. The covariant one particles are momentum eigenstates expressed by plane waves and extended in space. Although the Smatrix defined with initial and final states of these states hold the symmetries and are applied to isolated states, outgoing states for the amplitude of the event that they are detected at a finitetime interval T in experiments are expressed by microscopic states that they interact with, and are surrounded by matters in detectors and are not plane waves. These matterinduced effects modify the probabilities observed in realistic situations. The transition amplitudes and probabilities of the events are studied with the Smatrix, S[T], that satisfies the boundary condition at T. Using S[T], the finitesize corrections of the form of 1/T are found. The corrections to Fermi’s golden rule become larger than the original values in some situations for light particles. They break Lorentz invariance even in high energy region of short de Broglie wave lengths.  Highlights: •Smatrix S[T] for the finitetime interval in relativistic field theory. •S[T] satisfies the boundary condition and gives correction of 1/T . •The large corrections for light particles breaks Lorentz invariance. •The corrections have implications to neutrino experiments.
Kinematic projective quantum states for loop quantum gravity coupled to tensor fields
NASA Astrophysics Data System (ADS)
Okołów, Andrzej
20170401
We present a construction of kinematic quantum states for theories of tensor fields of an arbitrary sort. The construction is based on projective techniques by Kijowski. Applying projective quantum states for Loop Quantum Gravity (LQG) obtained by Lanéry and Thiemann we construct quantum states for LQG coupled to tensor fields.
Neutrino oscillations: quantum mechanics vs. quantum field theory
NASA Astrophysics Data System (ADS)
Akhmedov, Evgeny Kh.; Kopp, Joachim
20100401
A consistent description of neutrino oscillations requires either the quantummechanical (QM) wave packet approach or a quantum field theoretic (QFT) treatment. We compare these two approaches to neutrino oscillations and discuss the correspondence between them. In particular, we derive expressions for the QM neutrino wave packets from QFT and relate the free parameters of the QM framework, in particular the effective momentum uncertainty of the neutrino state, to the more fundamental parameters of the QFT approach. We include in our discussion the possibilities that some of the neutrino’s interaction partners are not detected, that the neutrino is produced in the decay of an unstable parent particle, and that the overlap of the wave packets of the particles involved in the neutrino production (or detection) process is not maximal. Finally, we demonstrate how the properly normalized oscillation probabilities can be obtained in the QFT framework without an ad hoc normalization procedure employed in the QM approach.
Neutrino oscillations: Quantum mechanics vs. quantum field theory
Akhmedov, Evgeny Kh.; Kopp, Joachim
20100101
A consistent description of neutrino oscillations requires either the quantummechanical (QM) wave packet approach or a quantum field theoretic (QFT) treatment. We compare these two approaches to neutrino oscillations and discuss the correspondence between them. In particular, we derive expressions for the QM neutrino wave packets from QFT and relate the free parameters of the QM framework, in particular the effective momentum uncertainty of the neutrino state, to the more fundamental parameters of the QFT approach. We include in our discussion the possibilities that some of the neutrino's interaction partners are not detected, that the neutrino is produced in the decay of an unstable parent particle, and that the overlap of the wave packets of the particles involved in the neutrino production (or detection) process is not maximal. Finally, we demonstrate how the properly normalized oscillation probabilities can be obtained in the QFT framework without an ad hoc normalization procedure employed in the QM approach.
Quantum fields on closed timelike curves
Pienaar, J. L.; Myers, C. R.; Ralph, T. C.
20111215
Recently, there has been much interest in the evolution of quantum particles on closed timelike curves (CTCs). However, such models typically assume pointlike particles with only two degrees of freedom; a very questionable assumption given the relativistic setting of the problem. We show that it is possible to generalize the Deutsch model of CTCs to fields using the equivalent circuit formalism. We give examples for coherent, squeezed, and singlephoton states interacting with the CTC via a beamsplitter. The model is then generalized further to account for the smooth transition to normal quantum mechanics as the CTC becomes much smaller than the size of the modes interacting on it. In this limit, we find that the system behaves like a standard quantummechanical feedback loop.
"Quantum Field Theory and QCD"
Jaffe, Arthur M.
20060225
This grant partially funded a meeting, "QFT & QCD: Past, Present and Future" held at Harvard University, Cambridge, MA on March 1819, 2005. The participants ranged from senior scientists (including at least 9 Nobel Prize winners, and 1 Fields medalist) to graduate students and undergraduates. There were several hundred persons in attendance at each lecture. The lectures ranged from superlative reviews of past progress, lists of important, unsolved questions, to provocative hypotheses for future discovery. The project generated a great deal of interest on the internet, raising awareness and interest in the open questions of theoretical physics.
Locality and entanglement in bandlimited quantum field theory
NASA Astrophysics Data System (ADS)
Pye, Jason; Donnelly, William; Kempf, Achim
20151101
We consider a model for a Planckscale ultraviolet cutoff which is based on Shannon sampling. Shannon sampling originated in information theory, where it expresses the equivalence of continuous and discrete representations of information. When applied to quantum field theory, Shannon sampling expresses a hard ultraviolet cutoff in the form of a bandlimitation. This introduces nonlocality at the cutoff scale in a way that is more subtle than a simple discretization of space: quantum fields can then be represented as either living on continuous space or, entirely equivalently, as living on any one lattice whose average spacing is sufficiently small. We explicitly calculate vacuum entanglement entropies in 1 +1 dimensions and we find a transition between logarithmic and linear scaling of the entropy, which is the expected 1 +1 dimensional analog of the transition from an area to a volume law. We also use entanglement entropy and mutual information as measures to probe in detail the localizability of the field degrees of freedom. We find that, even though neither translation nor rotation invariance are broken, each field degree of freedom occupies an incompressible volume of space, indicating a finite information density.
Model for noncancellation of quantum electric field fluctuations
Parkinson, Victor; Ford, L. H.
20111215
A localized charged particle oscillating near a reflecting boundary is considered as a model for noncancellation of vacuum fluctuations. Although the mean velocity of the particle is sinusoidal, the velocity variance produced by vacuum fluctuations can either grow or decrease linearly in time, depending upon the product of the oscillation frequency and the distance to the boundary. This amounts to heating or cooling arising from noncancellation of electric field fluctuations, which are otherwise anticorrelated in time. Similar noncancellations arise in quantum field effects in timedependent curved spacetimes. We give some estimates of the magnitude of the effect, and discuss its potential observability. We also compare the effects of vacuum fluctuations with the shot noise due to emission of a finite number of photons. We find that the two effects can be comparable in magnitude, but have distinct characteristics, and hence could be distinguished in an experiment.
Quantum processes in strong magnetic fields
NASA Technical Reports Server (NTRS)
Canuto, V.
19750101
Quantummechanical processes that occur in a piece of matter embedded in a magnetic field with a strength of the order of 10 to the 13th power G are described which either are entirely due to the presence of the field or become modified because of it. The conversion of rotational energy into electromagnetic energy in pulsars is analyzed as a mechanism for producing such a field, and it is shown that a strong magnetic field is not sufficient for quantum effects to play a significant role; in addition, the density must be adjusted to be as low as possible. The pressure and energy density of a free electron gas in a uniform magnetic field are evaluated, neutron betadecay in the presence of a strong field is examined, and the effect of such a field on neutrino reactions is discussed. The thermal history of a neutron star is studied, and it is concluded that a strong magnetic field helps to increase the cooling rate of the star by producing new channels through which neutrinos can carry away energy.
Quantum processes in strong magnetic fields
NASA Technical Reports Server (NTRS)
Canuto, V.
19750101
Quantummechanical processes that occur in a piece of matter embedded in a magnetic field with a strength of the order of 10 to the 13th power G are described which either are entirely due to the presence of the field or become modified because of it. The conversion of rotational energy into electromagnetic energy in pulsars is analyzed as a mechanism for producing such a field, and it is shown that a strong magnetic field is not sufficient for quantum effects to play a significant role; in addition, the density must be adjusted to be as low as possible. The pressure and energy density of a free electron gas in a uniform magnetic field are evaluated, neutron betadecay in the presence of a strong field is examined, and the effect of such a field on neutrino reactions is discussed. The thermal history of a neutron star is studied, and it is concluded that a strong magnetic field helps to increase the cooling rate of the star by producing new channels through which neutrinos can carry away energy.
Finitetime quantumtoclassical transition for a Schroedingercat state
Paavola, Janika; Hall, Michael J. W.; Paris, Matteo G. A.; Maniscalco, Sabrina
20110715
The transition from quantum to classical, in the case of a quantum harmonic oscillator, is typically identified with the transition from a quantum superposition of macroscopically distinguishable states, such as the Schroedingercat state, into the corresponding statistical mixture. This transition is commonly characterized by the asymptotic loss of the interference term in the Wigner representation of the cat state. In this paper we show that the quantumtoclassical transition has different dynamical features depending on the measure for nonclassicality used. Measures based on an operatorial definition have welldefined physical meaning and allow a deeper understanding of the quantumtoclassical transition. Our analysis shows that, for most nonclassicality measures, the Schroedingercat state becomes classical after a finite time. Moreover, our results challenge the prevailing idea that more macroscopic states are more susceptible to decoherence in the sense that the transition from quantum to classical occurs faster. Since nonclassicality is a prerequisite for entanglement generation our results also bridge the gap between decoherence, which is lost only asymptotically, and entanglement, which may show a ''sudden death''. In fact, whereas the loss of coherences still remains asymptotic, we emphasize that the transition from quantum to classical can indeed occur at a finite time.
Finitetime quantumtoclassical transition for a Schrödingercat state
NASA Astrophysics Data System (ADS)
Paavola, Janika; Hall, Michael J. W.; Paris, Matteo G. A.; Maniscalco, Sabrina
20110701
The transition from quantum to classical, in the case of a quantum harmonic oscillator, is typically identified with the transition from a quantum superposition of macroscopically distinguishable states, such as the Schrödingercat state, into the corresponding statistical mixture. This transition is commonly characterized by the asymptotic loss of the interference term in the Wigner representation of the cat state. In this paper we show that the quantumtoclassical transition has different dynamical features depending on the measure for nonclassicality used. Measures based on an operatorial definition have welldefined physical meaning and allow a deeper understanding of the quantumtoclassical transition. Our analysis shows that, for most nonclassicality measures, the Schrödingercat state becomes classical after a finite time. Moreover, our results challenge the prevailing idea that more macroscopic states are more susceptible to decoherence in the sense that the transition from quantum to classical occurs faster. Since nonclassicality is a prerequisite for entanglement generation our results also bridge the gap between decoherence, which is lost only asymptotically, and entanglement, which may show a “sudden death.” In fact, whereas the loss of coherences still remains asymptotic, we emphasize that the transition from quantum to classical can indeed occur at a finite time.
Casimir effect for the Higgs field at finite temperature
NASA Astrophysics Data System (ADS)
Santos, A. F.; Khanna, Faqir C.
20170801
In early 1970, it was postulated that there exists a zero spin quantum field, called Higgs field, that is present in all universe. The potential energy of the Higgs field is transferred to particles. Hence they acquire mass. These ideas were essential in fulfilling the basic need for a particle, called Higgs, with mass. These particles are called Higgs particles with spin zero with its mass to be ˜125 GeV. This raises the question as to its physical effects. If these particles are present, will they exhibit a Casimir effect and also obey the StefanBoltzmann Law? Assuming the dynamics of this field, will these effects change with temperature. The present calculation uses thermo field dynamics formalism to calculate temperature effects.
Quantum revivals in free field CFT
NASA Astrophysics Data System (ADS)
Dowker, J. S.
20170301
The recent work by Cardy (arXiv:1603.08267) on quantum revivals and higher dimensional CFT is revisited and enlarged upon for free fields. The expressions for the free energy used here are those derived some time ago. The calculation is extended to spin–half fields for which the power spectrum involves the odd divisor function. An explanation of the rational revivals for odd spheres is given in terms of wrongly quantised fields and modular transformations. Comments are made on the equivalence of operator counting and eigenvalue methods, which is quickly verified.
Remote State Preparation for Quantum Fields
NASA Astrophysics Data System (ADS)
Ber, Ran; Zohar, Erez
20160701
Remote state preparation is generation of a desired state by a remote observer. In spite of causality, it is well known, according to the ReehSchlieder theorem, that it is possible for relativistic quantum field theories, and a "physical" process achieving this task, involving superoscillatory functions, has recently been introduced. In this work we deal with nonrelativistic fields, and show that remote state preparation is also possible for them, hence obtaining a ReehSchliederlike result for general fields. Interestingly, in the nonrelativistic case, the process may rely on completely different resources than the ones used in the relativistic case.
3D Finite Element Analyses of the Egan Cavern Field
Klamerus, E.W.; Ehgartner, B.L.
19990201
Threedimensional finite element analyses were performed for the two gasfilled storage caverns at the Egan field, Jennings dome, Louisiana. The effects of cavern enlargement on surface subsidence, storage loss, and cavern stability were investigated. The finite element model simulated the leaching of caverns to 6 and 8 billion cubic feet (BCF) and examined their performance at various operating conditions. Operating pressures varied from 0.15 psi/ft to 0.9 psi/ft at the bottom of the lowest cemented casing. The analysis also examined the stability of the web or pillar of salt between the caverns under differential pressure loadings. The 50year simulations were performed using JAC3D, a three dimensional finite element analysis code for nonlinear quasistatic solids. A damage criterion based on onset of dilatancy was used to evaluate cavern instability. Dilation results from the development of microfractures in salt and, hence, potential increases in permeability onset occurs well before large scale failure. The analyses predicted stable caverns throughout the 50year period for the range of pressures investigated. Some localized salt damage was predicted near the bottom walls of the caverns if the caverns are operated at minimum pressure for long periods of time. Volumetric cavern closures over time due to creep were moderate to excessive depending on the salt creep properties and operating pressures. However, subsidence above the cavern field was small and should pose no problem, to surface facilities.
Anomalous critical fields in quantum critical superconductors
Putzke, C.; Walmsley, P.; Fletcher, J. D.; Malone, L.; Vignolles, D.; Proust, C.; Badoux, S.; See, P.; Beere, H. E.; Ritchie, D. A.; Kasahara, S.; Mizukami, Y.; Shibauchi, T.; Matsuda, Y.; Carrington, A.
20140101
Fluctuations around an antiferromagnetic quantum critical point (QCP) are believed to lead to unconventional superconductivity and in some cases to hightemperature superconductivity. However, the exact mechanism by which this occurs remains poorly understood. The ironpnictide superconductor BaFe2(As1−xPx)2 is perhaps the clearest example to date of a hightemperature quantum critical superconductor, and so it is a particularly suitable system to study how the quantum critical fluctuations affect the superconducting state. Here we show that the proximity of the QCP yields unexpected anomalies in the superconducting critical fields. We find that both the lower and upper critical fields do not follow the behaviour, predicted by conventional theory, resulting from the observed mass enhancement near the QCP. Our results imply that the energy of superconducting vortices is enhanced, possibly due to a microscopic mixing of antiferromagnetism and superconductivity, suggesting that a highly unusual vortex state is realized in quantum critical superconductors. PMID:25477044
Quantum Field Theory and the Standard Model
NASA Astrophysics Data System (ADS)
Schwartz, Matthew D.
20140301
Part I. Field Theory: 1. Microscopic theory of radiation; 2. Lorentz invariance and second quantization; 3. Classical Field Theory; 4. Oldfashioned perturbation theory; 5. Cross sections and decay rates; 6. The Smatrix and timeordered products; 7. Feynman rules; Part II. Quantum Electrodynamics: 8. Spin 1 and gauge invariance; 9. Scalar QED; 10. Spinors; 11. Spinor solutions and CPT; 12. Spin and statistics; 13. Quantum electrodynamics; 14. Path integrals; Part III. Renormalization: 15. The Casimir effect; 16. Vacuum polarization; 17. The anomalous magnetic moment; 18. Mass renormalization; 19. Renormalized perturbation theory; 20. Infrared divergences; 21. Renormalizability; 22. Nonrenormalizable theories; 23. The renormalization group; 24. Implications of Unitarity; Part IV. The Standard Model: 25. YangMills theory; 26. Quantum YangMills theory; 27. Gluon scattering and the spinorhelicity formalism; 28. Spontaneous symmetry breaking; 29. Weak interactions; 30. Anomalies; 31. Precision tests of the standard model; 32. QCD and the parton model; Part V. Advanced Topics: 33. Effective actions and Schwinger proper time; 34. Background fields; 35. Heavyquark physics; 36. Jets and effective field theory; Appendices; References; Index.
Finite to zerorange relativistic meanfield interactions
Niksic, T.; Vretenar, D.; Lalazissis, G. A.; Ring, P.
20080315
We study the relation between the finiterange (mesonexchange) and zerorange (pointcoupling) representations of effective nuclear interactions in the relativistic meanfield framework. Starting from the phenomenological interaction DDME2 with densitydependent mesonnucleon couplings, we construct a family of pointcoupling effective interactions for different values of the strength parameter of the isoscalarscalar derivative term. In the mesonexchange picture this corresponds to different values of the {sigma}meson mass. The parameters of the isoscalarscalar and isovectorvector channels of the pointcoupling interactions are adjusted to nuclear matter and groundstate properties of finite nuclei. By comparing results for infinite and semiinfinite nuclear matter, groundstate masses, charge radii, and collective excitations, we discuss constraints on the parameters of phenomenological pointcoupling relativistic effective interaction.
Tight finitekey analysis for quantum cryptography.
Tomamichel, Marco; Lim, Charles Ci Wen; Gisin, Nicolas; Renner, Renato
20120117
Despite enormous theoretical and experimental progress in quantum cryptography, the security of most current implementations of quantum key distribution is still not rigorously established. One significant problem is that the security of the final key strongly depends on the number, M, of signals exchanged between the legitimate parties. Yet, existing security proofs are often only valid asymptotically, for unrealistically large values of M. Another challenge is that most security proofs are very sensitive to small differences between the physical devices used by the protocol and the theoretical model used to describe them. Here we show that these gaps between theory and experiment can be simultaneously overcome by using a recently developed proof technique based on the uncertainty relation for smooth entropies.
Tight finitekey analysis for quantum cryptography
Tomamichel, Marco; Lim, Charles Ci Wen; Gisin, Nicolas; Renner, Renato
20120101
Despite enormous theoretical and experimental progress in quantum cryptography, the security of most current implementations of quantum key distribution is still not rigorously established. One significant problem is that the security of the final key strongly depends on the number, M, of signals exchanged between the legitimate parties. Yet, existing security proofs are often only valid asymptotically, for unrealistically large values of M. Another challenge is that most security proofs are very sensitive to small differences between the physical devices used by the protocol and the theoretical model used to describe them. Here we show that these gaps between theory and experiment can be simultaneously overcome by using a recently developed proof technique based on the uncertainty relation for smooth entropies. PMID:22252558
Marchiolli, Marcelo A.; Ruzzi, Maurizio; Galetti, Diogenes
20051015
By means of a mod(N)invariant operator basis, sparametrized phasespace functions associated with bounded operators in a finitedimensional Hilbert space are introduced in the context of the extended CahillGlauber formalism, and their properties are discussed in details. The discrete GlauberSudarshan, Wigner, and Husimi functions emerge from this formalism as specific cases of sparametrized phasespace functions where, in particular, a hierarchical process among them is promptly established. In addition, a phasespace description of quantum tomography and quantum teleportation is presented and new results are obtained.
OBTAINING POTENTIAL FIELD SOLUTIONS WITH SPHERICAL HARMONICS AND FINITE DIFFERENCES
Toth, Gabor; Van der Holst, Bart; Huang Zhenguang
20110510
Potential magnetic field solutions can be obtained based on the synoptic magnetograms of the Sun. Traditionally, a spherical harmonics decomposition of the magnetogram is used to construct the current and divergencefree magnetic field solution. This method works reasonably well when the order of spherical harmonics is limited to be small relative to the resolution of the magnetogram, although some artifacts, such as ringing, can arise around sharp features. When the number of spherical harmonics is increased, however, using the raw magnetogram data given on a grid that is uniform in the sine of the latitude coordinate can result in inaccurate and unreliable results, especially in the polar regions close to the Sun. We discuss here two approaches that can mitigate or completely avoid these problems: (1) remeshing the magnetogram onto a grid with uniform resolution in latitude and limiting the highest order of the spherical harmonics to the antialias limit; (2) using an iterative finite difference algorithm to solve for the potential field. The naive and the improved numerical solutions are compared for actual magnetograms and the differences are found to be rather dramatic. We made our new Finite Difference Iterative Potentialfield Solver (FDIPS) a publicly available code so that other researchers can also use it as an alternative to the spherical harmonics approach.
NASA Astrophysics Data System (ADS)
Yu. Moshin, Pavel; Reshetnyak, Alexander A.
20160701
We continue our research14 and extend the class of finite BRSTantiBRST transformations with oddvalued parameters λa, a = 1, 2, introduced in these works. In doing so, we evaluate the Jacobians induced by finite BRSTantiBRST transformations linear in functionallydependent parameters, as well as those induced by finite BRSTantiBRST transformations with arbitrary functional parameters. The calculations cover the cases of gauge theories with a closed algebra, dynamical systems with firstclass constraints, and general gauge theories. The resulting Jacobians in the case of linearized transformations are different from those in the case of polynomial dependence on the parameters. Finite BRSTantiBRST transformations with arbitrary parameters induce an extra contribution to the quantum action, which cannot be absorbed into a change of the gauge. These transformations include an extended case of functionallydependent parameters that implies a modified compensation equation, which admits nontrivial solutions leading to a Jacobian equal to unity. Finite BRSTantiBRST transformations with functionallydependent parameters are applied to the Standard Model, and an explicit form of functionallydependent parameters λa is obtained, providing the equivalence of path integrals in any 3parameter Rξlike gauges. The GribovZwanziger theory is extended to the case of the Standard Model, and a form of the Gribov horizon functional is suggested in the Landau gauge, as well as in Rξlike gauges, in a gaugeindependent way using fielddependent BRSTantiBRST transformations, and in Rξlike gauges using transverselike nonAbelian gauge fields.
Thermalization of field driven quantum systems
Fotso, H.; Mikelsons, K.; Freericks, J. K.
20140101
There is much interest in how quantum systems thermalize after a sudden change, because unitary evolution should preclude thermalization. The eigenstate thermalization hypothesis resolves this because all observables for quantum states in a small energy window have essentially the same value; it is violated for integrable systems due to the infinite number of conserved quantities. Here, we show that when a system is driven by a DC electric field there are five generic behaviors: (i) monotonic or (ii) oscillatory approach to an infinitetemperature steady state; (iii) monotonic or (iv) oscillatory approach to a nonthermal steady state; or (v) evolution to an oscillatory state. Examining the Hubbard model (which thermalizes under a quench) and the FalicovKimball model (which does not), we find both exhibit scenarios (i–iv), while only Hubbard shows scenario (v). This shows richer behavior than in interaction quenches and integrability in the absence of a field plays no role. PMID:24736404
Thermalization of field driven quantum systems
NASA Astrophysics Data System (ADS)
Fotso, H.; Mikelsons, K.; Freericks, J. K.
20140401
There is much interest in how quantum systems thermalize after a sudden change, because unitary evolution should preclude thermalization. The eigenstate thermalization hypothesis resolves this because all observables for quantum states in a small energy window have essentially the same value; it is violated for integrable systems due to the infinite number of conserved quantities. Here, we show that when a system is driven by a DC electric field there are five generic behaviors: (i) monotonic or (ii) oscillatory approach to an infinitetemperature steady state; (iii) monotonic or (iv) oscillatory approach to a nonthermal steady state; or (v) evolution to an oscillatory state. Examining the Hubbard model (which thermalizes under a quench) and the FalicovKimball model (which does not), we find both exhibit scenarios (iiv), while only Hubbard shows scenario (v). This shows richer behavior than in interaction quenches and integrability in the absence of a field plays no role.
Effective Particles in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Głazek, Stanisław D.; Trawiński, Arkadiusz P.
20170301
The concept of effective particles is introduced in the Minkowski spacetime Hamiltonians in quantum field theory using a new kind of the relativistic renormalization group procedure that does not integrate out highenergy modes but instead integrates out the large changes of invariant mass. The new procedure is explained using examples of known interactions. Some applications in phenomenology, including processes measurable in colliders, are briefly presented.
Quantum field theory of treasury bonds
NASA Astrophysics Data System (ADS)
Baaquie, Belal E.
20010701
The HeathJarrowMorton (HJM) formulation of treasury bonds in terms of forward rates is recast as a problem in path integration. The HJM model is generalized to the case where all the forward rates are allowed to fluctuate independently. The resulting theory is shown to be a twodimensional Gaussian quantum field theory. The no arbitrage condition is obtained and a functional integral derivation is given for the price of a futures and an options contract.
Quantum field theory of treasury bonds.
Baaquie, B E
20010701
The HeathJarrowMorton (HJM) formulation of treasury bonds in terms of forward rates is recast as a problem in path integration. The HJM model is generalized to the case where all the forward rates are allowed to fluctuate independently. The resulting theory is shown to be a twodimensional Gaussian quantum field theory. The no arbitrage condition is obtained and a functional integral derivation is given for the price of a futures and an options contract.
Thermal field theory of bosonic gases with finiterange effective interaction
NASA Astrophysics Data System (ADS)
Cappellaro, A.; Salasnich, L.
20170301
We study a dilute and ultracold Bose gas of interacting atoms by using an effective field theory which takes into account the finiterange effects of the interatomic potential. Within the formalism of functional integration from the grand canonical partition function, we derive beyondmeanfield analytical results which depend on both the scattering length and the effective range of the interaction. In particular, we calculate the equation of state of the bosonic system as a function of these interaction parameters both at zero and finite temperature including oneloop Gaussian fluctuation. In the case of zerorange effective interaction, we explicitly show that, due to quantum fluctuations, the bosonic system is thermodynamically stable only for very small values of the gas parameter. We find that a positive effective range above a critical threshold is necessary to remove the thermodynamical instability of the uniform configuration. Remarkably, also for relatively large values of the gas parameter, our finiterange results are in quite good agreement with recent zerotemperature Monte Carlo calculations obtained with hardsphere bosons.
Finite Difference Elastic Wave Field Simulation On GPU
NASA Astrophysics Data System (ADS)
Hu, Y.; Zhang, W.
20111201
Numerical modeling of seismic wave propagation is considered as a basic and important aspect in investigation of the Earth's structure, and earthquake phenomenon. Among various numerical methods, the finitedifference method is considered one of the most efficient tools for the wave field simulation. However, with the increment of computing scale, the power of computing has becoming a bottleneck. With the development of hardware, in recent years, GPU shows powerful computational ability and bright application prospects in scientific computing. Many works using GPU demonstrate that GPU is powerful . Recently, GPU has not be used widely in the simulation of wave field. In this work, we present forward finite difference simulation of acoustic and elastic seismic wave propagation in heterogeneous media on NVIDIA graphics cards with the CUDA programming language. We also implement perfectly matched layers on the graphics cards to efficiently absorb outgoing waves on the fictitious edges of the grid Simulations compared with the results on CPU platform shows reliable accuracy and remarkable efficiency. This work proves that GPU can be an effective platform for wave field simulation, and it can also be used as a practical tool for realtime strong ground motion simulation.
Exact scattering matrix of graphs in magnetic field and quantum noise
Caudrelier, Vincent; Mintchev, Mihail; Ragoucy, Eric
20140815
We consider arbitrary quantum wire networks modelled by finite, noncompact, connected quantum graphs in the presence of an external magnetic field. We find a general formula for the total scattering matrix of the network in terms of its local scattering properties and its metric structure. This is applied to a quantum ring with N external edges. Connecting the external edges of the ring to heat reservoirs, we study the quantum transport on the graph in ambient magnetic field. We consider two types of dynamics on the ring: the free Schrödinger and the free massless Dirac equations. For each case, a detailed study of the thermal noise is performed analytically. Interestingly enough, in presence of a magnetic field, the standard linear JohnsonNyquist law for the low temperature behaviour of the thermal noise becomes nonlinear. The precise regime of validity of this effect is discussed and a typical signature of the underlying dynamics is observed.
Magnetic field homogeneity perturbations in finite Halbach dipole magnets.
Turek, Krzysztof; Liszkowski, Piotr
20140101
Halbach hollow cylinder dipole magnets of a low or relatively low aspect ratio attract considerable attention due to their applications, among others, in compact NMR and MRI systems for investigating small objects. However, a complete mathematical framework for the analysis of magnetic fields in these magnets has been developed only for their infinitely long precursors. In such a case the analysis is reduced to twodimensions (2D). The paper details the analysis of the 3D magnetic field in the Halbach dipole cylinders of a finite length. The analysis is based on three equations in which the components of the magnetic flux density Bx, By and Bz are expanded to infinite power series of the radial coordinate r. The zeroth term in the series corresponds to a homogeneous magnetic field Bc, which is perturbed by the higher order terms due to a finite magnet length. This set of equations is supplemented with an equation for the field profile B(z) along the magnet axis, presented for the first time. It is demonstrated that the geometrical factors in the coefficients of particular powers of r, defined by intricate integrals are the coefficients of the Taylor expansion of the homogeneity profile (B(z)Bc)/Bc. As a consequence, the components of B can be easily calculated with an arbitrary accuracy. In order to describe perturbations of the field due to segmentation, two additional equations are borrowed from the 2D theory. It is shown that the 2D approach to the perturbations generated by the segmentation can be applied to the 3D Halbach structures unless r is not too close to the inner radius of the cylinder ri. The mathematical framework presented in the paper was verified with great precision by computations of B by a highly accurate integration of the magnetostatic Coulomb law and utilized to analyze the inhomogeneity of the magnetic field in the magnet with the accuracy better than 1 ppm.
Torque anomaly in quantum field theory
NASA Astrophysics Data System (ADS)
Fulling, S. A.; Mera, F. D.; Trendafilova, C. S.
20130201
The expectation values of energy density and pressure of a quantum field inside a wedgeshaped region appear to violate the expected relationship between torque and total energy as a function of angle. In particular, this is true of the wellknown DeutschCandelas stress tensor for the electromagnetic field, whose definition requires no regularization except possibly at the vertex. Unlike a similar anomaly in the pressure exerted by a reflecting boundary against a perpendicular wall, this problem cannot be dismissed as an artifact of an ad hoc regularization.
Quantum Physics, Fields and Closed Timelike Curves: The DCTC Condition in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Tolksdorf, Jürgen; Verch, Rainer
20170701
The DCTC condition has originally been proposed by David Deutsch as a condition on states of a quantum communication network that contains "backward timesteps" in some of its branches. It has been argued that this is an analogue for quantum processes in the presence of closed timelike curves (CTCs). The unusual properties of states of quantum communication networks that fulfill the DCTC condition have been discussed extensively in recent literature. In this work, the DCTC condition is investigated in the framework of quantum field theory in the local, operatoralgebraic approach due to Haag and Kastler. It is shown that the DCTC condition cannot be fulfilled in states that are analytic in the energy, or satisfy the ReehSchlieder property, for a certain class of processes and initial conditions. On the other hand, if a quantum field theory admits sufficiently many uncorrelated states across acausally related spacetime regions (as implied by the split property), then the DCTC condition can always be fulfilled approximately to arbitrary precision. As this result pertains to quantum field theory on globally hyperbolic spacetimes where CTCs are absent, one may conclude that interpreting the DCTC condition as characteristic for quantum processes in the presence of CTCs could be misleading, and should be regarded with caution. Furthermore, a construction of the quantized massless KleinGordon field on the Politzer spacetime, often viewed as spacetime analogue for quantum communication networks with backward timesteps, is proposed in this work.
Finite fielddependent symmetry in the Thirring model
NASA Astrophysics Data System (ADS)
Upadhyay, Sudhaker; Ganai, Prince A.
20160601
In this paper, we consider a Ddimensional massive Thirring model with (2
Finite coupling effects in double quantum dots near equilibrium
NASA Astrophysics Data System (ADS)
Xu, Xiansong; Thingna, Juzar; Wang, JianSheng
20170101
A weak coupling quantum master equation provides reliable steadystate results only in the van Hove limit, i.e., when the systemlead coupling approaches zero. Recently, J. Thingna et al. [Phys. Rev. E 88, 052127 (2013), 10.1103/PhysRevE.88.052127] proposed an alternative approach, based on an analytic continuation of the Redfield solution, to evaluate the steadystate reduced density matrix up to second order in the systembath coupling. The approach provides accurate results for harmonic oscillator and spinbosonic systems. We apply this approach to study steadystate fermionic systems and the calculation on an exactly solvable double quantum dot system shows that the method is rigorously valid up to second order in systemlead coupling only near equilibrium, i.e., linear response regime. We further compare to the Redfield and the secular Redfield (Lindbladtype) master equations that are inaccurate in all parameter regimes. Lastly, we consider the nontrivial problem of strong Coulomb interaction and illustrate the interplay between systemlead coupling, interdot tunneling, and Coulomb strength that can be captured only via the analytic continuation method.
Camjayi, Alberto; Arrachea, Liliana
20140122
We study the transport behavior induced by a small bias voltage through a quantum dot connected to onechannel finitesize wires. We describe the quantum dot using the HubbardAnderson impurity model and we obtain solutions by means of a quantum Monte Carlo method. We investigate the effect of a magnetic field applied at the quantum dot in the Kondo regime. We identify mesoscopic oscillations in the conductance, which are introduced by the magnetic field. This behavior is analogous to that observed as a function of the temperature.
Macroscopic quantum entanglement of a Kondo cloud at finite temperature.
Lee, SS B; Park, Jinhong; Sim, HS
20150206
We propose a variational approach for computing the macroscopic entanglement in a manybody mixed state, based on entanglement witness operators, and compute the entanglement of formation (EoF), a mixedstate generalization of the entanglement entropy, in single and twochannel Kondo systems at finite temperature. The thermal suppression of the EoF obeys powerlaw scaling at low temperature. The scaling exponent is halved from the single to the twochannel system, which is attributed, using a bosonization method, to the nonFermi liquid behavior of a Majorana fermion, a "half" of a complex fermion, emerging in the twochannel system. Moreover, the EoF characterizes the size and powerlaw tail of the Kondo screening cloud of the singlechannel system.
Zeno effect and ergodicity in finitetime quantum measurements
Sokolovski, D.
20111215
We demonstrate that an attempt to measure a nonlocal in time quantity, such as the time average {sub T} of a dynamical variable A, by separating Feynman paths into ever narrower exclusive classes traps the system in eigensubspaces of the corresponding operator A. Conversely, in a long measurement of {sub T} to a finite accuracy, the system explores its Hilbert space and is driven to a universal steady state in which the von Neumann ensemble average of A coincides with {sub T}. Both effects are conveniently analyzed in terms of singularities and critical points of the corresponding amplitude distribution and the Zenolike behavior is shown to be a consequence of the conservation of probability.
Anode distance effect on field electron emission from carbon nanotubes: a molecular/quantum mechanical simulation.
He, Chunshan; Wang, Weiliang; Deng, Shaozhi; Xu, Ningsheng; Li, Zhibing; Chen, Guihua; Peng, Jie
20090625
Field electron emission from singlewalled (5,5) carbon nanotubes was simulated with a quantum chemistry method, emphasizing the effect of distance between the anode and apex. The emission probability and the field enhancement factor were obtained for different anodeapex separations with two representative applied macroscopic fields. The quantum chemistry simulation was compared to the classical finite element calculation. It was found that the field enhancement factor was overestimated by about a factor 2 in the classical calculation (for the capped carbon nanotube). The effective work function lowering due to the field penetration into the apex has important contribution to the emission probability. A peculiar decrease of the effective work function with the anodeapex separation was found for the capped carbon nanotube, and its quantum mechanical origin is discussed.
NASA Astrophysics Data System (ADS)
Umezawa, H.
Throughout the course of its development in the past four decades quantum field theory has gradually acquired a very rich structure (much richer in fact than it was originally intended) and now provides us with an effective method in the analysis of many diverse areas of physics; condensed matter physics, high energy particle physics general relativity and cosmology are among the more notable examples. Since condensed matter physics deals with those phenomena in which a system of quanta exist together with a variety of macroscopic objects at finite temperature, it may be said to manifest the fundamental properties of quantum field theory in its widest sense. Thus condensed matter physics has served as a powerful motivating force throughout the growth and development of quantum field theory. This process was indeed initiated by the celebrated Matsubara formalism of finite temperature Green's function method. This process is by no means complete since recent developments in many areas of physics demand a more sophisticated understanding with regard to the fundamental nature of quantum field theory. A brief description of this maturing process of quantum field theory in the past, present and prospects for the future will be the main content of this article.
Influence of finite volume and magnetic field effects on the QCD phase diagram
NASA Astrophysics Data System (ADS)
Magdy, Niseem; Csanád, M.; Lacey, Roy A.
20170201
The 2 + 1 SU(3) Polyakov linear sigma model is used to investigate the respective influence of a finite volume and a magnetic field on the quarkhadron phase boundary in the plane of baryon chemical potential ({μ }B) versus temperature (T) of the quantum chromodynamics (QCD) phase diagram. The calculated results indicate sizable shifts of the quarkhadron phase boundary to lower values of ({μ }B {and} T) for increasing magnetic field strength, and an opposite shift to higher values of ({μ }B {and} T) for decreasing system volume. Such shifts could have important implications for the extraction of the thermodynamic properties of the QCD phase diagram from heavy ion data.
NASA Astrophysics Data System (ADS)
Dekker, H.
19840801
The mechanical model of an oscillator coupled to a continuum transmission line (string) is reconsidered in a twosided version. Its dynamics is solved exactly and explicitly, for arbitrary length of the strings, within the Lagrange formalism. For infinite length the oscillator becomes linearly damped for all times. The quantum mechanics of the oscillator reveals a logarithmic ultraviolet divergence in the momentum fluctuations. This divergence (i) is now clearly shown to be an exact consequence of the model; (ii) it exists for any length of the strings, and (iii) cannot be removed by renormalization.
Semianalytical quantum model for graphene fieldeffect transistors
Pugnaghi, Claudio; Grassi, Roberto Gnudi, Antonio; Di Lecce, Valerio; Gnani, Elena; Reggiani, Susanna; Baccarani, Giorgio
20140921
We develop a semianalytical model for monolayer graphene fieldeffect transistors in the ballistic limit. Two types of devices are considered: in the first device, the source and drain regions are doped by charge transfer with Schottky contacts, while, in the second device, the source and drain regions are doped electrostatically by a back gate. The model captures two important effects that influence the operation of both devices: (i) the finite density of states in the source and drain regions, which limits the number of states available for transport and can be responsible for negative output differential resistance effects, and (ii) quantum tunneling across the potential steps at the sourcechannel and drainchannel interfaces. By comparison with a selfconsistent nonequilibrium Green's function solver, we show that our model provides very accurate results for both types of devices, in the bias region of quasisaturation as well as in that of negative differential resistance.
A master functional for quantum field theory
NASA Astrophysics Data System (ADS)
Anselmi, Damiano
20130401
We study a new generating functional of oneparticle irreducible diagrams in quantum field theory, called master functional, which is invariant under the most general perturbative changes of field variables. The usual functional Γ does not behave as a scalar under the transformation law inherited from its very definition as the Legendre transform of W=ln Z, although it does behave as a scalar under an unusual transformation law. The master functional, on the other hand, is the Legendre transform of an improved functional W with respect to the sources coupled to both elementary and composite fields. The inclusion of certain improvement terms in W and Z is necessary to make this new Legendre transform well defined. The master functional behaves as a scalar under the transformation law inherited from its very definition. Moreover, it admits a proper formulation, obtained extending the set of integrated fields to socalled proper fields, which allows us to work without passing through Z, W or Γ. In the proper formulation the classical action coincides with the classical limit of the master functional, and correlation functions and renormalization are calculated applying the usual diagrammatic rules to the proper fields. Finally, the most general change of field variables, including the map relating bare and renormalized fields, is a linear redefinition of the proper fields.
Smooth and fast versus instantaneous quenches in quantum field theory
NASA Astrophysics Data System (ADS)
Das, Sumit R.; Galante, Damián A.; Myers, Robert C.
20150801
We examine in detail the relationship between smooth fast quantum quenches, characterized by a time scale δ t, and instantaneous quenches, within the framework of exactly solvable mass quenches in free scalar field theory. Our earlier studies [1, 2] highlighted that the two protocols remain distinct in the limit δ t → 0 because of the relation of the quench rate to the UV cutoff, i.e., 1 /δ t ≪ Λ always holds in the fast smooth quenches while 1 /δ t ˜ Λ for instantaneous quenches. Here we study UV finite quantities like correlators at finite spatial distances and the excess energy produced above the final ground state energy. We show that at late times and large distances (compared to the quench time scale) the smooth quench correlator approaches that for the instantaneous quench. At early times, we find that for small spatial separation and small δ t, the correlator scales universally with δ t, exactly as in the scaling of renormalized one point functions found in earlier work. At larger separation, the dependence on δ t drops out. The excess energy density is finite (for finite mδ t) and scales in a universal fashion for all d. However, the scaling behaviour produces a divergent result in the limit mδ t → 0 for d ≥ 4, just as in an instantaneous quench, where it is UV divergent for d ≥ 4. We argue that similar results hold for arbitrary interacting theories: the excess energy density produced is expected to diverge for scaling dimensions Δ > d/2.
Effects of the Chemical Potential in twodimensional Quantum Field Theories
NASA Astrophysics Data System (ADS)
Maciel, Soraya G.; Perez, Silvana; Rocha, C.
20100201
In this talk we study the effects of a nonzero chemical potential in (1+1) dimensions quantum field models at finite temperature. We start by considering massless fermions in an abelian gauge field background and calculate the npoint amplitudes using the real time formalism. Our calculation shows that the chiral anomaly is unaffected by the presence of a chemical potential at finite temperature. We also find that retarded amplitudes vanish. We then consider the imaginary time formalism and find that the two and threepoint functions vanish, this result being consistent with the real time calculations.
NASA Astrophysics Data System (ADS)
Batalin, Igor A.; Bering, Klaus; Lavrov, Peter M.; Tyutin, Igor V.
20141101
In the framework of Sp(2) extended Lagrangian fieldantifield BV formalism, we study systematically the role of finite fielddependent BRSTBV transformations. We have proved that the Jacobian of a finite BRSTBV transformation is capable of generating arbitrary finite change of the gaugefixing function in the path integral.
Comments on conformal Killing vector fields and quantum field theory
Brown, M.R.; Ottewill, A.C.; Siklos, S.T.C.
19821015
We give a comprehensive analysis of those vacuums for flat and conformally flat spacetimes which can be defined by timelike, hypersurfaceorthogonal, conformal Killing vector fields. We obtain formulas for the difference in stressenergy density between any two such states and display the correspondence with the renormalized stress tensors. A brief discussion is given of the relevance of these results to quantummechanical measurements made by noninertial observers moving through flat space.
GPU and APU computations of Finite Time Lyapunov Exponent fields
NASA Astrophysics Data System (ADS)
Conti, Christian; Rossinelli, Diego; Koumoutsakos, Petros
20120301
We present GPU and APU accelerated computations of FiniteTime Lyapunov Exponent (FTLE) fields. The calculation of FTLEs is a computationally intensive process, as in order to obtain the sharp ridges associated with the Lagrangian Coherent Structures an extensive resampling of the flow field is required. The computational performance of this resampling is limited by the memory bandwidth of the underlying computer architecture. The present technique harnesses dataparallel execution of manycore architectures and relies on fast and accurate evaluations of moment conserving functions for the mesh to particle interpolations. We demonstrate how the computation of FTLEs can be efficiently performed on a GPU and on an APU through OpenCL and we report over one order of magnitude improvements over multithreaded executions in FTLE computations of bluff body flows.
Murguia, Gabriela; Moreno, Matias; Torres, Manuel
20090420
A well known example in quantum electrodynamics (QED) shows that Coulomb scattering of unpolarized electrons, calculated to lowest order in perturbation theory, yields a results that exactly coincides (in the nonrelativistic limit) with the Rutherford formula. We examine an analogous example, the classical and perturbative quantum scattering of an electron by a magnetic field confined in an infinite solenoid of finite radius. The results obtained for the classical and the quantum differential cross sections display marked differences. While this may not be a complete surprise, one should expect to recover the classical expression by applying the classical limit to the quantum result. This turn not to be the case. Surprisingly enough, it is shown that the classical result can not be recuperated even if higher order corrections are included. To recover the classic correspondence of the quantum scattering problem a suitable nonperturbative methodology should be applied.
Coherent control in quantum transport: amplification, filtering and switching at finite bias
NASA Astrophysics Data System (ADS)
Thethi, Rajpal; Emary, Clive
20170601
We consider coherent feedback control of quantum transport and focus on the application of simple controllers and the effects of a finite bias voltage. We show that simple singleparameter controllers can give rise to a range of useful effects such as amplification of changes in plant transmission, increased resolution of energy filtration, and the detection of differences between otherwise indistinguishable plants. We explore how these effects are impacted by the phaseaveraging effects associated with finite bias and identify important voltage scales for the maintenance of the functionalities achieved through feedback control.
Finitekey analysis of a practical decoystate highdimensional quantum key distribution
NASA Astrophysics Data System (ADS)
Bao, Haize; Bao, Wansu; Wang, Yang; Zhou, Chun; Chen, Ruike
20160501
Compared with twolevel quantum key distribution (QKD), highdimensional QKD enables two distant parties to share a secret key at a higher rate. We provide a finitekey security analysis for the recently proposed practical highdimensional decoystate QKD protocol based on timeenergy entanglement. We employ two methods to estimate the statistical fluctuation of the postselection probability and give a tighter bound on the securekey capacity. By numerical evaluation, we show the finitekey effect on the securekey capacity in different conditions. Moreover, our approach could be used to optimize parameters in practical implementations of highdimensional QKD.
Nonlinear quantum equations: Classical field theory
RegoMonteiro, M. A.; Nobre, F. D.
20131015
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 KleinGordon 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 qplane 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 KleinGordon 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.
NASA Astrophysics Data System (ADS)
Shah, Nayana; Lopatin, Andrei
20070901
A microscopic analysis of the superconducting quantum critical point realized via a pairbreaking quantum phase transition is presented. Finitetemperature crossovers are derived for the electrical conductivity, which is a key probe of superconducting fluctuations. By using the diagrammatic formalism for disordered systems, we are able to incorporate the interplay between fluctuating Cooper pairs and electrons, that is outside the scope of a timedependent GinzburgLandau or effective bosonic action formalism. It is essential to go beyond the standard approximation in order to capture the zerotemperature correction which results purely from the (dynamic) quantum fluctuations and dictates the behavior of the conductivity in an entire lowtemperature quantum regime. All dynamic contributions are of the same order and conspire to add up to a negative total, thereby inhibiting the conductivity as a result of superconducting fluctuations. On the contrary, the classical and the intermediate regimes are dominated by the positive bosonic channel. Our theory is applicable in one, two, and three dimensions and is relevant for experiments on superconducting nanowires, doubly connected cylinders, thin films, and bulk in the presence of magnetic impurities, magnetic field, or other pair breakers. A window of nonmonotonic behavior is predicted to exist as either the temperature or the pairbreaking parameter is swept.
Korotaev, P. Yu. Kaputkina, N. E.; Lozovik, Yu. E.; Vekilov, Yu. Kh.
20111015
The energy spectra and transport of electronic excitations in onedimensional aperiodic sequences of quantum dots of ThueMorse and doubleperiodic type are studied. The influence of external magnetic and electric fields on the energy spectra and transport is considered. For aperiodic sequences of quantum dots, in contrast to aperiodic sequences of atoms, the influence of relatively small magnetic and electric fields is essential, but localization occurs at finite values of the perturbations. The transmission coefficient is determined using the quasiclassical approximation with the Coulomb blockade taken into account. The resonance tunneling is studied.
A systematic study of finite BRSTBV transformations in fieldantifield formalism
NASA Astrophysics Data System (ADS)
Batalin, Igor A.; Lavrov, Peter M.; Tyutin, Igor V.
20141101
We study systematically finite BRSTBV transformations in the fieldantifield formalism. We present explicitly their Jacobians and the form of a solution to the compensation equation determining the functional field dependence of finite Fermionic parameters, necessary to generate arbitrary finite change of gaugefixing functions in the path integral.
Subsystems of a finite quantum system and Belllike inequalities
NASA Astrophysics Data System (ADS)
Vourdas, A.
20140501
The set of subsystems Σ(m) of a finite quantum system Σ(n) with variables in Bbb Z(n), together with logical connectives, is a Heyting algebra. The probabilities τ(mρn)=Tr[(m)ρn] (where (m) is the projector to Σ(m)) are compatible with associativity of the join in the Heyting algebra, only if the variables belong to the same chain. Consequently, contextuality in the present formalism, has the chains as contexts. Various Belllike inequalities are discussed. They are violated, and this proves that quantum mechanics is a contextual theory.
Finite speed heat transport in a quantum spin chain after quenched local cooling
NASA Astrophysics Data System (ADS)
Fries, Pascal; Hinrichsen, Haye
20170401
We study the dynamics of an initially thermalized spin chain in the quantum XYmodel, after sudden coupling to a heat bath of lower temperature at one end of the chain. In the semiclassical limit we see an exponential decay of the systembath heatflux by exact solution of the reduced dynamics. In the full quantum description however, we numerically find the heatflux to reach intermediate plateaus where it is approximately constant—a phenomenon that we attribute to the finite speed of heat transport via spin waves.
Jain, Shweta Sharma, Prerana; Chhajlani, R. K.
20150731
The Jeans instability of selfgravitating quantum plasma is examined considering the effects of viscosity, finite Larmor radius (FLR) corrections and rotation. The analysis is done by normal mode analysis theory with the help of relevant linearized perturbation equations of the problem. The general dispersion relation is obtained using the quantum magneto hydrodynamic model. The modified condition of Jeans instability is obtained and the numerical calculations have been performed to show the effects of various parameters on the growth rate of Jeans instability.
Role of work in matter exchange between finite quantum systems
NASA Astrophysics Data System (ADS)
Jeon, Euijin; Talkner, Peter; Yi, Juyeon; Kim, Yong Woon
20170901
Close to equilibrium, the exchange of particles and heat between macroscopic systems at different temperatures and different chemical potentials is known to be governed by a matrix of transport coefficients which are positive and symmetric. We investigate the amounts of heat and particles that are exchanged between two small quantum systems within a given time, and find them characterized by a transport matrix which neither needs to be symmetric nor positive. At larger times even spontaneous transport can be observed in the total absence of temperature and chemical potential differences provided that the two systems are different in size. All these deviations from standard transport behavior can be attributed to the fact that work is done on the system in the processes contacting and separating those parts of the system that initially possess different temperatures and chemical potentials. The standard transport properties are recovered for vanishing work and also in the limit of large systems and sufficiently large contact times. The general results are illustrated by an example.
Inertial mass and the quantum vacuum fields
NASA Astrophysics Data System (ADS)
Haisch, Bernard; Rueda, Alfonso; Dobyns, York
20010501
Even when the Higgs particle is finally detected, it will continue to be a legitimate question to ask whether the inertia of matter as a reaction force opposing acceleration is an intrinsic or extrinsic property of matter. General relativity specifies which geodesic path a free particle will follow, but geometrodynamics has no mechanism for generating a reaction force for deviation from geodesic motion. We discuss a different approach involving the electromagnetic zeropoint field (ZPF) of the quantum vacuum. It has been found that certain asymmetries arise in the ZPF as perceived from an accelerating reference frame. In such a frame the Poynting vector and momentum flux of the ZPF become nonzero. Scattering of this quantum radiation by the quarks and electrons in matter can result in an accelerationdependent reaction force. Both the ordinary and the relativistic forms of Newton's second law, the equation of motion, can be derived from the electrodynamics of such ZPFparticle interactions. Conjectural arguments are given why this interaction should take place in a resonance at the Compton frequency, and how this could simultaneously provide a physical basis for the de Broglie wavelength of a moving particle. This affords a suggestive perspective on a deep connection between electrodynamics, the origin of inertia and the quantum wave nature of matter.
Quantum key distribution with finite resources: Secret key rates via Renyi entropies
Abruzzo, Silvestre; Kampermann, Hermann; Mertz, Markus; Bruss, Dagmar
20110915
A realistic quantum key distribution (QKD) protocol necessarily deals with finite resources, such as the number of signals exchanged by the two parties. We derive a bound on the secret key rate which is expressed as an optimization problem over Renyi entropies. Under the assumption of collective attacks by an eavesdropper, a computable estimate of our bound for the sixstate protocol is provided. This bound leads to improved key rates in comparison to previous results.
Bilinear covariants and spinor fields duality in quantum Clifford algebras
Abłamowicz, Rafał; Gonçalves, Icaro; Rocha, Roldão da
20141015
Classification of quantum spinor fields according to quantum bilinear covariants is introduced in a context of quantum Clifford algebras on Minkowski spacetime. Once the bilinear covariants are expressed in terms of algebraic spinor fields, the duality between spinor and quantum spinor fields can be discussed. Thus, by endowing the underlying spacetime with an arbitrary bilinear form with an antisymmetric part in addition to a symmetric spacetime metric, quantum algebraic spinor fields and deformed bilinear covariants can be constructed. They are thus compared to the classical (non quantum) ones. Classes of quantum spinor fields classes are introduced and compared with Lounesto's spinor field classification. A physical interpretation of the deformed parts and the underlying Zgrading is proposed. The existence of an arbitrary bilinear form endowing the spacetime already has been explored in the literature in the context of quantum gravity [S. W. Hawking, “The unpredictability of quantum gravity,” Commun. Math. Phys. 87, 395 (1982)]. Here, it is shown further to play a prominent role in the structure of Dirac, Weyl, and Majorana spinor fields, besides the most general flagpoles and flagdipoles. We introduce a new duality between the standard and the quantum spinor fields, by showing that when Clifford algebras over vector spaces endowed with an arbitrary bilinear form are taken into account, a mixture among the classes does occur. Consequently, novel features regarding the spinor fields can be derived.
Gravity quantized: Loop quantum gravity with a scalar field
Domagala, Marcin; Kaminski, Wojciech; Giesel, Kristina; Lewandowski, Jerzy
20101115
...''but we do not have quantum gravity.'' This phrase is often used when analysis of a physical problem enters the regime in which quantum gravity effects should be taken into account. In fact, there are several models of the gravitational field coupled to (scalar) fields for which the quantization procedure can be completed using loop quantum gravity techniques. The model we present in this paper consists of the gravitational field coupled to a scalar field. The result has similar structure to the loop quantum cosmology models, except that it involves all the local degrees of freedom of the gravitational field because no symmetry reduction has been performed at the classical level.
Carrier relaxation in (In,Ga)As quantum dots with magnetic fieldinduced anharmonic level structure
NASA Astrophysics Data System (ADS)
Kurtze, H.; Bayer, M.
20160701
Sophisticated models have been worked out to explain the fast relaxation of carriers into quantum dot ground states after nonresonant excitation, overcoming the originally proposed phonon bottleneck. We apply a magnetic field along the quantum dot heterostructure growth direction to transform the confined level structure, which can be approximated by a FockDarwin spectrum, from a nearly equidistant level spacing at zero field to strong anharmonicity in finite fields. This changeover leaves the ground state carrier population rise time unchanged suggesting that fast relaxation is maintained upon considerable changes of the level spacing. This corroborates recent models explaining the relaxation by polaron formation in combination with quantum kinetic effects.
Carrier relaxation in (In,Ga)As quantum dots with magnetic fieldinduced anharmonic level structure
Kurtze, H.; Bayer, M.
20160704
Sophisticated models have been worked out to explain the fast relaxation of carriers into quantum dot ground states after nonresonant excitation, overcoming the originally proposed phonon bottleneck. We apply a magnetic field along the quantum dot heterostructure growth direction to transform the confined level structure, which can be approximated by a Fock–Darwin spectrum, from a nearly equidistant level spacing at zero field to strong anharmonicity in finite fields. This changeover leaves the ground state carrier population rise time unchanged suggesting that fast relaxation is maintained upon considerable changes of the level spacing. This corroborates recent models explaining the relaxation by polaron formation in combination with quantum kinetic effects.
Haag's Theorem and Parameterized Quantum Field Theory
NASA Astrophysics Data System (ADS)
Seidewitz, Edwin
20170101
``Haag's theorem is very inconvenient; it means that the interaction picture exists only if there is no interaction''. In traditional quantum field theory (QFT), Haag's theorem states that any field unitarily equivalent to a free field must itself be a free field. But the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field, but which must still account for interactions. So, the usual derivation of the scattering matrix in QFT is mathematically ill defined. Nevertheless, perturbative QFT is currently the only practical approach for addressing realistic scattering, and it has been very successful in making empirical predictions. This success can be understood through an alternative derivation of the Dyson series in a covariant formulation of QFT using an invariant, fifth path parameter in addition to the usual four position parameters. The parameterization provides an additional degree of freedom that allows Haag's Theorem to be avoided, permitting the consistent use of a form of interaction picture in deriving the Dyson expansion. The extra symmetry so introduced is then broken by the choice of an interacting vacuum.
Finitesize analysis of a continuousvariable quantum key distribution
Leverrier, Anthony; Grangier, Philippe
20100615
The goal of this paper is to extend the framework of finitesize analysis recently developed for quantum key distribution to continuousvariable protocols. We do not solve this problem completely here, and we mainly consider the finitesize effects on the parameter estimation procedure. Despite the fact that some questions are left open, we are able to give an estimation of the secret key rate for protocols which do not contain a postselection procedure. As expected, these results are significantly more pessimistic than those obtained in the asymptotic regime. However, we show that recent continuousvariable protocols are able to provide fully secure secret keys in the finitesize scenario, over distances larger than 50 km.
NASA Astrophysics Data System (ADS)
Wang, Chao; Huang, Peng; Huang, Duan; Lin, Dakai; Zeng, Guihua
20160201
Practical security of the continuousvariable quantum key distribution (CVQKD) system with finite sampling bandwidth of analogtodigital converter (ADC) at the receiver's side is investigated. We find that the finite sampling bandwidth effects may decrease the lower bound of secret key rate without awareness of the legitimate communicators. This leaves security loopholes for Eve to attack the system. In addition, this effect may restrains the linear relationship of secret key bit rate with repetition rate of the system; subsequently, there is a saturation value for the secret key bit rate with the repetition rate. To resist such kind of effects, we propose a dual sampling detection approach in which two ADCs are employed so that the finite sampling bandwidth effects are removed.
FINITE ELEMENT MODEL FOR TIDES AND CURRENTS WITH FIELD APPLICATIONS.
Walters, Roy A.
19880101
A finite element model, based upon the shallow water equations, is used to calculate tidal amplitudes and currents for two fieldscale test problems. Because tides are characterized by line spectra, the governing equations are subjected to harmonic decomposition. Thus the solution variables are the real and imaginary parts of the amplitude of sea level and velocity rather than a time series of these variables. The time series is recovered through synthesis. This scheme, coupled with a modified form of the governing equations, leads to high computational efficiency and freedom from excessive numerical noise. Two testcases are presented. The first is a solution for eleven tidal constituents in the English Channel and southern North Sea, and three constituents are discussed. The second is an analysis of the frequency response and tidal harmonics for south San Francisco Bay.
Finite element modeling of electromagnetic fields and waves using NASTRAN
NASA Technical Reports Server (NTRS)
Moyer, E. Thomas, Jr.; Schroeder, Erwin
19890101
The various formulations of Maxwell's equations are reviewed with emphasis on those formulations which most readily form analogies with Navier's equations. Analogies involving scalar and vector potentials and electric and magnetic field components are presented. Formulations allowing for media with dielectric and conducting properties are emphasized. It is demonstrated that many problems in electromagnetism can be solved using the NASTRAN finite element code. Several fundamental problems involving time harmonic solutions of Maxwell's equations with known analytic solutions are solved using NASTRAN to demonstrate convergence and mesh requirements. Mesh requirements are studied as a function of frequency, conductivity, and dielectric properties. Applications in both low frequency and high frequency are highlighted. The low frequency problems demonstrate the ability to solve problems involving media inhomogeneity and unbounded domains. The high frequency applications demonstrate the ability to handle problems with large boundary to wavelength ratios.
Systolic multipliers for finite fields GF(2 exp m)
NASA Technical Reports Server (NTRS)
Yeh, C.S.; Reed, I. S.; Truong, T. K.
19840101
Two systolic architectures are developed for performing the productsum computation AB + C in the finite field GF(2 exp m) of 2 exp m elements, where A, B, and C are arbitrary elements of GF(2 exp m). The first multiplier is a serialin, serialout onedimensional systolic array, while the second multiplier is a parallelin, parallelout twodimensional systolic array. The first multiplier requires a smaller number of basic cells than the second multiplier. The second multiplier needs less average time per computation than the first multiplier, if a number of computations are performed consecutively. To perform single computations both multipliers require the same computational time. In both cases the architectures are simple and regular and possess the properties of concurrency and modularity. As a consequence, they are well suited for use in VLSI systems.
Causality Is Inconsistent With Quantum Field Theory
Wolf, Fred Alan
20111129
Causality in quantum field theory means the vanishing of commutators for spacelike separated fields (VCSSF). I will show that VCSSF is not tenable. For VCSSF to be tenable, and therefore, to have both retarded and advanced propagators vanish in the elsewhere, a superposition of negative energy antiparticle and positive energy particle propagators, traveling forward in time, and a superposition of negative energy particle and positive energy antiparticle propagators, traveling backward in time, are required. Hence VCSSF predicts nonvanishing probabilities for both negative energy particles in the forwardthroughtime direction and positive energy antiparticles in the backwardsthroughtime direction. Therefore, since VCSSF is unrealizable in a stable universe, tachyonic propagation must occur in denial of causality.
NASA Astrophysics Data System (ADS)
Moretti, Valter; Pastorello, Davide
20161201
This work concerns some issues about the interplay of standard and geometric (Hamiltonian) approaches to finitedimensional quantum mechanics, formulated in the projective space. Our analysis relies upon the notion and the properties of socalled frame functions, introduced by Gleason to prove his celebrated theorem. In particular, the problem of associating quantum states with positive Liouville densities is tackled from an axiomatic point of view, proving a theorem classifying all possible correspondences. A similar result is established for classicallike observables (i.e. real scalar functions on the projective space) representing quantum ones. These correspondences turn out to be encoded in a oneparameter class and, in both cases, the classicallike objects representing quantum ones result to be frame functions. The requirements of U(n) covariance and (convex) linearity play a central role in the proof of those theorems. A new characterization of classicallike observables describing quantum observables is presented, together with a geometric description of the C∗algebra structure of the set of quantum observables in terms of classicallike ones.
Nonperturbative studies in quantum field theory
Abada, A.
19920101
This dissertation is composed of three different research topics. The first part deals with the Study of the socalled local lattice Yukawa theory. The motivation for this study is to investigate the interior of the phase diagram of this theory. A strong y expansion (y being the bare Yukawa coupling) is performed of the partition function and show that within the (finite) range of convergence of the series expansion, the lattice Yukawa theory is equivalent to a purely bosonic theory, with a shifted action. The author explicitly calculated the shifted action to the fourth order in 1/y and find that it is composed of competing interactions. This suggests that away from y = [infinity] towards the interior of the phase diagram, there is a more complicated ordering than simple ferromagnetic or antiferromagnetic. In the second part, the question is addressed of formation of bound states out of constituent fields in an exactly soluble theory, i.e. multifermion electrodynamics in two spacetime dimensions. The author exactly calculates the correlation function corresponding to a neutral composite fermion operator and discuss the pole structure of its Fourier transform. It does not exhibit a simple pole in p[sup 2], hence the corresponding neutral composite operator does not create an asymptotic state in the spectrum of the theory. In part three, the author puts multifermion QED[sub 2] in a heat bath and address the same question as in part two. The author first exactly calculates a bosonic correlation function at finite temperature and density, and discuss its behavior. The author then exactly calculates the correlation function corresponding to the neutral composite fermion operator at finite temperature and density and discusses its behavior. It is concluded that the temperature does not help the composite fermion operator create a particle in the spectrum of the theory.
Nonequilibrium Kondo transport through a quantum dot in a magnetic field
NASA Astrophysics Data System (ADS)
Smirnov, Sergey; Grifoni, Milena
20130701
We analyze the universal transport properties of a strongly interacting quantum dot in the Kondo regime when the quantum dot is placed in an external magnetic field. The quantum dot is described by the asymmetric Anderson model with the spin degeneracy removed by the magnetic field resulting in Zeeman splitting. Using an analytical expression for the tunneling density of states found from a Keldysh effective field theory, we obtain in the whole energy range the universal differential conductance and analytically demonstrate its Fermiliquid and logarithmic behavior at low and high energies, respectively, as a function of the magnetic field. We also show results on the zerotemperature differential conductance as a function of the bias voltage at different magnetic fields as well as results on finitetemperature effects out of equilibrium and at a finite magnetic field. The modern nonequilibrium experimental issues of the critical magnetic field, at which the zero bias maximum of the differential conductance starts to split into two maxima, as well as the distance between these maxima as a function of the magnetic field, are also addressed.
Quantum field theory and gravity in causal sets
NASA Astrophysics Data System (ADS)
Sverdlov, Roman M.
Causal set is a model of space time that allows to reconcile discreteness and manifest relativistic invariance. This is done by viewing space time as finite, partially ordered set. The elements of the set are viewed as points of space time, or events; the partial ordering between them is viewed as causal relations. It has been shown that, in discrete scenario, the information about causal relations between events can, indeed, approximate the metric. The goal of this thesis is to introduce matter fields and their Lagrangians into causal set context. This is a two step process. The first step is to redefine gauge fields, gravity, and distances in such a way that no reference to Lorentz index is made. This is done by defining gauge fields as twopoint real valued functions, and gravitational field as causal structure itself. Once the above is done, Lagrangians have to be defined in a way that they don't refer to Lorentzian indices either. This is done by introducing a notion of type 1 and type 2 Lagrangian generators, coupled with respective machinery that "translates" each generator into corresponding Lagrangian. The fields that are subject to these generators are, respectively, defined as type 1 and type 2. The main difference between two kinds of fields is the prediction of different behavior in different dimensions of type 2 fields. However, despite our inability to travel to different dimensions, gravity was shown to be type 2 based on the erroneous predictions of its 4dimensional behavior if it was viewed as type 1. However, no erroneous predictions are made if nongravitational fields are viewed as either type 1 or type 2, thus the nature of the latter is still an open question. Finally, an attempt was made to provide interpretation of quantum mechanics that would allow to limit fluctuations of causal structure to allow some topological background. However, due to its controversial nature, it is placed in the Appendix.
Finite temperature quantum embedding theories for correlated systems
NASA Astrophysics Data System (ADS)
Zgid, Dominika; Gull, Emanuel
20170201
The cost of the exact solution of the manyelectron problem is believed to be exponential in the number of degrees of freedom, necessitating approximations that are controlled and accurate but numerically tractable. In this paper, we show that one of these approximations, the selfenergy embedding theory (SEET), is derivable from a universal functional and therefore implicitly satisfies conservation laws and thermodynamic consistency. We also show how other approximations, such as the dynamical mean field theory and its combinations with manybody perturbation theory, can be understood as a special case of SEET and discuss how the additional freedom present in SEET can be used to obtain systematic convergence of results.
FiniteTemperature Spin Dynamics in a Perturbed Quantum Critical Ising Chain with an E8 Symmetry
NASA Astrophysics Data System (ADS)
Wu, Jianda; Kormos, Márton; Si, Qimiao
20141201
A spectrum exhibiting E8 symmetry is expected to arise when a small longitudinal field is introduced in the transversefield Ising chain at its quantum critical point. Evidence for this spectrum has recently come from neutron scattering measurements in cobalt niobate, a quasionedimensional Ising ferromagnet. Unlike its zerotemperature counterpart, the finitetemperature dynamics of the model has not yet been determined. We study the dynamical spin structure factor of the model at low frequencies and nonzero temperatures, using the form factor method. Its frequency dependence is singular, but differs from the diffusion form. The temperature dependence of the nuclear magnetic resonance (NMR) relaxation rate has an activated form, whose prefactor we also determine. We propose NMR experiments as a means to further test the applicability of the E8 description for CoNb2O6 .
An iterative finite difference method for solving the quantum hydrodynamic equations of motion
Kendrick, Brian K
20100101
The quantum hydrodynamic equations of motion associated with the de BroglieBohm description of quantum mechanics describe a time evolving probability density whose 'fluid' elements evolve as a correlated ensemble of particle trajectories. These equations are intuitively appealing due to their similarities with classical fluid dynamics and the appearance of a generalized Newton's equation of motion in which the total force contains both a classical and quantum contribution. However, the direct numerical solution of the quantum hydrodynamic equations (QHE) is fraught with challenges: the probability 'fluid' is highlycompressible, it has zero viscosity, the quantum potential ('pressure') is nonlinear, and if that weren't enough the quantum potential can also become singular during the course of the calculations. Collectively these properties are responsible for the notorious numerical instabilities associated with a direct numerical solution of the QHE. The most successful and stable numerical approach that has been used to date is based on the Moving Least Squares (MLS) algorithm. The improved stability of this approach is due to the repeated local least squares fitting which effectively filters or reduces the numerical noise which tends to accumulate with time. However, this method is also subject to instabilities if it is pushed too hard. In addition, the stability of the MLS approach often comes at the expense of reduced resolution or fidelity of the calculation (i.e., the MLS filtering eliminates the higherfrequency components of the solution which may be of interest). Recently, a promising new solution method has been developed which is based on an iterative solution of the QHE using finite differences. This method (referred to as the Iterative Finite Difference Method or IFDM) is straightforward to implement, computationally efficient, stable, and its accuracy and convergence properties are well understood. A brief overview of the IFDM will be presented
Quantum Field Theory in Condensed Matter Physics
NASA Astrophysics Data System (ADS)
Tsvelik, Alexei M.
20070101
Preface; Acknowledgements; Part I. Introduction to Methods: 1. QFT: language and goals; 2. Connection between quantum and classical: path integrals; 3. Definitions of correlation functions: Wick's theorem; 4. Free bosonic field in an external field; 5. Perturbation theory: Feynman diagrams; 6. Calculation methods for diagram series: divergences and their elimination; 7. Renormalization group procedures; 8. O(N)symmetric vector model below the transition point; 9. Nonlinear sigma models in two dimensions: renormalization group and 1/Nexpansion; 10. O(3) nonlinear sigma model in the strong coupling limit; Part II. Fermions: 11. Path integral and Wick's theorem for fermions; 12. Interaction electrons: the Fermi liquid; 13. Electrodynamics in metals; 14. Relativistic fermions: aspects of quantum electrodynamics; 15. AharonovBohm effect and transmutation of statistics; Part III. Strongly Fluctuating Spin Systems: Introduction; 16. SchwingerWigner quantization procedure: nonlinear sigma models; 17. O(3) nonlinear sigma model in (2+1) dimensions: the phase diagram; 18. Order from disorder; 19. JordanWigner transformations for spin S=1/2 models in D=1, 2, 3; 20. Majorana representation for spin S=1/2 magnets: relationship to Z2 lattice gauge theories; 21. Path integral representations for a doped antiferromagnet; Part IV. Physics in the World of One Spatial Dimension: Introduction; 22. Model of the free bosonic massless scalar field; 23. Relevant and irrelevant fields; 24. KosterlitzThouless transition; 25. Conformal symmetry; 26. Virasoro algebra; 27. Differential equations for the correlation functions; 28. Ising model; 29. Onedimensional spinless fermions: TomonagaLuttinger liquid; 30. Onedimensional fermions with spin: spincharge separation; 31. KacMoody algebras: WessZuminoNovikovWitten model; 32. WessZuminoNovikovWitten model in the Lagrangian form: nonAbelian bosonization; 33. Semiclassical approach to WessZuminoNovikovWitten models; 34
Magneticfield dependence of the impurity states in a domeshaped quantum dot
NASA Astrophysics Data System (ADS)
Niculescu, E. C.; Stan, C.; Cristea, M.; Truscă, C.
20170801
Using the finite element method, the effect of magnetic fields on the donor states and transition energies in a InAs/GaAs quantum dot coupled to its wetting layers is investigated. Results are obtained for different impurity locations. We found that the diamagnetic shift of the ground state energy increases monotonously with the applied field and can be described by a simple function which interpolates between the low and high magneticfield behavior. Frequencies associated to the transitions between the Slike ground state and P (P+) excited states range in terahertz region and show a magnetic fieldinduced red (blue) shift, irrespectively of the impurity position.
Quantum corrections to the cosmological evolution of conformally coupled fields
Cembranos, Jose A.R.; Olive, Keith A.; Peloso, Marco; Uzan, JeanPhilippe Email: olive@physics.umn.edu Email: uzan@iap.fr
20090701
Because the source term for the equations of motion of a conformally coupled scalar field, such as the dilaton, is given by the trace of the matter energy momentum tensor, it is commonly assumed to vanish during the radiation dominated epoch in the early universe. As a consequence, such fields are generally frozen in the early universe. Here we compute the finite temperature radiative correction to the source term and discuss its consequences on the evolution of such fields in the early universe. We discuss in particular, the case of scalar tensor theories of gravity which have general relativity as an attractor solution. We show that, in some cases, the universe can experience an early phase of contraction, followed by a nonsingular bounce, and standard expansion. This can have interesting consequences for the abundance of thermal relics; for instance, it can provide a solution to the gravitino problem. We conclude by discussing the possible consequences of the quantum corrections to the evolution of the dilaton.
Studies on Quantum Field Theory and Statistical Mechanics
NASA Astrophysics Data System (ADS)
Zhang, Shoucheng
This dissertation is a summary of research in various areas of theoretical physics and is divided into three parts. In the first part, quantum fluctuations of the recently proposed superconducting cosmic strings are studied. It is found that vortices on the string world sheet represent an important class of fluctuation modes which tend to disorder the system. Both heuristic arguments and detailed renormalization group analysis reveal that these vortices do not appear in bound pairs but rather form a gas of free vortices. Based on this observation we argue that this fluctuation mode violates the topological conservation law on which superconductivity is based. Anomalies and topological aspects of supersymmetric quantum field theories are studied in the second part of this dissertation. Using the superspace formulation of the N = 1 spinning string, we obtain a path integral measure which is free from the worldsheet general coordinate as well as the supersymmetry anomalies and therefore determine the conformal anomaly and critical dimension of the spinning string. We also apply Fujikawa's formalism to computer the chiral anomaly in conformal as well as ordinary supergravity. Finally, we given a Noethermethod construction of the supersymmetrized ChernSimons term in five dimensional supergravity. In the last part of this dissertation, the soliton excitations in the quarterfilled PeierlsHubbard model are investigated in both the large and the small U limit. For a strictly one dimensional system at zero temperature, we find that solitons in both limits are in onetoone correspondence, while in the presence of weak three dimensional couplings or at finite temperature, the large U systems differ qualitatively from the small U systems in that the spin associated with the solitons ceases to be a sharp quantum observable.
Protected gates for topological quantum field theories
NASA Astrophysics Data System (ADS)
Beverland, Michael E.; Buerschaper, Oliver; Koenig, Robert; Pastawski, Fernando; Preskill, John; Sijher, Sumit
20160201
We study restrictions on localitypreserving unitary logical gates for topological quantum codes in two spatial dimensions. A localitypreserving operation is one which maps local operators to local operators — for example, a constantdepth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically local boundedstrength Hamiltonian. Localitypreserving logical gates of topological codes are intrinsically fault tolerant because spatially localized errors remain localized, and hence sufficiently dilute errors remain correctable. By invoking general properties of twodimensional topological field theories, we find that the localitypreserving logical gates are severely limited for codes which admit nonabelian anyons, in particular, there are no localitypreserving logical gates on the torus or the sphere with M punctures if the braiding of anyons is computationally universal. Furthermore, for Ising anyons on the Mpunctured sphere, localitypreserving gates must be elements of the logical Pauli group. We derive these results by relating logical gates of a topological code to automorphisms of the Verlinde algebra of the corresponding anyon model, and by requiring the logical gates to be compatible with basis changes in the logical Hilbert space arising from local Fmoves and the mapping class group.
Protected gates for topological quantum field theories
Beverland, Michael E.; Pastawski, Fernando; Preskill, John; Buerschaper, Oliver; Koenig, Robert; Sijher, Sumit
20160215
We study restrictions on localitypreserving unitary logical gates for topological quantum codes in two spatial dimensions. A localitypreserving operation is one which maps local operators to local operators — for example, a constantdepth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically local boundedstrength Hamiltonian. Localitypreserving logical gates of topological codes are intrinsically fault tolerant because spatially localized errors remain localized, and hence sufficiently dilute errors remain correctable. By invoking general properties of twodimensional topological field theories, we find that the localitypreserving logical gates are severely limited for codes which admit nonabelian anyons, in particular, there are no localitypreserving logical gates on the torus or the sphere with M punctures if the braiding of anyons is computationally universal. Furthermore, for Ising anyons on the Mpunctured sphere, localitypreserving gates must be elements of the logical Pauli group. We derive these results by relating logical gates of a topological code to automorphisms of the Verlinde algebra of the corresponding anyon model, and by requiring the logical gates to be compatible with basis changes in the logical Hilbert space arising from local Fmoves and the mapping class group.
The $\\hbar$ Expansion in Quantum Field Theory
Brodsky, Stanley J.; Hoyer, Paul; /Southern Denmark U., CP3Origins /Helsinki U. /Helsinki Inst. of Phys.
20101027
We show how expansions in powers of Planck's constant {h_bar} = h = 2{pi} can give new insights into perturbative and nonperturbative properties of quantum field theories. Since {h_bar} is a fundamental parameter, exact Lorentz invariance and gauge invariance are maintained at each order of the expansion. The physics of the {h_bar} expansion depends on the scheme; i.e., different expansions are obtained depending on which quantities (momenta, couplings and masses) are assumed to be independent of {h_bar}. We show that if the coupling and mass parameters appearing in the Lagrangian density are taken to be independent of {h_bar}, then each loop in perturbation theory brings a factor of {h_bar}. In the case of quantum electrodynamics, this scheme implies that the classical charge e, as well as the fine structure constant are linear in {h_bar}. The connection between the number of loops and factors of {h_bar} is more subtle for bound states since the binding energies and boundstate momenta themselves scale with {h_bar}. The {h_bar} expansion allows one to identify equaltime relativistic bound states in QED and QCD which are of lowest order in {h_bar} and transform dynamically under Lorentz boosts. The possibility to use retarded propagators at the Born level gives valencelike wavefunctions which implicitly describe the sea constituents of the bound states normally present in its Fock state representation.
Charge transfer in algebraic quantum field theory
NASA Astrophysics Data System (ADS)
Wright, Jill Dianne
We discuss aspects of the algebraic structure of quantum field theory. We take the view that the superselection structure of a theory should be determinable from the vacuum representation of the observable algebra, and physical properties of the charge. Hence one determines the nature of the charge transfer operations: the automorphisms of the observable algebra corresponding to the movement of charge along spacetime paths. New superselection sectors are obtained from the vacuum sector by an automorphism which is a limit of charge transfer operations along paths with an endpoint tending to spacelike infinity. Roberts has shown that for a gauge theory of the first kind, the charge transfer operations for a given charge form a certain kind of 1cocycle over Minkowski space. The local 1cohomology group of their equivalence classes corresponds to the superselection structure. The exact definition of the cohomology group depends on the properties of the charge. Using displaced Fock representations of free fields, we develop model field theories which illustrate this structure. The cohomological classification of displaced Fock representations has been elucidated by Araki. For more general representations, explicit determination of the cohomology group is a hard problem. Using our models, we can illustrate ways in which fields with reasonable physical properties depart fromthe abovementioned structure. In 1+1 dimensions, we use the StreaterWilde model to illustrate explicitly the representationdependence of the cohomology structure, and the directiondependence of the limiting charge transfer operation. The cohomology structure may also be representationdependent in higherdimensional theories without strict localization of charge, for example the electromagnetic field. The algebraic structure of the electromagnetic field has many other special features, which we discuss in relation to the concept of charge transfer. We also give some indication of the modifications
Quantumcorrelation breaking channels, broadcasting scenarios, and finite Markov chains
NASA Astrophysics Data System (ADS)
Korbicz, J. K.; Horodecki, P.; Horodecki, R.
20121001
One of the classical results concerning quantum channels is the characterization of entanglementbreaking channels [M. Horodecki, P. W. Shor, and M. B. Ruskai, Rev. Math. Phys.RMPHEX0129055X10.1142/S0129055X03001709 15, 629 (2003)]. We address the question whether there exists a similar characterization on the level of quantum correlations which may go beyond entanglement. The answer is fully affirmative in the case of breaking quantum correlations down to the, socalled, QC (quantumclassical) type, while it is no longer true in the CC (classicalclassical) case. The corresponding channels turn out to be measurement maps. Our study also reveals an unexpected link between quantum state and local correlation broadcasting and finite Markov chains. We present a possibility of broadcasting via non von Neumann measurements, which relies on the PerronFrobenius theorem. Surprisingly, this is not the typical generalized controllednot (cnot) gate scenario appearing naturally in this context.
Atomic beam deflection in a quantum field
Graham, L.A.; Bharucha, C.; Moore, F.L.
19930501
Atomic beam deflection in a quantum field is studied theoretically for the case of an atom passing through the mode of a resonant optical cavity. Deflection probability is calculated for a coupling rate g of order g/2{pi}=1 MHz, which is experimentally feasible in a short optical cavity. Atomic velocities are taken in the range of 110 m/s, which can be reached with current cooling and trapping techniques. We calculate deflection for a coherent state with mean photon number
NASA Astrophysics Data System (ADS)
Ramos, E.; Franco, R.; SilvaValencia, J.; Figueira, M. S.
20141101
We study thermoelectric transport properties through a gate defined Tcoupled quantum dot, describing the system at base with the single impurity Anderson model (SIAM), whose corresponding Green's functions are calculated employing the finite correlation U atomic approach. We compute, with the linear approximation for the thermoelectric transport coefficients, the electrical and thermal conductance (G and K), the thermopower S, the product of the thermoelectric figure of merit and the temperature ZT, for all the regimes of the SIAM: empty quantum dot, intermediate valence, Kondo, and double occupation, at different temperatures; the treatment employed extends the results obtained for the limit of infinite UCoulomb repulsion in the quantum dot, and has a manybody character, which is absent in Green's function descriptions that employ mean field approximations. Our main result connects the ZT behavior with the interplay between the thermopower and the violation of the WiedemannFranz relation; the results are in good agreement with other recent theoretical papers that employ the numerical renormalization group (NRG), different Green's function approximations, and some experimental reports.
Quantum field theory in spaces with closed timelike curves
NASA Astrophysics Data System (ADS)
Boulware, D. G.
Gott spacetime has closed timelike curves, but no locally anomalous stressenergy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 27(pi). A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, onshell, particles in the acausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the acausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.
Relativistic mean field models for finite nuclei and neutron stars
NASA Astrophysics Data System (ADS)
Chen, WeiChia
In this dissertation we have created theoretical models for finite nuclei, nuclear matter, and neutron stars within the framework of relativistic mean field (RMF) theory, and we have used these models to investigate the elusive isovector sector and related physics, in particular, the neutronskin thickness of heavy nuclei, the nuclear symmetry energy, and the properties of neutron stars. To build RMF models that incorporate collective excitations in finite nuclei in addition to their groundstate properties, we have extended the nonrelativistic sum rule approach to the relativistic domain. This allows an efficient estimate of giant monopole energies. Moreover, we have combined an exact shellmodellike approach with the meanfield calculation to describe pairing correlations in openshell nuclei. All the ingredients were then put together to establish the calibration scheme. We have also extended the transformation between model parameters and pseudo data of nuclear matter within the RMF context. Performing calibration in this pseudo data space can not only facilitate the searching algorithm but also make the pseudo data genuine model predictions. This calibration scheme is also supplemented by a covariance analysis enabling us to extract the information content of a model, including theoretical uncertainties and correlation coefficients. A series of RMF models subject to the same isoscalar constraints but one differing isovector assumption were then created using this calibration scheme. By comparing their predictions of the nuclear matter equation of state to both experimental and theoretical constraints, we found that a small neutron skin of about 0.16 fm in Pb208 is favored, indicating that the symmetry energy should be soft. To obtain stronger evidence, we proceeded to examine the evolution of the isotopic chains in both oxygen and calcium. Again, it was found that the model with such small neutron skin and soft symmetry energy can best describe both isotopic
Probing the quantum entanglement under finite temperature environment in nonineritial frames
NASA Astrophysics Data System (ADS)
Zhang, RenJie; Xu, Shuai; Song, XueKe; Shi, JiaDong; Ye, Liu
20140801
In this paper, we investigate the dynamics of quantum entanglement of a twoqubit quantum system coupled with generalized amplitude damping (GAD) channel of nonzero temperature in noninertial frames. The results show that the concurrence decreases with the increase of acceleration and channel parameter r has a decisive impact on the entanglement. Accidentally, we manifest the inequivalence of the quantization for a Dirac field under the GAD channel in the noninertial frames.
Group Field Theory and Loop Quantum Gravity
NASA Astrophysics Data System (ADS)
Oriti, Daniele
The following sections are included: * GFT from LQG Perspective: The Underlying Ideas * GFT Kinematics: Hilbert Space and Observables * The Quantum Dynamics * The Continuum Limit of Quantum Geometry in GFT * Extracting Effective Continuum Physics from GFTs * Conclusions * References
NASA Astrophysics Data System (ADS)
Beswick, Benjamin T.; Hughes, Ifan G.; Gardiner, Simon A.; Astier, Hippolyte P. A. G.; Andersen, Mikkel F.; Daszuta, Boris
20161201
Atom interferometers are a useful tool for precision measurements of fundamental physical phenomena, ranging from the local gravitationalfield strength to the atomic finestructure constant. In such experiments, it is desirable to implement a highmomentumtransfer "beam splitter," which may be achieved by inducing quantum resonance in a finitetemperature laserdriven atomic gas. We use Monte Carlo simulations to investigate these quantum resonances in the regime where the gas receives laser pulses of finite duration and derive an ɛ classical model for the dynamics of the gas atoms which is capable of reproducing quantum resonant behavior for both zerotemperature and finitetemperature noninteracting gases. We show that this model agrees well with the fully quantum treatment of the system over a time scale set by the choice of experimental parameters. We also show that this model is capable of correctly treating the timereversal mechanism necessary for implementing an interferometer with this physical configuration and that it explains an unexpected universality in the dynamics.
Quantum reduced loop gravity: Extension to gauge vector field
NASA Astrophysics Data System (ADS)
Bilski, Jakub; Alesci, Emanuele; Cianfrani, Francesco; Donà, Pietro; Marcianò, Antonino
20170501
Within the framework of quantum reduced loop gravity, we quantize the Hamiltonian for a gauge vector field. The regularization can be performed using tools analogous to the ones adopted in full loop quantum gravity, while the matrix elements of the resulting operator between basis states are analytic coefficients. This analysis is the first step toward deriving the full quantum gravity corrections to the vector field semiclassical dynamics.
Path Integral Monte Carlo finitetemperature electronic structure of quantum dots
NASA Astrophysics Data System (ADS)
Leino, Markku; Rantala, Tapio T.
20030301
Quantum Monte Carlo methods allow a straightforward procedure for evaluation of electronic structures with a proper treatment of electronic correlations. This can be done even at finite temperatures [1]. We apply the Path Integral Monte Carlo (PIMC) simulation method [2] for one and two electrons in a single and double quantum dots. With this approach we evaluate the electronic distributions and correlations, and finite temperature effects on those. Temperature increase broadens the oneelectron distribution as expected. This effect is smaller for correlated electrons than for single ones. The simulated one and two electron distributions of a single and two coupled quantum dots are also compared to those from experiments and other theoretical (0 K) methods [3]. Computational capacity is found to become the limiting factor in simulations with increasing accuracy. This and other essential aspects of PIMC and its capability in this type of calculations are also discussed. [1] R.P. Feynman: Statistical Mechanics, Addison Wesley, 1972. [2] D.M. Ceperley, Rev.Mod.Phys. 67, 279 (1995). [3] M. Pi, A. Emperador and M. Barranco, Phys.Rev.B 63, 115316 (2001).
Dirac's equation and the nature of quantum field theory
NASA Astrophysics Data System (ADS)
Plotnitsky, Arkady
20121101
This paper reexamines the key aspects of Dirac's derivation of his relativistic equation for the electron in order advance our understanding of the nature of quantum field theory. Dirac's derivation, the paper argues, follows the key principles behind Heisenberg's discovery of quantum mechanics, which, the paper also argues, transformed the nature of both theoretical and experimental physics visàvis classical physics and relativity. However, the limit theory (a crucial consideration for both Dirac and Heisenberg) in the case of Dirac's theory was quantum mechanics, specifically, Schrödinger's equation, while in the case of quantum mechanics, in Heisenberg's version, the limit theory was classical mechanics. Dirac had to find a new equation, Dirac's equation, along with a new type of quantum variables, while Heisenberg, to find new theory, was able to use the equations of classical physics, applied to different, quantummechanical variables. In this respect, Dirac's task was more similar to that of Schrödinger in his work on his version of quantum mechanics. Dirac's equation reflects a more complex character of quantum electrodynamics or quantum field theory in general and of the corresponding (highenergy) experimental quantum physics visàvis that of quantum mechanics and the (lowenergy) experimental quantum physics. The final section examines this greater complexity and its implications for fundamental physics.
From scalar field theories to supersymmetric quantum mechanics
NASA Astrophysics Data System (ADS)
Bazeia, D.; Bemfica, F. S.
20170401
In this work, we report a new result that appears when one investigates the route that starts from a scalar field theory and ends on a supersymmetric quantum mechanics. The subject has been studied before in several distinct ways and here, we unveil an interesting novelty, showing that the same scalar field model may describe distinct quantum mechanical problems.
Quantum radiation produced by the entanglement of quantum fields
NASA Astrophysics Data System (ADS)
Iso, Satoshi; Oshita, Naritaka; Tatsukawa, Rumi; Yamamoto, Kazuhiro; Zhang, Sen
20170101
We investigate the quantum radiation produced by an UnruhDe Witt detector in a uniformly accelerating motion coupled to the vacuum fluctuations. Quantum radiation is nonvanishing, which is consistent with the previous calculation by Lin and Hu [Phys. Rev. D 73, 124018 (2006), 10.1103/PhysRevD.73.124018]. We infer that this quantum radiation from the UnruhDe Witt detector is generated by the nonlocal correlation of the Minkowski vacuum state, which has its origin in the entanglement of the state between the left and the right Rindler wedges.
Electric Field Screening by the Proximity of Two KnifeEdge Field Emitters of Finite Width
NASA Astrophysics Data System (ADS)
Wong, P.; Tang, W.; Lau, Y. Y.; Hoff, B.
20151101
Field emitter arrays have the potential to provide high current density, low voltage operation, and high pulse repetition for radar and communication. It is well known that packing density of the field emitter arrays significantly affect the emission current. Previously we calculated analytically the electric field profile of twodimensional knifeedge cathodes with arbitrary separation by using a SchwarzChristoffel transformation. Here we extend this previous work to include the finite width of two identical emitters. From the electric field profile, the field enhancement factor, thereby the severity of the electric field screening, are determined. It is found that for two identical emitters with finite width, the magnitude of the electric field on the knifeedge cathodes depends strongly on the ratio h / a and h / r , where h is the height of the knifeedge cathode, 2a is the distance between the cathodes, and 2 r represents their width. Particleincell simulations are performed to compare with the analytical results on the emission current distribution. P. Y. Wong was supported by a Directed Energy Summer Scholar internship at Air Force Research Laboratory, Kirtland AFB, and by AFRL Award No. FA94511410374.
Quantum time delay in the gravitational field of a rotating mass
NASA Astrophysics Data System (ADS)
Battista, Emmanuele; Tartaglia, Angelo; Esposito, Giampiero; Lucchesi, David; Ruggiero, Matteo Luca; Valko, Pavol; Dell'Agnello, Simone; Di Fiore, Luciano; Simo, Jules; Grado, Aniello
20170801
We examine quantum corrections of time delay arising in the gravitational field of a spinning oblate source. Lowenergy quantum effects occurring in Kerr geometry are derived within a framework where general relativity is fully seen as an effective field theory. By employing such a pattern, gravitational radiative modifications of Kerr metric are derived from the energymomentum tensor of the source, which at lowest order in the fields is modelled as a point mass. Therefore, in order to describe a quantum corrected version of time delay in the case in which the source body has a finite extension, we introduce a hybrid scheme where quantum fluctuations affect only the monopole term occurring in the multipole expansion of the Newtonian potential. The predicted quantum deviation from the corresponding classical value turns out to be too small to be detected in the next future, showing that new models should be examined in order to test lowenergy quantum gravity within the solar system.
The effective field theory treatment of quantum gravity
Donoghue, John F.
20120924
This is a pedagogical introduction to the treatment of quantum general relativity as an effective field theory. It starts with an overview of the methods of effective field theory and includes an explicit example. Quantum general relativity matches this framework and I discuss gravitational examples as well as the limits of the effective field theory. I also discuss the insights from effective field theory on the gravitational effects on running couplings in the perturbative regime.
Practical continuousvariable quantum key distribution without finite sampling bandwidth effects.
Li, Huasheng; Wang, Chao; Huang, Peng; Huang, Duan; Wang, Tao; Zeng, Guihua
20160905
In a practical continuousvariable quantum key distribution system, finite sampling bandwidth of the employed analogtodigital converter at the receiver's side may lead to inaccurate results of pulse peak sampling. Then, errors in the parameters estimation resulted. Subsequently, the system performance decreases and security loopholes are exposed to eavesdroppers. In this paper, we propose a novel data acquisition scheme which consists of two parts, i.e., a dynamic delay adjusting module and a statistical power feedbackcontrol algorithm. The proposed scheme may improve dramatically the data acquisition precision of pulse peak sampling and remove the finite sampling bandwidth effects. Moreover, the optimal peak sampling position of a pulse signal can be dynamically calibrated through monitoring the change of the statistical power of the sampled data in the proposed scheme. This helps to resist against some practical attacks, such as the wellknown local oscillator calibration attack.
Boche, H. Email: janis.noetzel@tum.de; Nötzel, J. Email: janis.noetzel@tum.de
20141215
This work is motivated by a quite general question: Under which circumstances are the capacities of information transmission systems continuous? The research is explicitly carried out on finite arbitrarily varying quantum channels (AVQCs). We give an explicit example that answers the recent question whether the transmission of messages over AVQCs can benefit from assistance by distribution of randomness between the legitimate sender and receiver in the affirmative. The specific class of channels introduced in that example is then extended to show that the unassisted capacity does have discontinuity points, while it is known that the randomnessassisted capacity is always continuous in the channel. We characterize the discontinuity points and prove that the unassisted capacity is always continuous around its positivity points. After having established shared randomness as an important resource, we quantify the interplay between the distribution of finite amounts of randomness between the legitimate sender and receiver, the (nonzero) probability of a decoding error with respect to the average error criterion and the number of messages that can be sent over a finite number of channel uses. We relate our results to the entanglement transmission capacities of finite AVQCs, where the role of shared randomness is not yet well understood, and give a new sufficient criterion for the entanglement transmission capacity with randomness assistance to vanish.
NASA Astrophysics Data System (ADS)
Boche, H.; Nötzel, J.
20141201
This work is motivated by a quite general question: Under which circumstances are the capacities of information transmission systems continuous? The research is explicitly carried out on finite arbitrarily varying quantum channels (AVQCs). We give an explicit example that answers the recent question whether the transmission of messages over AVQCs can benefit from assistance by distribution of randomness between the legitimate sender and receiver in the affirmative. The specific class of channels introduced in that example is then extended to show that the unassisted capacity does have discontinuity points, while it is known that the randomnessassisted capacity is always continuous in the channel. We characterize the discontinuity points and prove that the unassisted capacity is always continuous around its positivity points. After having established shared randomness as an important resource, we quantify the interplay between the distribution of finite amounts of randomness between the legitimate sender and receiver, the (nonzero) probability of a decoding error with respect to the average error criterion and the number of messages that can be sent over a finite number of channel uses. We relate our results to the entanglement transmission capacities of finite AVQCs, where the role of shared randomness is not yet well understood, and give a new sufficient criterion for the entanglement transmission capacity with randomness assistance to vanish.
Quantum Phase Transition in the Finite JaynesCummings Lattice Systems
NASA Astrophysics Data System (ADS)
Hwang, MyungJoong; Plenio, Martin B.
20160901
Phase transitions are commonly held to occur only in the thermodynamical limit of a large number of system components. Here, we exemplify at the hand of the exactly solvable JaynesCummings (JC) model and its generalization to finite JC lattices that finite component systems of coupled spins and bosons may exhibit quantum phase transitions (QPTs). For the JC model we find a continuous symmetrybreaking QPT, a photonic condensate with a macroscopic occupation as the ground state, and a Goldstone mode as a lowenergy excitation. For the two site JC lattice we show analytically that it undergoes a Mottinsulator to superfluid QPT. We identify as the underlying principle of the emergence of finite system QPTs the combination of increasing atomic energy and increasing interaction strength between the atom and the bosonic mode, which allows for the exploration of an increasingly large portion of the infinite dimensional Hilbert space of the bosonic mode. This suggests that finite system phase transitions will be present in a broad range of physical systems.
Biased decoystate measurementdeviceindependent quantum key distribution with finite resources
NASA Astrophysics Data System (ADS)
Zhou, Chun; Bao, WanSu; Zhang, Hailong; Li, HongWei; Wang, Yang; Li, Yuan; Wang, Xiang
20150201
Measurementdeviceindependent quantum key distribution (MDIQKD) can remove all the sidechannel attacks from imperfections in the detection side. However, finitesize resources undoubtedly influence its performance and the achievable finite secret key rates of MDIQKD are typically lower than that of standard decoystate QKD. In this paper, we introduce the efficient decoystate method with biased basis choice into the finitekey analysis and propose a decoystate protocol for MDIQKD. By applying vacuum + weak decoystate method, we analytically derive concise formulas for estimating the lower bound of singlephoton yield and the upper bound of phase error rate in the case of finite resources. The simulations show that proper basis choice combined with deliberate intensity choice can substantially enhance the performance of decoystate MDIQKD and, without a full optimization program, our protocol can bring a longdistance implementation (168 km on standard optical fiber) of MDIQKD with a reasonable data size of total transmitting signals (N =1015 ).
Quantumannealing correction at finite temperature: Ferromagnetic p spin models
NASA Astrophysics Data System (ADS)
Matsuura, Shunji; Nishimori, Hidetoshi; Vinci, Walter; Albash, Tameem; Lidar, Daniel A.
20170201
The performance of opensystem quantum annealing is adversely affected by thermal excitations out of the ground state. While the presence of energy gaps between the ground and excited states suppresses such excitations, error correction techniques are required to ensure full scalability of quantum annealing. Quantum annealing correction (QAC) is a method that aims to improve the performance of quantum annealers when control over only the problem (final) Hamiltonian is possible, along with decoding. Building on our earlier work [S. Matsuura et al., Phys. Rev. Lett. 116, 220501 (2016), 10.1103/PhysRevLett.116.220501], we study QAC using analytical tools of statistical physics by considering the effects of temperature and a transverse field on the penalty qubits in the ferromagnetic p body infiniterange transversefield Ising model. We analyze the effect of QAC on second (p =2 ) and first (p ≥3 ) order phase transitions, and construct the phase diagram as a function of temperature and penalty strength. Our analysis reveals that for sufficiently low temperatures and in the absence of a transverse field on the penalty qubit, QAC breaks up a single, large freeenergy barrier into multiple smaller ones. We find theoretical evidence for an optimal penalty strength in the case of a transverse field on the penalty qubit, a feature observed in QAC experiments. Our results provide further compelling evidence that QAC provides an advantage over unencoded quantum annealing.
Electricfield distribution in a quantum superlattice with an injecting contact: Exact solution
NASA Astrophysics Data System (ADS)
Maksimenko, V. A.; Makarov, V. V.; Koronovskii, A. A.; Hramov, A. E.; Venckevičius, R.; Valušis, G.; Balanov, A. G.; Kusmartsev, F. V.; Alekseev, K. N.
20160401
A very simple model describing steadystate electron transport along a quantum superlattice of a finite length taking into account an arbitrary electrical characteristic of the injecting contact is considered. In the singleminiband approximation, exact formulas for the spatial distribution of the electric field in the superlattice are derived for different types of contact. Conditions under which the field is uniform are identified. Analytical expressions for the currentvoltage characteristics are obtained. In the context of the developed theory, the possibility of attaining uniformfield conditions in a diode structure with a natural siliconcarbide superlattice is discussed.
Inglis, Stephen; Melko, Roger G
20130101
We implement a WangLandau sampling technique in quantum Monte Carlo (QMC) simulations for the purpose of calculating the Rényi entanglement entropies and associated mutual information. The algorithm converges an estimate for an analog to the density of states for stochastic series expansion QMC, allowing a direct calculation of Rényi entropies without explicit thermodynamic integration. We benchmark results for the mutual information on twodimensional (2D) isotropic and anisotropic Heisenberg models, a 2D transverse field Ising model, and a threedimensional Heisenberg model, confirming a critical scaling of the mutual information in cases with a finitetemperature transition. We discuss the benefits and limitations of broad sampling techniques compared to standard importance sampling methods.
NASA Astrophysics Data System (ADS)
Warehime, Mick; Alexander, Millard H.
20140701
We restate the application of the finite element method to collinear triatomic reactive scattering dynamics with a novel treatment of the scattering boundary conditions. The method provides directly the reactive scattering wave function and, subsequently, the probability current density field. Visualizing these quantities provides additional insight into the quantum dynamics of simple chemical reactions beyond simplistic onedimensional models. Application is made here to a symmetric reaction (H+H2), a heavylightlight reaction (F+H2), and a heavylightheavy reaction (F+HCl). To accompany this article, we have written a MATLAB code which is fast, simple enough to be accessible to a wide audience, as well as generally applicable to any problem that can be mapped onto a collinear atomdiatom reaction. The code and user's manual are available for download from http://www2.chem.umd.edu/groups/alexander/FEM.
Warehime, Mick; Alexander, Millard H.
20140714
We restate the application of the finite element method to collinear triatomic reactive scattering dynamics with a novel treatment of the scattering boundary conditions. The method provides directly the reactive scattering wave function and, subsequently, the probability current density field. Visualizing these quantities provides additional insight into the quantum dynamics of simple chemical reactions beyond simplistic onedimensional models. Application is made here to a symmetric reaction (H+H{sub 2}), a heavylightlight reaction (F+H{sub 2}), and a heavylightheavy reaction (F+HCl). To accompany this article, we have written a MATLAB code which is fast, simple enough to be accessible to a wide audience, as well as generally applicable to any problem that can be mapped onto a collinear atomdiatom reaction. The code and user's manual are available for download from http://www2.chem.umd.edu/groups/alexander/FEM.
Entanglement negativity in quantum field theory.
Calabrese, Pasquale; Cardy, John; Tonni, Erik
20120928
We develop a systematic method to extract the negativity in the ground state of a 1+1 dimensional relativistic quantum field theory, using a path integral formalism to construct the partial transpose ρ(A)(T(2) of the reduced density matrix of a subsystem [formula: see text], and introducing a replica approach to obtain its trace norm which gives the logarithmic negativity E=ln//ρ(A)(T(2))//. This is shown to reproduce standard results for a pure state. We then apply this method to conformal field theories, deriving the result E~(c/4)ln[ℓ(1)ℓ(2)/(ℓ(1)+ℓ(2))] for the case of two adjacent intervals of lengths ℓ(1), ℓ(2) in an infinite system, where c is the central charge. For two disjoint intervals it depends only on the harmonic ratio of the four end points and so is manifestly scale invariant. We check our findings against exact numerical results in the harmonic chain.
On the existence of finite amplitude, transverse Alfven waves in the interplanetary magnetic field
NASA Technical Reports Server (NTRS)
Sari, J. W.
19770101
Interplanetary magnetic field data from the Mariner 10 spacecraft were examined for evidence of small and finite amplitude transverse Alfven waves, general finite amplitude Alfven waves, and magnetosonic waves. No evidence for transverse Alfven waves was found. Instead, the field fluctuations were found to be dominated by the general finite amplitude Alfven wave. Such wave modes correspond to nonplanewave solutions of the nonlinear magnetohydrodynamic equations.
Nonadditive probabilities and quantum logic in finite quantum systems
NASA Astrophysics Data System (ADS)
Vourdas, A.
20150401
A quantum system Σ(d) with variables in Z(d) and with Hilbert space H(d), is considered. It is shown that the additivity relation of Kolmogorov probabilities, is not valid in the Birkhoffvon Neumann orthocomplemented modular lattice of subspaces L(d). A second lattice Λ(d) which is distributive and contains the subsystems of Σ(d) is also considered. It is shown that in this case also, the additivity relation of Kolmogorov probabilities is not valid. This suggests that a more general (than Kolmogorov) probability theory is needed, and here we adopt the DempsterShafer probability theory. In both of these lattices, there are sublattices which are Boolean algebras, and within these ‘islands’ quantum probabilities are additive.
Quantum phase slips in the presence of finiterange disorder.
Khlebnikov, Sergei; Pryadko, Leonid P
20050902
To study the effect of disorder on quantum phase slips (QPSs) in superconducting wires, we consider the plasmononly model where disorder can be incorporated into a firstprinciples instanton calculation. We consider weak but general finiterange disorder and compute the form factor in the QPS rate associated with momentum transfer. We find that the system maps onto dissipative quantum mechanics, with the dissipative coefficient controlled by the wave (plasmon) impedance Z of the wire and with a superconductorinsulator transition at Z = 6.5 k. We speculate that the system will remain in this universality class after resistive effects at the QPS core are taken into account.
NASA Astrophysics Data System (ADS)
Majka; Staszel, P.; Natowitz, J. B.; Cibor, J.; Hagel, K.; Li, J.; Mdeiwayeh, N.; Wada, R.; Zhao, Y.
19961001
Quantum statistical thermodynamics has been used to calculate the number of available states and their occupation for fermions and bosons at temperature, T_in, of finite nuclear sytems. An apparent temperature of these systems, T_app, has been calculated from double yield ratios of two isotope pairs. The importance of employing the quantum statistics when high densities and/or low temperatures are involved is shown. However, at high temperatures and low densities, the system behaves as a MaxwellBoltzmann gas. Sequental decays of fragments from excited states influence the double yield ratio observable, causing problems with the temperature extraction. The model has been applied to study the high temperature branch of the "caloric curve".
Modeling Finite Faults Using the Adjoint Wave Field
NASA Astrophysics Data System (ADS)
Hjörleifsdóttir, V.; Liu, Q.; Tromp, J.
20041201
Timereversal acoustics, a technique in which an acoustic signal is recorded by an array of transducers, timereversed, and retransmitted, is used, e.g., in medical therapy to locate and destroy gallstones (for a review see Fink, 1997). As discussed by Tromp et al. (2004), timereversal techniques for locating sources are closely linked to socalled `adjoint methods' (Talagrand and Courtier, 1987), which may be used to evaluate the gradient of a misfit function. Tromp et al. (2004) illustrate how a (finite) source inversion may be implemented based upon the adjoint wave field by writing the change in the misfit function, δ χ, due to a change in the momentdensity tensor, δ m, as an integral of the adjoint strain field ɛ x,t) over the fault plane Σ : δ χ = ∫ 0T∫_Σ ɛ x,Tt) :δ m(x,t) d2xdt. We find that if the real fault plane is located at a distance δ h in the direction of the fault normal hat n, then to first order an additional factor of ∫ 0T∫_Σ δ h (x) ∂ n ɛ x,Tt):m(x,t) d2xdt is added to the change in the misfit function. The adjoint strain is computed by using the timereversed difference between data and synthetics recorded at all receivers as simultaneous sources and recording the resulting strain on the fault plane. In accordance with timereversal acoustics, all the resulting waves will constructively interfere at the position of the original source in space and time. The level of convergence will be deterimined by factors such as the sourcereceiver geometry, the frequency of the recorded data and synthetics, and the accuracy of the velocity structure used when back propagating the wave field. The terms ɛ x,Tt) and ∂ n ɛ x,Tt):m(x,t) can be viewed as sensitivity kernels for the moment density and the faultplane location respectively. By looking at these quantities we can make an educated choice of fault parametrization given the data in hand. The process can then be repeated to invert for the best source model, as
Li, S; Yang, Q X; Smith, M B
19940101
Twodimensional (2D) finite element analysis has been used to solve the full set of Maxwell's equations for the 2D magnetic field of radiofrequency (RF) coils. The field histogram method has been applied to evaluate and optimize the magnetic field homogeneity of some commonly used RF coils: the saddle coil, the slotted tube resonator, the multiple elements coil and the birdcage resonator, as well as the radial plate coil. Each coil model represents a crosssection of an infinitely long cylinder. The optimum configuration of each of these five RF coils is suggested. It was found that field homogeneity is more strongly dependent on the coil's window angle than on any other parameter. Additionally, eddy currents in the coil's conductive elements distort the current and magnetic field distribution. The frequency dependence of this eddy current distortion is analyzed and discussed.
Finitetemperature electron correlations in the framework of a dynamic localfield correction
Schweng, H.K.; Boehm, H.M. )
19930715
The quantummechanical version of the SingwiTosiLandSjoelander (STLS) approximation is applied to finite temperatures. This approximation has two main advantages. First, it includes a dynamic localfield correction and second, it gives positive values for the pairdistribution function in the shortrange region at zero temperature. This is even valid for rather low densities. After a description of the numerical difficulties arising with the use of a dynamic approximation, the results for the staticstructure factor and the pairdistribution function are discussed thoroughly. Detailed work is performed on the static part of the localfield correction, with special emphasis put on the investigation of its structure. A peak is found at a wave vector [ital q][approx]2.8 (in units of the Fermi wave vector) for small temperatures, which tends towards higher values of [ital q] with increasing temperature. This peak causes an attractive particlehole interaction in a certain [ital q] region and thus gives rise to the appearance of a chargedensity wave. A parametric description is given for the static localfield correction in order to simplify further applications. Furthermore, the exchangeandcorrelation free energy is considered. The results are compared with the STLS results and with the modified convolution approach.
Relativistic Quantum Mechanics and Introduction to Field Theory
NASA Astrophysics Data System (ADS)
Yndurain, Francisco J.
This is an advanced textbook meant as a primer in quantum theory for graduate students. A full relativistic treatment of particle dynamics needs to be based on quantum field theory. However, there exists a variety of processes that can be discussed with concepts like potentials, classical current distributions, prescribed external fields dealt with in the framework of relativistic quantum mechanics. Then, in an introduction to field theory the author emphasizes the deduction of the said potentials or currents. The unique feature of this book is the modern presentation of the subject together with many exercises and furthermore the underlying concept to combine a reference book on relativistic quantum mechanics with an introduction into quantum field theory.
NASA Astrophysics Data System (ADS)
Dai, YanWei; Shi, QianQian; Cho, Sam Young; Batchelor, Murray T.; Zhou, HuanQiang
20170601
The finitetemperature phase diagram is obtained for an infinite honeycomb lattice with spin1 /2 Ising interaction J by using thermalstate fidelity and the von Neumann entropy based on the infinite projected entangled pair state algorithm with ancillas. The tensor network representation of the fidelity, which is defined as an overlap measurement between two thermal states, is presented for thermal states on the honeycomb lattice. We show that the fidelity per lattice site and the von Neumann entropy can capture the phase transition temperatures for an applied magnetic field, consistent with the transition temperatures obtained via the transverse magnetizations, which indicates that a continuous phase transition occurs in the system. In the temperaturemagnetic field plane, the phase boundary for finite temperature is found to be well approximated by the functional form (kBTc) 2+hc2/2 =a J2 with a single numerical fitting coefficient a =2.298 (7 ) , where Tc and hc are the critical temperature and field with Boltzmann constant kB. The critical temperature in the absence of magnetic field is estimated as kBTc/J =√{a }≃1.516 (2 ) , compared with the exact result kBTc/J =1.51865 ⋯ . For the quantum state at zero temperature, this phase boundary function gives the critical field estimate hc/J =√{2 a }≃2.144 (3 ) , compared to the known value hc/J =2.13250 (4 ) calculated from a cluster Monte Carlo approach.
Quantum Gravity Effects in Scalar, Vector and Tensor Field Propagation
NASA Astrophysics Data System (ADS)
Dutta, Anindita
Quantum theory of gravity deals with the physics of the gravitational field at Planck length scale (1035 m). Even though it is experimentally hard to reach the Planck length scale, on can look for evidence of quantum gravity that is detectable in astrophysics. In this thesis, we try to find effects of loop quantum gravity corrections on observable phenomena. We show that the quantum fluctuation strain for LIGO data would be 10 125 on the Earth. Th correction is, however, substantial near the black hole horizon. We discuss the effect of this for scalar field propagation followed by vector and tensor fields. For the scalar field, the correction introduces a new asymmetry; for the vector field, we found a new perturbation solution and for the tensor field, we found the corrected Einstein equations which are yet to solve. These will affect phenomena like Hawking radiation, black hole entropy and gravitational waves.
NASA Technical Reports Server (NTRS)
Ransom, Jonathan B.
20020101
A multifunctional interface method with capabilities for variablefidelity modeling and multiple method analysis is presented. The methodology provides an effective capability by which domains with diverse idealizations can be modeled independently to exploit the advantages of one approach over another. The multifunctional method is used to couple independently discretized subdomains, and it is used to couple the finite element and the finite difference methods. The method is based on a weighted residual variational method and is presented for twodimensional scalarfield problems. A verification test problem and a benchmark application are presented, and the computational implications are discussed.
Quantum analysis applied to thermo field dynamics on dissipative systems
Hashizume, Yoichiro; Okamura, Soichiro; Suzuki, Masuo
20150310
Thermo field dynamics is one of formulations useful to treat statistical mechanics in the scheme of field theory. In the present study, we discuss dissipative thermo field dynamics of quantum damped harmonic oscillators. To treat the effective renormalization of quantum dissipation, we use the SuzukiTakano approximation. Finally, we derive a dissipative von Neumann equation in the Lindbrad form. In the present treatment, we can easily obtain the initial damping shown previously by Kubo.
Quantum states of neutrons in the Earth's gravitational field.
Nesvizhevsky, Valery V; Börner, Hans G; Petukhov, Alexander K; Abele, Hartmut; Baessler, Stefan; Ruess, Frank J; Stöferle, Thilo; Westphal, Alexander; Gagarski, Alexei M; Petrov, Guennady A; Strelkov, Alexander V
20020117
The discrete quantum properties of matter are manifest in a variety of phenomena. Any particle that is trapped in a sufficiently deep and wide potential well is settled in quantum bound states. For example, the existence of quantum states of electrons in an electromagnetic field is responsible for the structure of atoms, and quantum states of nucleons in a strong nuclear field give rise to the structure of atomic nuclei. In an analogous way, the gravitational field should lead to the formation of quantum states. But the gravitational force is extremely weak compared to the electromagnetic and nuclear force, so the observation of quantum states of matter in a gravitational field is extremely challenging. Because of their charge neutrality and long lifetime, neutrons are promising candidates with which to observe such an effect. Here we report experimental evidence for gravitational quantum bound states of neutrons. The particles are allowed to fall towards a horizontal mirror which, together with the Earth's gravitational field, provides the necessary confining potential well. Under such conditions, the falling neutrons do not move continuously along the vertical direction, but rather jump from one height to another, as predicted by quantum theory.
Spacetime resolved quantum field theory
NASA Astrophysics Data System (ADS)
Grobe, R.
20091101
We have solved simplified model versions of the timedependent Dirac and Yukawa equation numerically to study the time evolution of electrons, positrons and photons with full spatial resolution. The goal is to better understand how various particle creation and annihilation processes that require quantum field theory can be visualized. There are many open ended questions that we will address. Are particles and their antimatter companions created instantly, or do they require a certain minimum amount of time? Are they created at precisely the same location? What is the difference between a bare and a physical particle? Forces between two particles are usually understood on a microscopic level as the result of an exchange of bosonic particles. How can the same microscopic exchange mechanism lead to a repulsion as well as an attraction? Do these force intermediating particles ``know'' about the charges of the two interacting particles? How can one visualize this exchange? Does it really make sense to distinguish between virtual and real particles? We also examine how a bare electron can trigger the creation of a cloud of virtual photons around it.[4pt] In collaboration with R. Wagner, Intense Laser Physics Theory Unit, Illinois State University; C. Gerry, Lehman College and ILPISU; T. Cheng and Q. Su, Intense Laser Physics Theory Unit, Illinois State University.
Quantum field theory constrains traversable wormhole geometries
Ford, L.H. ; Roman, T.A. 
19960501
Recently a bound on negative energy densities in fourdimensional Minkowski spacetime was derived for a minimally coupled, quantized, massless, scalar field in an arbitrary quantum state. The bound has the form of an uncertaintyprincipletype constraint on the magnitude and duration of the negative energy density seen by a timelike geodesic observer. When spacetime is curved and/or has boundaries, we argue that the bound should hold in regions small compared to the minimum local characteristic radius of curvature or the distance to any boundaries, since spacetime can be considered approximately Minkowski on these scales. We apply the bound to the stressenergy of static traversable wormhole spacetimes. Our analysis implies that either the wormhole must be only a little larger than Planck size or that there is a large discrepancy in the length scales which characterize the wormhole. In the latter case, the negative energy must typically be concentrated in a thin band many orders of magnitude smaller than the throat size. These results would seem to make the existence of macroscopic traversable wormholes very improbable. {copyright} {ital 1996 The American Physical Society.}
NASA Astrophysics Data System (ADS)
Krönke, Sven; Knörzer, Johannes; Schmelcher, Peter
20150501
We explore the correlated quantum dynamics of a single atom, regarded as an open system, with a spatiotemporally localized coupling to a finite bosonic environment. The single atom, initially prepared in a coherent state of low energy, oscillates in a onedimensional harmonic trap and thereby periodically penetrates an interacting ensemble of NA bosons held in a displaced trap. We show that the interspecies energy transfer accelerates with increasing NA and becomes less complete at the same time. Systemenvironment correlations prove to be significant except for times when the excess energy distribution among the subsystems is highly imbalanced. These correlations result in incoherent energy transfer processes, which accelerate the early energy donation of the single atom and stochastically favour certain energy transfer channels, depending on the instantaneous direction of transfer. Concerning the subsystem states, the energy transfer is mediated by noncoherent states of the single atom and manifests itself in singlet and doublet excitations in the finite bosonic environment. These comprehensive insights into the nonequilibrium quantum dynamics of an open system are gained by ab initio simulations of the total system with the recently developed multilayer multiconfiguration timedependent Hartree method for bosons.
An implementation problem for boson fields and quantum Girsanov transform
Ji, Un Cig; Obata, Nobuaki
20160815
We study an implementation problem for quadratic functions of annihilation and creation operators on a boson field in terms of quantum white noise calculus. The implementation problem is shown to be equivalent to a linear differential equation for white noise operators containing quantum white noise derivatives. The solution is explicitly obtained and turns out to form a class of white noise operators including generalized Fourier–Gauss and Fourier–Mehler transforms, Bogoliubov transform, and a quantum extension of the Girsanov transform.
Euclidean quantum field theory: Curved spacetimes and gauge fields
NASA Astrophysics Data System (ADS)
Ritter, William Gordon
This thesis presents a new formulation of quantum field theory (QFT) on curved spacetimes, with definite advantages over previous formulations, and an introduction to the millennium prize problem on fourdimensional gauge theory. Our constructions are completely rigorous, making QFT on curved spacetimes into a subfield of mathematics, and we achieve the first analytic control over nonperturbative aspects of interacting theories on curved spacetimes. The success of Euclidean path integrals to capture nonperturbative aspects of QFT has been striking. The Euclidean path integral is the most accurate method of calculating strongcoupling effects in gauge theory (such as glueball masses). Euclidean methods are also useful in the study of black holes, as evidenced by the HartleHawking calculation of blackhole radiance. From a mathematical point of view, on flat spacetimes the Euclidean functional integral provides the most elegant method of constructing examples of interacting relativistic field theories. Yet until now, the incrediblyuseful Euclidean path integral had never been given a definitive mathematical treatment on curved backgrounds. It is our aim to rectify this situation. Along the way, we discover that the Dirac operator on an arbitrary Clifford bundle has a resolvent kernel which is the Laplace transform of a positive measure. In studying spacetime symmetries, we discover a new way of constructing unitary representations of noncompact Lie groups. We also define and explore an interesting notion of convergence for Laplacians. The same mathematical framework applies to scalar fields, fermions, and gauge fields. The later chapters are devoted to gauge theory. We present a rigorous, selfcontained introduction to the subject, aimed at mathematicians and using the language of modern mathematics, with a view towards nonperturbative renormalization in four dimensions. The latter ideas are unfinished. A completion of the final chapter would imply the construction
Realization of vector fields for quantum groups as pseudodifferential operators on quantum spaces
Chu, ChongSun; Zumino, B.
19950124
The vector fields of the quantum Lie algebra are described for the quantum groups GL{sub q}(n), SL{sub q}(N) and SO{sub q}(N) as pseudodifferential operators on the linear quantum spaces covariant under the corresponding quantum group. Their expressions are simple and compact. It is pointed out that these vector fields satisfy certain characteristic polynomial identities. The real forms SU{sub q}(N) and SO{sub q}(N,R) are discussed in detail.
A VLSI architecture for performing finite field arithmetic with reduced table lookup
NASA Technical Reports Server (NTRS)
Hsu, I. S.; Truong, T. K.; Reed, I. S.
19860101
A new table lookup method for finding the log and antilog of finite field elements has been developed by N. Glover. In his method, the log and antilog of a field element is found by the use of several smaller tables. The method is based on a use of the Chinese Remainder Theorem. The technique often results in a significant reduction in the memory requirements of the problem. A VLSI architecture is developed for a special case of this new algorithm to perform finite field arithmetic including multiplication, division, and the finding of an inverse element in the finite field.
A VLSI architecture for performing finite field arithmetic with reduced table lookup
NASA Technical Reports Server (NTRS)
Hsu, I. S.; Truong, T. K.; Reed, I. S.
19860101
A new table lookup method for finding the log and antilog of finite field elements has been developed by N. Glover. In his method, the log and antilog of a field element is found by the use of several smaller tables. The method is based on a use of the Chinese Remainder Theorem. The technique often results in a significant reduction in the memory requirements of the problem. A VLSI architecture is developed for a special case of this new algorithm to perform finite field arithmetic including multiplication, division, and the finding of an inverse element in the finite field.
Constraints on RG flow for four dimensional quantum field theories
NASA Astrophysics Data System (ADS)
Jack, I.; Osborn, H.
20140601
The response of four dimensional quantum field theories to a Weyl rescaling of the metric in the presence of local couplings and which involve a, the coefficient of the Euler density in the energy momentum tensor trace on curved space, is reconsidered. Previous consistency conditions for the anomalous terms, which implicitly define a metric G on the space of couplings and give rise to gradient flow like equations for a, are derived taking into account the role of lower dimension operators. The results for infinitesimal Weyl rescaling are integrated to finite rescalings e2σ to a form which involves running couplings gσ and which interpolates between IR and UV fixed points. The results are also restricted to flat space where they give rise to broken conformal Ward identities. Expressions for the three loop Yukawa βfunctions for a general scalar/fermion theory are obtained and the three loop contribution to the metric G for this theory is also calculated. These results are used to check the gradient flow equations to higher order than previously. It is shown that these are only valid when β→B, a modified βfunction, and that the equations provide strong constraints on the detailed form of the three loop Yukawa βfunction. N=1 supersymmetric WessZumino theories are also considered as a special case. It is shown that the metric for the complex couplings in such theories may be restricted to a hermitian form.
Coupled field induced conversion between destructive and constructive quantum interference
NASA Astrophysics Data System (ADS)
Jiang, Xiangqian; Sun, Xiudong
20161201
We study the control of quantum interference in a fourlevel atom driven by three coherent fields forming a closed loop. The spontaneous emission spectrum shows two sets of peaks which are dramatically influenced by the fields. Due to destructive quantum interference, a dark line can be observed in the emission spectrum, and the condition of the dark line is given. We found that the conversion between destructive and constructive quantum interference can be achieved through controlling the Rabi frequency of the external fields.
Coupled field induced conversion between destructive and constructive quantum interference
Jiang, Xiangqian Sun, Xiudong
20161215
We study the control of quantum interference in a fourlevel atom driven by three coherent fields forming a closed loop. The spontaneous emission spectrum shows two sets of peaks which are dramatically influenced by the fields. Due to destructive quantum interference, a dark line can be observed in the emission spectrum, and the condition of the dark line is given. We found that the conversion between destructive and constructive quantum interference can be achieved through controlling the Rabi frequency of the external fields.
Tunnelling of the 3rd kind: A test of the effective nonlocality of quantum field theory
NASA Astrophysics Data System (ADS)
Gardiner, Simon A.; Gies, Holger; Jaeckel, Joerg; Wallace, Chris J.
20130301
Integrating out virtual quantum fluctuations in an originally local quantum field theory results in an effective theory which is nonlocal. In this letter we argue that tunnelling of the 3rd kind —where particles traverse a barrier by splitting into a pair of virtual particles which recombine only after a finite distance— provides a direct test of this nonlocality. We sketch a quantumoptical setup to test this effect, and investigate observable effects in a simple toy model.
NASA Astrophysics Data System (ADS)
Kawakami, Shun; Sasaki, Toshihiko; Koashi, Masato
20170701
An essential step in quantum key distribution is the estimation of parameters related to the leaked amount of information, which is usually done by sampling of the communication data. When the data size is finite, the final key rate depends on how the estimation process handles statistical fluctuations. Many of the present security analyses are based on the method with simple random sampling, where hypergeometric distribution or its known bounds are used for the estimation. Here we propose a concise method based on Bernoulli sampling, which is related to binomial distribution. Our method is suitable for the BennettBrassard 1984 (BB84) protocol with weak coherent pulses [C. H. Bennett and G. Brassard, Proceedings of the IEEE Conference on Computers, Systems and Signal Processing (IEEE, New York, 1984), Vol. 175], reducing the number of estimated parameters to achieve a higher key generation rate compared to the method with simple random sampling. We also apply the method to prove the security of the differentialquadraturephaseshift (DQPS) protocol in the finitekey regime. The result indicates that the advantage of the DQPS protocol over the phaseencoding BB84 protocol in terms of the key rate, which was previously confirmed in the asymptotic regime, persists in the finitekey regime.
Keyleakage evaluation of authentication in quantum key distribution with finite resources
NASA Astrophysics Data System (ADS)
Zhou, Chun; Bao, WanSu; Li, HongWei; Wang, Yang; Fu, XiangQun
20140401
Partial information leakages of generation key undoubtedly influence the security of practical Quantum Key Distribution (QKD) system. In this paper, based on finitekey analysis and deep investigation on privacy amplification, we present a method for characterizing information leakages gained by adversary in each authentication round and therefore take the theory derived by Cederlöf and Larsson (IEEE Trans Inf Theory 54:17351741, 2008) into practical case. As the authentication key is fed from one round of generation keys to the next except the first round, by considering its security weakness due to information leakages and finite size effect, we further propose a universal formula for calculating the lifetime of initial authentication key used in QKD with finite resources. Numerical simulations indicate that our bound for estimating information leakages strictly characterizes the stability of practical QKD against informationleakagebased attacks, and our calculation formula in terms of lifetime can precisely evaluate the usage time of initial authentication key. Our work provides a practical solution for evaluating authentication security of QKD.
Tight finitekey analysis of a practical decoystate quantum key distribution with unstable sources
NASA Astrophysics Data System (ADS)
Wang, Yang; Bao, WanSu; Zhou, Chun; Jiang, MuSheng; Li, HongWei
20160901
The decoystate quantum key distribution (QKD) protocol has been widely used in commercial QKD systems. Several QKD field networks show its practicability and commercial prospects. Importantly, practical decoystate QKD systems should be characterized with device imperfections. In this paper, for the case without intensity fluctuations, we present the parameter estimation based on the Chernoff bound for a practical decoystate QKD protocol and compare performances of that based on Hoeffding's inequality and the Chernoff bound, respectively. Taking intensity fluctuations into consideration, we present the finitekey analysis with composable security against general attacks based on Azuma's inequality. Our numerical results show that the finitekey analysis based on the Chernoff bound is tighter than Hoeffding's inequality when the total number of transmitting signals N <1 ×1012 . Moreover, the intensity fluctuations' influence is more obvious when the data size of total transmitting signals is small. Our results emphasize the importance of the stability of the intensity modulator as well as the accurate estimation of emitted pulse's intensity.
Femtosecond measurements of electric fields: from classical amplitudes to quantum fluctuations
NASA Astrophysics Data System (ADS)
Riek, Claudius; Seletskiy, Denis V.; Leitenstorfer, Alfred
20170301
Ultrabroadband electrooptic sampling is presented as an extremely sensitive technique to detect electric field amplitudes in free space. The temporal resolution provided by fewfemtosecond laser pulses results in a bandwidth exceeding 100 THz, potentially covering the entire infrared spectral range. A pedagogic introduction to the operational principle of the method is given along the lines of a classical coherent input field and a zincblendetype electrooptic sensor. We then show that even the bare vacuum fluctuations of the electric field in the quantum ground state may be detected. This timedomain approach to quantum physics operates directly on subcycle scales where no local energy conservation holds. Therefore, signals may be obtained from purely virtual photons without amplification to finite intensity.
Infinitetime average of local fields in an integrable quantum field theory after a quantum quench.
Mussardo, G
20130906
The infinitetime average of the expectation values of local fields of any interacting quantum theory after a global quench process are key quantities for matching theoretical and experimental results. For quantum integrable field theories, we show that they can be obtained by an ensemble average that employs a particular limit of the form factors of local fields and quantities extracted by the generalized Bethe ansatz.
NASA Astrophysics Data System (ADS)
Yuan, JianHui; Chen, Ni; Mo, Hua; Zhang, Yan; Zhang, ZhiHai
20151201
A detailed investigation of the second harmonic generation in symmetrical and asymmetrical Gaussian potential quantum wells under the influence of applied electric field by using the compactdensitymatrix approach and the finite difference method. The results show that the secondharmonic generation susceptibility obtained in two cases can reach the magnitude of 104 m/V, which depend dramatically on the applied electric field and the structural parameters. Finally, the resonant peak and its corresponding to the resonant energy are also taken into account.
NASA Astrophysics Data System (ADS)
Krönke, Sven; Knörzer, Johannes; Schmelcher, Peter
20150501
We explore the correlated quantum dynamics of a single atom with a spatiotemporally localized coupling to a finite bosonic ensemble [arXiv:1410.8676]. The single atom is initially prepared in a coherent state of low energy and oscillates in a harmonic trap. An ensemble of NA interacting bosons is held in a displaced trap such that it is periodically penetrated by the single atom. The nonequilibrium quantum dynamics of the total system is simulated by means of an abinitio method. Here, we focus on characterizing the impact of the peculiar interspecies coupling and the thereby induced interspecies correlations on the subsystem states: At instants of not too imbalanced excess energy distribution among the subsystems, interspecies correlations prove to be significant. A phasespace analysis for the single atom reveals that these correlations manifests themselves in short phases of strong deviations from a coherent state. In the bosonic ensemble, the single atom mainly induces singlet and delayed doublet excitations, for which we offer analytical insights with a stroboscopic timedependent perturbation theory approach. When increasing the ensemble size, its maximal dynamical quantum depletion is shown to decrease faster than 1 /NA for a fixed excess energy.
Family of finite geometry lowdensity paritycheck codes for quantum key expansion
NASA Astrophysics Data System (ADS)
Hsu, KungChuan; Brun, Todd A.
20130601
We consider a quantum key expansion (QKE) protocol based on entanglementassisted quantum errorcorrecting codes (EAQECCs). In these protocols, a seed of a previously shared secret key is used in the postprocessing stage of a standard quantum key distribution protocol like the BennettBrassard 1984 protocol, in order to produce a larger secret key. This protocol was proposed by Luo and Devetak, but codes leading to good performance have not been investigated. We look into a family of EAQECCs generated by classical finite geometry (FG) lowdensity paritycheck (LDPC) codes, for which very efficient iterative decoders exist. A critical observation is that almost all errors in the resulting secret key result from uncorrectable block errors that can be detected by an additional syndrome check and an additional sampling step. Bad blocks can then be discarded. We make some changes to the original protocol to avoid the consumption of the preshared key when the protocol fails. This allows us to greatly reduce the bit error rate of the key at the cost of a minor reduction in the key production rate, but without increasing the consumption rate of the preshared key. We present numerical simulations for the family of FG LDPC codes, and show that this improved QKE protocol has a good net key production rate even at relatively high error rates, for appropriate choices of these codes.
Finitesize key in the Bennett 1992 quantumkeydistribution protocol for Rényi entropies
NASA Astrophysics Data System (ADS)
Mafu, Mhlambululi; Garapo, Kevin; Petruccione, Francesco
20131201
A realistic quantumkeydistribution protocol necessarily runs with finite resources. Usually, security proofs for existing quantum key distribution are asymptotic in the sense that certain parameters are exceedingly large compared to practical realistic values. In this paper, we derive bounds on the secret key rates for the Bennett 1992 protocol, which includes a preprocessing step. The derivation for a finitesize key is expressed as an optimization problem by using results from the uncertainty relations and the smooth Rényi entropies.
The principle of stationary variance in quantum field theory
NASA Astrophysics Data System (ADS)
Siringo, Fabio
20140201
The principle of stationary variance is advocated as a viable variational approach to quantum field theory (QFT). The method is based on the principle that the variance of energy should be at its minimum when the state of a quantum system reaches its best approximation for an eigenstate. While not too much popular in quantum mechanics (QM), the method is shown to be valuable in QFT and three special examples are given in very different areas ranging from Heisenberg model of antiferromagnetism (AF) to quantum electrodynamics (QED) and gauge theories.
Avoiding Haag's Theorem with Parameterized Quantum Field Theory
NASA Astrophysics Data System (ADS)
Seidewitz, Ed
20170301
Under the normal assumptions of quantum field theory, Haag's theorem states that any field unitarily equivalent to a free field must itself be a free field. Unfortunately, the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field but must still account for interactions. Thus, the traditional perturbative derivation of the scattering matrix in quantum field theory is mathematically ill defined. Nevertheless, perturbative quantum field theory is currently the only practical approach for addressing scattering for realistic interactions, and it has been spectacularly successful in making empirical predictions. This paper explains this success by showing that Haag's Theorem can be avoided when quantum field theory is formulated using an invariant, fifth path parameter in addition to the usual four position parameters, such that the Dyson perturbation expansion for the scattering matrix can still be reproduced. As a result, the parameterized formalism provides a consistent foundation for the interpretation of quantum field theory as used in practice and, perhaps, for better dealing with other mathematical issues.
Quantum limits to mass sensing in a gravitational field
NASA Astrophysics Data System (ADS)
Seveso, Luigi; Peri, Valerio; Paris, Matteo G. A.
20170601
We address the problem of estimating the mass of a quantum particle in a gravitational field and seek the ultimate bounds to precision of quantumlimited detection schemes. In particular, we study the effect of the field on the achievable sensitivity and address the question of whether quantumness of the probe state may provide a precision enhancement. The ultimate bounds to precision are quantified in terms of the corresponding quantum Fisher information. Our results show that states with no classical limit perform better than semiclassical ones and that a nontrivial interplay exists between the external field and the statistical model. More intense fields generally lead to a better precision, with the exception of position measurements in the case of freelyfalling systems.
Advancements in the Field of Quantum Dots
NASA Astrophysics Data System (ADS)
Mishra, Sambeet; Tripathy, Pratyasha; Sinha, Swami Prasad.
20120801
Quantum dots are defined as very small semiconductor crystals of size varying from nanometer scale to a few micron i.e. so small that they are considered dimensionless and are capable of showing many chemical properties by virtue of which they tend to be lead at one minute and gold at the second minute.Quantum dots house the electrons just the way the electrons would have been present in an atom, by applying a voltage. And therefore they are very judiciously given the name of being called as the artificial atoms. This application of voltage may also lead to the modification of the chemical nature of the material anytime it is desired, resulting in lead at one minute to gold at the other minute. But this method is quite beyond our reach. A quantum dot is basically a semiconductor of very tiny size and this special phenomenon of quantum dot, causes the band of energies to change into discrete energy levels. Band gaps and the related energy depend on the relationship between the size of the crystal and the exciton radius. The height and energy between different energy levels varies inversely with the size of the quantum dot. The smaller the quantum dot, the higher is the energy possessed by it.There are many applications of the quantum dots e.g. they are very wisely applied to:Light emitting diodes: LEDs eg. White LEDs, Photovoltaic devices: solar cells, Memory elements, Biology : =biosensors, imaging, Lasers, Quantum computation, Flatpanel displays, Photodetectors, Life sciences and so on and so forth.The nanometer sized particles are able to display any chosen colour in the entire ultraviolet visible spectrum through a small change in their size or composition.
Optimal Use of Finite Land Resources. Field Test Version.
ERIC Educational Resources Information Center
Mills, Stephen R.; And Others
This module, a component of a larger teaching model, seeks to present several concepts to the teacher. It seeks to develop awareness and understanding of use of finite land resources including types of land use and abuse; stewardship of land resources; natural systems functioning; human system demands on the natural environment; carrying capacity;…
NASA Astrophysics Data System (ADS)
Khrennikov, Andrei
20170201
The scientific methodology based on two descriptive levels, ontic (reality as it is) and epistemic (observational), is briefly presented. Following Schrödinger, we point to the possible gap between these two descriptions. Our main aim is to show that, although ontic entities may be unaccessible for observations, they can be useful for clarification of the physical nature of operational epistemic entities. We illustrate this thesis by the concrete example: starting with the concrete ontic model preceding quantum mechanics (the latter is treated as an epistemic model), namely, prequantum classical statistical field theory (PCSFT), we propose the natural physical interpretation for the basic quantum mechanical entitythe quantum state ("wave function"). The correspondence PCSFT ↦ QM is not straightforward, it couples the covariance operators of classical (prequantum) random fields with the quantum density operators. We use this correspondence to clarify the physical meaning of the pure quantum state and the superposition principleby using the formalism of classical field correlations.
NASA Astrophysics Data System (ADS)
Elbaz, Edgard
This book gives a new insight into the interpretation of quantum mechanics (stochastic, integral paths, decoherence), a completely new treatment of angular momentum (graphical spin algebra) and an introduction to Fermion fields (Dirac equation) and Boson fields (e.m. and Higgs) as well as an introduction to QED (quantum electrodynamics), supersymmetry and quantum cosmology.
Dynamical properties of the sineGordon quantum spin magnet CuPM at zero and finite temperature
NASA Astrophysics Data System (ADS)
Tiegel, Alexander C.; Honecker, Andreas; Pruschke, Thomas; Ponomaryov, Alexey; Zvyagin, Sergei A.; Feyerherm, Ralf; Manmana, Salvatore R.
20160301
The material copper pyrimidine dinitrate (CuPM) is a quasionedimensional spin system described by the spin1/2 X X Z Heisenberg antiferromagnet with DzyaloshinskiiMoriya interactions. Based on numerical results obtained by the densitymatrix renormalization group, exact diagonalization, and accompanying electron spin resonance (ESR) experiments we revisit the spin dynamics of this compound in an applied magnetic field. Our calculations for momentum and frequencyresolved dynamical quantities give direct access to the intensity of the elementary excitations at both zero and finite temperature. This allows us to study the system beyond the lowenergy description by the quantum sineGordon model. We find a deviation from the Lorentz invariant dispersion for the singlesoliton resonance. Furthermore, our calculations only confirm the presence of the strongest boundary bound state previously derived from a boundary sineGordon field theory, while composite boundarybulk excitations have too low intensities to be observable. Upon increasing the temperature, we find a temperatureinduced crossover of the soliton and the emergence of new features, such as interbreather transitions. The latter observation is confirmed by our ESR experiments on CuPM over a wide range of the applied field.
Quantum magnetism in low dimensions and large magnetic fields
NASA Astrophysics Data System (ADS)
Giamarchi, Thierry
20140301
The ability to control the properties of magnetic insulators by magnetic fields large enough to fully polarize the system has opened a host of possibilities. In addition to the intrinsic interest of such questions for magnetic systems, is has been shown that such systems could be efficiently used as quantum simulators to emulate problems pertaining to itinerant fermionic or bosonic systems. The magnetic field can then be viewed as similar to a gate voltage controlling the number of ``particles'' allowing an unprecedented level of control. In parallel with the experimental developments, progress on the theoretical front both on the numerical and the analytical side, have allowed a remarkable level of accuracy in obtaining the physical properties and in particular the correlation functions of these systems. A comparison between theoretical predictions without adjustable parameters or fudging with results from NMR, Neutrons or other probes such as ESR is thus now possible. This has allowed for example to test quantitatively the physics of TomonagaLuttinger liquids and also to tackle the effects of the interactions between spinons by comparing the physics of weak rung ladders with the one of strong rung ones. Comparison between the neutron results and theoretical calculations of the correlation functions has also been demonstrated as a way to reconstruct efficiently the Hamiltonian from the experimental data. I will review the recent results obtained in this domain with the different experimental compounds and will discuss the open questions and challenges. This concerns in particular the issues of finite temperatures, higher dimensional systems and effects of disorder. This work was supported in part by the Swiss NSF under MaNEP and Division II
Finite Momentum Pairing and Spatially Varying Order Parameter in Proximitized HgTe Quantum Wells
NASA Astrophysics Data System (ADS)
Yacoby, Amir
Conventional swave superconductivity is understood to arise from singlet pairing of electrons with opposite Fermi momenta, forming Cooper pairs whose net momentum is zero. Several recent studies have focused on structures where such conventional swave superconductors are coupled to systems with an unusual configuration of electronic spin and momentum at the Fermi surface. Under these conditions, the nature of the paired state can be modified and the system may even undergo a topological phase transition. Here we present measurements and theoretical calculations of several HgTe quantum wells coupled to either aluminum or niobium superconductors and subject to a magnetic field in the plane of the quantum well. By studying the oscillatory response of Josephson interference to the magnitude of the inplane magnetic field, we find that the induced pairing within the quantum well oscillates between singlet and triplet pairing and is spatially varying. Cooper pairs acquire a tunable momentum that grows with magnetic field strength, directly reflecting the response of the spindependent Fermi surfaces to the inplane magnetic field. Our new understanding of the interplay between spin physics and superconductivity introduces a way to spatially engineer the order parameter, as well as a general framework within which to investigate electronic spin texture at the Fermi surface of materials.
Chang, WengLong; Ren, TingTing; Feng, Mang
20150101
In this paper, it is shown that the proposed quantum algorithm for implementing Boolean circuits generated from the DNAbased algorithm solving the vertexcover problem of any graph G with m edges and n vertices is the optimal quantum algorithm. Next, it is also demonstrated that mathematical solutions of the same biomolecular solutions are represented in terms of a unit vector in the finitedimensional Hilbert space. Furthermore, for testing our theory, a nuclear magnetic resonance (NMR) experiment of three quantum bits to solve the simplest vertexcover problem is completed.
Quantum transport in a twolevel quantum dot driven by coherent and stochastic fields
NASA Astrophysics Data System (ADS)
Ke, ShaSha; Miao, LingE.; Guo, Zhen; Guo, Yong; Zhang, HuaiWu; Lü, HaiFeng
20161201
We study theoretically the current and shot noise properties flowing through a twolevel quantum dot driven by a strong coherent field and a weak stochastic field. The interaction x(t) between the quantum dot and the stochastic field is assumed to be a GaussianMarkovian random process with zero mean value and correlation function < x (t) x (t ‧) > = Dκe  κ  t  t ‧  , where D and κ are the strength and bandwidth of the stochastic field, respectively. It is found that the stochastic field could enhance the resonant effect between the quantum dot and the coherent field, and generate new resonant points. At the resonant points, the state population difference between two levels is suppressed and the current is considerably enhanced. The zerofrequency shot noise of the current varies dramatically between sub and superPoissonian characteristics by tuning the stochastic field appropriately.
Efficiency at maximum power output of quantum heat engines under finitetime operation.
Wang, Jianhui; He, Jizhou; Wu, Zhaoqi
20120301
We study the efficiency at maximum power, η(m), of irreversible quantum Carnot engines (QCEs) that perform finitetime cycles between a hot and a cold reservoir at temperatures T(h) and T(c), respectively. For QCEs in the reversible limit (long cycle period, zero dissipation), η(m) becomes identical to the Carnot efficiency η(C)=1T(c)/T(h). For QCE cycles in which nonadiabatic dissipation and the time spent on two adiabats are included, the efficiency η(m) at maximum power output is bounded from above by η(C)/(2η(C)) and from below by η(C)/2. In the case of symmetric dissipation, the CurzonAhlborn efficiency η(CA)=1√(T(c)/T(h)) is recovered under the condition that the time allocation between the adiabats and the contact time with the reservoir satisfy a certain relation.
Efficiency at maximum power output of quantum heat engines under finitetime operation
NASA Astrophysics Data System (ADS)
Wang, Jianhui; He, Jizhou; Wu, Zhaoqi
20120301
We study the efficiency at maximum power, ηm, of irreversible quantum Carnot engines (QCEs) that perform finitetime cycles between a hot and a cold reservoir at temperatures Th and Tc, respectively. For QCEs in the reversible limit (long cycle period, zero dissipation), ηm becomes identical to the Carnot efficiency ηC=1Tc/Th. For QCE cycles in which nonadiabatic dissipation and the time spent on two adiabats are included, the efficiency ηm at maximum power output is bounded from above by ηC/(2ηC) and from below by ηC/2. In the case of symmetric dissipation, the CurzonAhlborn efficiency ηCA=1Tc/Th is recovered under the condition that the time allocation between the adiabats and the contact time with the reservoir satisfy a certain relation.
MatrixProductState Algorithm for Finite Fractional Quantum Hall Systems
NASA Astrophysics Data System (ADS)
Liu, Zhao; Bhatt, R. N.
20150901
Exact diagonalization is a powerful tool to study fractional quantum Hall (FQH) systems. However, its capability is limited by the exponentially increasing computational cost. In order to overcome this difficulty, densitymatrixrenormalizationgroup (DMRG) algorithms were developed for much larger system sizes. Very recently, it was realized that some model FQH states have exact matrixproductstate (MPS) representation. Motivated by this, here we report a MPS code, which is closely related to, but different from traditional DMRG language, for finite FQH systems on the cylinder geometry. By representing the manybody Hamiltonian as a matrixproductoperator (MPO) and using singlesite update and density matrix correction, we show that our code can efficiently search the ground state of various FQH systems. We also compare the performance of our code with traditional DMRG. The possible generalization of our code to infinite FQH systems and other physical systems is also discussed.
NASA Astrophysics Data System (ADS)
Darrall, Bradley T.
For the first time true variational principles are formulated for the analysis of the continuum problems of heat diffusion, dynamic thermoelasticity, poroelasticity, and timedependent quantum mechanics. This is accomplished by considering the stationarity of a mixed convolved action, which can be seen as a modern counterpart to the original actions posed in Hamilton's principle and its many extensions. By including fractional derivatives, convolution integrals, and mixed variables into the definition of the action these new variational principles overcome the shortcomings of the many other variational methods based on Hamilton's principle, namely the inability to include dissipation in a consistent manner and the unjustified need to constrain variations on the primary unknowns of a system at the end of the time interval. These new variational principles then provide ideal weak forms from which novel timespace finite element methods having certain attractive properties are formulated.
Quantum phase transitions in the Heisenberg J1J2 triangular antiferromagnet in a magnetic field
NASA Astrophysics Data System (ADS)
Ye, Mengxing; Chubukov, Andrey V.
20170101
We present the zerotemperature phase diagram of a Heisenberg antiferromagnet on a frustrated triangular lattice with nearestneighbor (J1) and nextnearestneighbor (J2) interactions, in a magnetic field. We show that the classical model has an accidental degeneracy for all J2/J1 and all fields, but the degeneracy is lifted by quantum fluctuations. We show that at large spin S , for J2/J1<1 /8 , quantum fluctuations select the same sequence of three sublattice coplanar states in a field as for J2=0 , and for 1 /8
Quantum fields with noncommutative target spaces
NASA Astrophysics Data System (ADS)
Balachandran, A. P.; Queiroz, A. R.; Marques, A. M.; TeotonioSobrinho, P.
20080501
Quantum field theories (QFT’s) on noncommutative spacetimes are currently under intensive study. Usually such theories have world sheet noncommutativity. In the present work, instead, we study QFT’s with commutative world sheet and noncommutative target space. Such noncommutativity can be interpreted in terms of twisted statistics and is related to earlier work of Oeckl [R. Oeckl, Commun. Math. Phys. 217, 451 (2001).CMPHAY0010361610.1007/s002200100375], and others [A. P. Balachandran, G. Mangano, A. Pinzul, and S. Vaidya, Int. J. Mod. Phys. A 21, 3111 (2006)IMPAEF0217751X10.1142/S0217751X06031764; A. P. Balachandran, A. Pinzul, and B. A. Qureshi, Phys. Lett. B 634, 434 (2006)PYLBAJ0370269310.1016/j.physletb.2006.02.006; A. P. Balachandran, A. Pinzul, B. A. Qureshi, and S. Vaidya, arXiv:hepth/0608138; A. P. Balachandran, T. R. Govindarajan, G. Mangano, A. Pinzul, B. A. Qureshi, and S. Vaidya, Phys. Rev. D 75, 045009 (2007)PRVDAQ0556282110.1103/PhysRevD.75.045009; A. Pinzul, Int. J. Mod. Phys. A 20, 6268 (2005)IMPAEF0217751X10.1142/S0217751X05029290; G. Fiore and J. Wess, Phys. Rev. D 75, 105022 (2007)PRVDAQ0556282110.1103/PhysRevD.75.105022; Y. Sasai and N. Sasakura, Prog. Theor. Phys. 118, 785 (2007)PTPKAV0033068X10.1143/PTP.118.785]. The twisted spectra of their free Hamiltonians has been found earlier by Carmona et al. [J. M. Carmona, J. L. Cortes, J. Gamboa, and F. Mendez, Phys. Lett. B 565, 222 (2003)PYLBAJ0370269310.1016/S03702693(03)007287; J. M. Carmona, J. L. Cortes, J. Gamboa, and F. Mendez, J. High Energy Phys.JHEPFG10298479 03 (2003) 05810.1088/11266708/2003/03/058]. We review their derivation and then compute the partition function of one such typical theory. It leads to a deformed blackbody spectrum, which is analyzed in detail. The difference between the usual and the deformed blackbody spectrum appears in the region of high frequencies. Therefore we expect that the deformed blackbody radiation may potentially be used to compute a
The Physical Renormalization of Quantum Field Theories
Binger, Michael William.; /Stanford U., Phys. Dept. /SLAC
20070220
The profound revolutions in particle physics likely to emerge from current and future experiments motivates an improved understanding of the precise predictions of the Standard Model and new physics models. Higher order predictions in quantum field theories inevitably requires the renormalization procedure, which makes sensible predictions out of the naively divergent results of perturbation theory. Thus, a robust understanding of renormalization is crucial for identifying and interpreting the possible discovery of new physics. The results of this thesis represent a broad set of investigations in to the nature of renormalization. The author begins by motivating a more physical approach to renormalization based on gaugeinvariant Green's functions. The resulting effective charges are first applied to gauge coupling unification. This approach provides an elegant formalism for understanding all threshold corrections, and the gauge couplings unify in a more physical manner compared to the usual methods. Next, the gaugeinvariant threegluon vertex is studied in detail, revealing an interesting and rich structure. The effective coupling for the threegluon vertex, {alpha}(k{sub 1}{sup 2}, k{sub 2}{sup 2}, k{sub 3}{sup 2}), depends on three momentum scales and gives rise to an effective scale Q{sub eff}{sup 2}(k{sub 1}{sup 2}, k{sub 2}{sup 2}, k{sub 3}{sup 2}) which governs the (sometimes surprising) behavior of the vertex. The effects of nonzero internal masses are important and have a complicated threshold and pseudothreshold structure. The pinchtechnique effective charge is also calculated to twoloops and several applications are discussed. The Higgs boson mass in Split Supersymmetry is calculated to twoloops, including all oneloop threshold effects, leading to a downward shift in the Higgs mass of a few GeV. Finally, the author discusses some ideas regarding the overall structure of perturbation theory. This thesis lays the foundation for a comprehensive multi
Quantum field theory on timelike hypersurfaces in Rindler space
NASA Astrophysics Data System (ADS)
Colosi, Daniele; Rätzel, Dennis
20130601
The general boundary formulation of quantum field theory is applied to a massive scalar field in twodimensional Rindler space. The field is quantized according to both the SchrödingerFeynman quantization prescription and the holomorphic one in two different spacetime regions: a region bounded by two Cauchy surfaces and a region bounded by one timelike curve. An isomorphism is constructed between the Hilbert spaces associated with these two boundaries. This isomorphism preserves the probabilities that can be extracted from the free and the interacting quantum field theories, proving the equivalence of the Smatrices defined in the two settings, when both apply.
Approximate quasiisodynamicity at a finite aspect ratio in a stellarator vacuum magnetic field
Mikhailov, M. I.; Nührenberg, J. Zille, R.
20151215
A stellarator vacuum field is found in which, at a finite aspect ratio (A ≈ 40), the contours of the second adiabatic invariant of nearly all particles reflected inside that surface are poloidally closed.
Zitterbewegung and quantum revivals in monolayer graphene quantum dots in magnetic fields
NASA Astrophysics Data System (ADS)
García, Trinidad; Cordero, Nicolás A.; Romera, Elvira
20140201
The wavepacket evolution in graphene quantum dots in magnetic fields has been theoretically studied. By analyzing an effective Hamiltonian model we show the wavepacket dynamics exhibits three types of periodicities (Zitterbewegung, classical, and revival times). The influence of the size of the quantum dot and the strength of the external magnetic field in these periodicities has been considered. In addition, we have found that valley degeneracy breaking is shown by both classical and revival times.
NASA Astrophysics Data System (ADS)
Strečka, Jozef; Verkholyak, Taras
20161001
Magnetic properties of the ferrimagnetic mixed spin(1/2,S) Heisenberg chains are examined using quantum Monte Carlo simulations for two different quantum spin numbers S=1 and 3/2. The calculated magnetization curves at finite temperatures are confronted with zerotemperature magnetization data obtained within the density matrix renormalization group method, which imply an existence of two quantum critical points determining a breakdown of the gapped LiebMattis ferrimagnetic phase and TomonagaLuttinger spinliquid phase, respectively. While a square root behavior of the magnetization accompanying each quantum critical point is gradually smoothed upon rising temperature, the susceptibility and isothermal entropy change data at low temperatures provide a stronger evidence of the zerotemperature quantum critical points through marked local maxima and minima, respectively.
NASA Astrophysics Data System (ADS)
Strečka, Jozef; Verkholyak, Taras
20170601
Magnetic properties of the ferrimagnetic mixed spin(1/2, S) Heisenberg chains are examined using quantum Monte Carlo simulations for two different quantum spin numbers S=1 and 3/2. The calculated magnetization curves at finite temperatures are confronted with zerotemperature magnetization data obtained within the density matrix renormalization group method, which imply an existence of two quantum critical points determining a breakdown of the gapped LiebMattis ferrimagnetic phase and TomonagaLuttinger spinliquid phase, respectively. While a square root behavior of the magnetization accompanying each quantum critical point is gradually smoothed upon rising temperature, the susceptibility and isothermal entropy change data at low temperatures provide a stronger evidence of the zerotemperature quantum critical points through marked local maxima and minima, respectively.
Finitekey analysis for timeenergy highdimensional quantum key distribution
NASA Astrophysics Data System (ADS)
Niu, Murphy Yuezhen; Xu, Feihu; Shapiro, Jeffrey H.; Furrer, Fabian
20161101
Timeenergy highdimensional quantum key distribution (HDQKD) leverages the highdimensional nature of timeenergy entangled biphotons and the loss tolerance of singlephoton detection to achieve longdistance key distribution with high photon information efficiency. To date, the generalattack security of HDQKD has only been proven in the asymptotic regime, while HDQKD's finitekey security has only been established for a limited set of attacks. Here we fill this gap by providing a rigorous HDQKD security proof for general attacks in the finitekey regime. Our proof relies on an entropic uncertainty relation that we derive for time and conjugatetime measurements that use dispersive optics, and our analysis includes an efficient decoystate protocol in its parameter estimation. We present numerically evaluated secretkey rates illustrating the feasibility of secure and composable HDQKD over metropolitanarea distances when the system is subjected to the most powerful eavesdropping attack.
Quantum Monte Carlo simulations of the BCSBEC crossover at finite temperature
NASA Astrophysics Data System (ADS)
Bulgac, Aurel; Drut, Joaquín E.; Magierski, Piotr
20080801
The quantum Monte Carlo method for spin (1)/(2) fermions at finite temperature is formulated for dilute systems with an s wave interaction. The motivation and the formalism are discussed along with descriptions of the algorithm and various numerical issues. We report on results for the energy, entropy, and chemical potential as a function of temperature. We give upper bounds on the critical temperature Tc for the onset of superfluidity, obtained by studying the finitesize scaling of the condensate fraction. All of these quantities were computed for couplings around the unitary regime in the range 0.5⩽(kFa)1⩽0.2 , where a is the s wave scattering length and kF is the Fermi momentum of a noninteracting gas at the same density. In all cases our data are consistent with normal Fermi gas behavior above a characteristic temperature T0>Tc , which depends on the coupling and is obtained by studying the deviation of the caloric curve from that of a free Fermi gas. For Tc
Quantum wires as sensors of the electric field: a model into quantum plasmonics
NASA Astrophysics Data System (ADS)
Alves, R. A.; Costa, J. C.; Gomes, M.; Silva, Nuno A.; Guerreiro, A.
20170401
This paper presents a study for a fibre optic sensor based on quantum wires to detect and measure the amplitude and direction of a static electric field. This study is supported by the analogy of the fluid equations describing the free electrons in the quantum wires and the Madelung formalism of Quantum Mechanics. In this context, it is possible to construct a diatomic plasmonic molecule whose energy levels can be Stark shifted by an external electric field and readout using a light beam tuned to the Rabi oscillations of these levels. Choosing the adequate design parameters it is possible to estimate a sensitivity of 100nm/NC1.
QubitProgrammable Operations on Quantum Light Fields
Barbieri, Marco; Spagnolo, Nicolò; Ferreyrol, Franck; Blandino, Rémi; Smith, Brian J.; TualleBrouri, Rosa
20150101
Engineering quantum operations is a crucial capability needed for developing quantum technologies and designing new fundamental physics tests. Here we propose a scheme for realising a controlled operation acting on a travelling continuousvariable quantum field, whose functioning is determined by a discrete input qubit. This opens a new avenue for exploiting advantages of both information encoding approaches. Furthermore, this approach allows for the program itself to be in a superposition of operations, and as a result it can be used within a quantum processor, where coherences must be maintained. Our study can find interest not only in general quantum state engineering and information protocols, but also details an interface between different physical platforms. Potential applications can be found in linking optical qubits to optical systems for which coupling is best described in terms of their continuous variables, such as optomechanical devices. PMID:26468614
Cosmology from group field theory formalism for quantum gravity.
Gielen, Steffen; Oriti, Daniele; Sindoni, Lorenzo
20130719
We identify a class of condensate states in the group field theory (GFT) formulation of quantum gravity that can be interpreted as macroscopic homogeneous spatial geometries. We then extract the dynamics of such condensate states directly from the fundamental quantum GFT dynamics, following the procedure used in ordinary quantum fluids. The effective dynamics is a nonlinear and nonlocal extension of quantum cosmology. We also show that any GFT model with a kinetic term of Laplacian type gives rise, in a semiclassical (WKB) approximation and in the isotropic case, to a modified Friedmann equation. This is the first concrete, general procedure for extracting an effective cosmological dynamics directly from a fundamental theory of quantum geometry.
Dirac fields in loop quantum gravity and big bang nucleosynthesis
NASA Astrophysics Data System (ADS)
Bojowald, Martin; Das, Rupam; Scherrer, Robert J.
20080401
Big bang nucleosynthesis requires a fine balance between equations of state for photons and relativistic fermions. Several corrections to equation of state parameters arise from classical and quantum physics, which are derived here from a canonical perspective. In particular, loop quantum gravity allows one to compute quantum gravity corrections for Maxwell and Dirac fields. Although the classical actions are very different, quantum corrections to the equation of state are remarkably similar. To lowest order, these corrections take the form of an overall expansiondependent multiplicative factor in the total density. We use these results, along with the predictions of big bang nucleosynthesis, to place bounds on these corrections and especially the patch size of discrete quantum gravity states.
Dirac fields in loop quantum gravity and big bang nucleosynthesis
Bojowald, Martin; Das, Rupam; Scherrer, Robert J.
20080415
Big bang nucleosynthesis requires a fine balance between equations of state for photons and relativistic fermions. Several corrections to equation of state parameters arise from classical and quantum physics, which are derived here from a canonical perspective. In particular, loop quantum gravity allows one to compute quantum gravity corrections for Maxwell and Dirac fields. Although the classical actions are very different, quantum corrections to the equation of state are remarkably similar. To lowest order, these corrections take the form of an overall expansiondependent multiplicative factor in the total density. We use these results, along with the predictions of big bang nucleosynthesis, to place bounds on these corrections and especially the patch size of discrete quantum gravity states.
QubitProgrammable Operations on Quantum Light Fields.
Barbieri, Marco; Spagnolo, Nicolò; Ferreyrol, Franck; Blandino, Rémi; Smith, Brian J; TualleBrouri, Rosa
20151015
Engineering quantum operations is a crucial capability needed for developing quantum technologies and designing new fundamental physics tests. Here we propose a scheme for realising a controlled operation acting on a travelling continuousvariable quantum field, whose functioning is determined by a discrete input qubit. This opens a new avenue for exploiting advantages of both information encoding approaches. Furthermore, this approach allows for the program itself to be in a superposition of operations, and as a result it can be used within a quantum processor, where coherences must be maintained. Our study can find interest not only in general quantum state engineering and information protocols, but also details an interface between different physical platforms. Potential applications can be found in linking optical qubits to optical systems for which coupling is best described in terms of their continuous variables, such as optomechanical devices.
Aspects of nonlocality in quantum field theory, quantum gravity and cosmology
NASA Astrophysics Data System (ADS)
Barvinsky, A. O.
20150201
This paper contains a collection of essays on nonlocal phenomena in quantum field theory, gravity and cosmology. Mechanisms of nonlocal contributions to the quantum effective action are discussed within the covariant perturbation expansion in field strengths and spacetime curvatures. Euclidean version of the SchwingerKeldysh technique for quantum expectation values is presented as a special rule of obtaining the nonlocal effective equations of motion for the mean quantum field from the Euclidean effective action. This rule is applied to a new model of ghost free nonlocal cosmology which can generate the de Sitter (dS) cosmological evolution at an arbitrary value of Λ — a model of dark energy with the dynamical scale selected by a kind of a scaling symmetry breaking mechanism. This model is shown to interpolate between the superhorizon phase of a scalar mediated gravity and the short distance general relativistic limit in a special metric frame related by a nonlocal conformal transformation to the original metric.
Estimates on Functional Integrals of Quantum Mechanics and Nonrelativistic Quantum Field Theory
NASA Astrophysics Data System (ADS)
Bley, Gonzalo A.; Thomas, Lawrence E.
20170101
We provide a unified method for obtaining upper bounds for certain functional integrals appearing in quantum mechanics and nonrelativistic quantum field theory, functionals of the form {E[{exp}(A_T)]} , the (effective) action {A_T} being a function of particle trajectories up to time T. The estimates in turn yield rigorous lower bounds for ground state energies, via the FeynmanKac formula. The upper bounds are obtained by writing the action for these functional integrals in terms of stochastic integrals. The method is illustrated in familiar quantum mechanical settings: for the hydrogen atom, for a Schrödinger operator with {1/x^2} potential with small coupling, and, with a modest adaptation of the method, for the harmonic oscillator. We then present our principal applications of the method, in the settings of nonrelativistic quantum field theories for particles moving in a quantized Bose field, including the optical polaron and Nelson models.
Dissipative quantum transport in macromolecules: Effective field theory approach
NASA Astrophysics Data System (ADS)
Schneider, E.; a Beccara, S.; Faccioli, P.
20130801
We introduce an atomistic approach to the dissipative quantum dynamics of charged or neutral excitations propagating through macromolecular systems. Using the FeynmanVernon path integral formalism, we analytically trace out from the density matrix the atomic coordinates and the heat bath degrees of freedom. This way we obtain an effective field theory which describes the realtime evolution of the quantum excitation and is fully consistent with the fluctuationdissipation relation. The main advantage of the fieldtheoretic approach is that it allows us to avoid using the Keldysh contour formulation. This simplification makes it straightforward to derive Feynman diagrams to analytically compute the effects of the interaction of the propagating quantum excitation with the heat bath and with the molecular atomic vibrations. For illustration purposes, we apply this formalism to investigate the loss of quantum coherence of holes propagating through a poly(3alkylthiophene) polymer.
Robust quantum memory using magneticfieldindependent atomic qubits
NASA Astrophysics Data System (ADS)
Langer, C.; Ozeri, R.; Jost, J. D.; Demarco, B.; BenKish, A.; Blakestad, B.; Britton, J.; Chiaverini, J.; Hume, D. B.; Itano, W. M.; Leibfried, D.; Reichle, R.; Rosenband, T.; Schmidt, P.; Wineland, D. J.
20060301
Scalable quantum information processing requires physical systems capable of reliably storing coherent superpositions for times over which quantum error correction can be implemented. We experimentally demonstrate a robust quantum memory using a magneticfieldindependent hyperfine transition in ^9Be^+ atomic ion qubits at a field B = 0.01194 T. Qubit superpositions are created and analyzed with twophoton stimulatedRaman transitions. We observe the single physical qubit memory coherence time to be greater than 10 seconds, an improvement of approximately five orders of magnitude from previous experiments. The probability of memory error for this qubit during the measurement period (the longest timescale in our system) is approximately 1.4 x 105 which is below faulttolerance threshold for common quantum error correcting codes.
AuxiliaryField Quantum Monte Carlo Method for Strongly Paired Fermions
20111207
effective range: E/EFG = ξ + SkF re + · · · . A method is introduced to allow the use of a BCS trial wave function in the auxiliaryfield quantum Monte...down by 0.02 to enable comparison of the slopes. universal in continuum Hamiltonians: ξ (re) = ξ + SkF re. Of course, a finiterange purely attractive...find results consistent with a universal dependence of the groundstate energy upon the effective range:E/EFG = ξ + SkF re + · · · with S = 0.12(0.03
Quantum electron levels in the field of a charged black hole
Dokuchaev, V. I.; Eroshenko, Yu. N.
20151215
Stationary solutions of the Dirac equation in the metric of the charged Reissner–Nordstrom black hole are found. In the case of an extremal black hole, the normalization integral of the wave functions is finite, and the regular stationary solution is physically selfconsistent. The presence of quantum electron levels under the Cauchy horizon can have an impact on the final stage of the Hawking evaporation of the black hole, as well as on the particle scattering in the field of the black hole.
Nearfield levitated quantum optomechanics with nanodiamonds
NASA Astrophysics Data System (ADS)
Juan, M. L.; MolinaTerriza, G.; Volz, T.; RomeroIsart, O.
20160801
We theoretically show that the dipole force of an ensemble of quantum emitters embedded in a dielectric nanosphere can be exploited to achieve nearfield optical levitation. The key ingredient is that the polarizability from the ensemble of embedded quantum emitters can be larger than the bulk polarizability of the sphere, thereby enabling the use of repulsive optical potentials and consequently the levitation using optical near fields. In levitated cavity quantum optomechanics, this could be used to boost the singlephoton coupling by combining larger polarizability to mass ratio, larger field gradients, and smaller cavity volumes while remaining in the resolved sideband regime and at room temperature. A case study is done with a nanodiamond containing a high density of siliconvacancy color centers that is optically levitated in the evanescent field of a tapered nanofiber and coupled to a highfinesse microsphere cavity.
Timedelayed quantum feedback for traveling optical fields
Yanagisawa, M.
20100915
Quantum nonlinear feedback control is developed for traveling optical fields. We first describe the discretization of the traveling optical fields. The discretetime formulation is used to describe the stochastic master equation subject to homodyne measurement. Nonlinear feedback is formulated by directly feeding the measurement outcomes back to the traveling field through a multiplicative action. Since the measurement outcomes have a correlation with the system, the multiplicative feedback control can create nonlinear effects in the traveling field. In this formulation, a time delay is naturally introduced in the feedback loop. This is essentially different from instantaneous feedback in a continuoustime setting. As an example of the feedback scheme, a quantum nondemolition sum gate is considered. Numerical results show that quantum superposition state can be created by applying the feedback to a squeezed state.
Quantum Field Theory and Decoherence in the Early Universe
NASA Astrophysics Data System (ADS)
Koksma, J. F.
20110601
Quantum field theory is indispensable for understanding many aspects of cosmology, both in the early Universe and today. For example, quantum processes could be paramount to understand the nature of the mysterious dark energy resulting in the Universe’s recently observed accelerated expansion. Inspired by these considerations, this PhD thesis is concerned with two aspects of quantum field theory relevant to cosmology: quantum backreaction and decoherence. Quantum backreaction is a line of research where the impact of quantum fluctuations on the background spacetime geometry in perturbative quantum gravity is investigated. The cosmological constant problem and the process of quantum backreaction are intimately related: quantum backreaction might provide us with a dynamical mechanism to effectively make the cosmological constant almost vanish. We investigate the quantum backreaction of the trace anomaly and of fermions. We find that the trace anomaly does not dynamically influence the effective value of the cosmological constant. We furthermore evaluate the fermion propagator in FLRW spacetimes with constant deceleration. Although the dynamics resulting from the oneloop stressenergy tensor need yet to be investigated, we find that we certainly cannot exclude a significant effect due to the quantum backreaction on the Universe’s expansion. Decoherence is a quantum theory which addresses the quantumtoclassical transition of a particular system. The idea of the decoherence formalism is that a macroscopic system cannot be separated from its environment. The framework of decoherence is widely used, e.g. in quantum computing, black hole physics, inflationary perturbation theory, and in elementary particle physics, such as electroweak baryogenesis models. We formulate a novel “correlator approach” to decoherence: neglecting observationally inaccessible correlators gives rise to an increase in entropy of the system, as perceived by an observer. This is inspired
TrappedIon Quantum Logic with Global Radiation Fields
NASA Astrophysics Data System (ADS)
Weidt, S.; Randall, J.; Webster, S. C.; Lake, K.; Webb, A. E.; Cohen, I.; Navickas, T.; Lekitsch, B.; Retzker, A.; Hensinger, W. K.
20161101
Trapped ions are a promising tool for building a largescale quantum computer. However, the number of required radiation fields for the realization of quantum gates in any proposed ionbased architecture scales with the number of ions within the quantum computer, posing a major obstacle when imagining a device with millions of ions. Here, we present a fundamentally different approach for trappedion quantum computing where this detrimental scaling vanishes. The method is based on individually controlled voltages applied to each logic gate location to facilitate the actual gate operation analogous to a traditional transistor architecture within a classical computer processor. To demonstrate the key principle of this approach we implement a versatile quantum gate method based on longwavelength radiation and use this method to generate a maximally entangled state of two quantum engineered clock qubits with fidelity 0.985(12). This quantum gate also constitutes a simpletoimplement tool for quantum metrology, sensing, and simulation.
TrappedIon Quantum Logic with Global Radiation Fields.
Weidt, S; Randall, J; Webster, S C; Lake, K; Webb, A E; Cohen, I; Navickas, T; Lekitsch, B; Retzker, A; Hensinger, W K
20161125
Trapped ions are a promising tool for building a largescale quantum computer. However, the number of required radiation fields for the realization of quantum gates in any proposed ionbased architecture scales with the number of ions within the quantum computer, posing a major obstacle when imagining a device with millions of ions. Here, we present a fundamentally different approach for trappedion quantum computing where this detrimental scaling vanishes. The method is based on individually controlled voltages applied to each logic gate location to facilitate the actual gate operation analogous to a traditional transistor architecture within a classical computer processor. To demonstrate the key principle of this approach we implement a versatile quantum gate method based on longwavelength radiation and use this method to generate a maximally entangled state of two quantum engineered clock qubits with fidelity 0.985(12). This quantum gate also constitutes a simpletoimplement tool for quantum metrology, sensing, and simulation.
NASA Astrophysics Data System (ADS)
Fujiwara, Kunio
19910101
A novel approach has been made to the divergence problem in local field theories, in which the notion of “locality” is still retained but loses its absolute meaning, just like “simultaneity”. The basic idea is to introduce a pureimaginary elementary length into 3dimensional space, while keeping “time” structureless so as to retain the unitarity of theSmatrix. Consequently, light becomes dispersive at sufficiently short wavelengths, and Lorentz transformation becomes a pointtostring transformation. When reformulated to meet the new Lorentz invariance, all the localfield (in the above sense) theories in a flat space become finite,while retaining their conventional form. This has been demonstrated by the derivation of finitized Coulomb potential and correct highmomentum behavior of quantumelectrodynamic coupling constant. For diagrams including gravitons, evaluation of the superficial degrees of divergence shows that only a restricted number of 1(and 2) loop diagrams might be divergent, while those of more than 3 loops are definitely convergent, thus indicating possible renormalizability (or something better) of quantum gravity in Einstein's formalism of general relativity. Since 4dimensional simple supergravity removes 1and 2loop divergence, a combination of the theory and the present one might lead to a more interesting result.
A novel quantum field approach to photoexcited insulators
NASA Astrophysics Data System (ADS)
Klotins, E.
20160701
In order to predict optical properties of insulating materials under intensive laser excitation, we generalized methods of quantum electrodynamics, allowing us to simulate excitation of electrons and holes, interacting with each other and acoustic phonons. The prototypical model considers a twoband dielectric material characterized by the dispersion relations for electron and hole states. We developed a universal description of excited electrons, holes and acoustic phonons within joint quantum kinetics formalism. Illustrative solutions for the quasiparticle birthannihilation operators, applicable at short laser pulses at 0 K, are obtained by the transition from the macroscopic description to the quantum field formalism.
Quantum field between moving mirrors: A three dimensional example
NASA Technical Reports Server (NTRS)
Hacyan, S.; Jauregui, Roco; Villarreal, Carlos
19950101
The scalar quantum field uniformly moving plates in three dimensional space is studied. Field equations for Dirichlet boundary conditions are solved exactly. Comparison of the resulting wavefunctions with their instantaneous static counterpart is performed via Bogolubov coefficients. Unlike the one dimensional problem, 'particle' creation as well as squeezing may occur. The time dependent Casimir energy is also evaluated.
NASA Astrophysics Data System (ADS)
Hart, Sean; Ren, Hechen; Kosowsky, Michael; BenShach, Gilad; Leubner, Philipp; Brüne, Christoph; Buhmann, Hartmut; Molenkamp, Laurens W.; Halperin, Bertrand I.; Yacoby, Amir
20170101
Conventional swave superconductivity arises from singlet pairing of electrons with opposite Fermi momenta, forming Cooper pairs with zero net momentum. Recent studies have focused on coupling swave superconductors to systems with an unusual configuration of electronic spin and momentum at the Fermi surface, where the nature of the paired state can be modified and the system may even undergo a topological phase transition. Here we present measurements and theoretical calculations of HgTe quantum wells coupled to aluminium or niobium superconductors and subject to a magnetic field in the plane of the quantum well. We find that this magnetic field tunes the momentum of Cooper pairs in the quantum well, directly reflecting the response of the spindependent Fermi surfaces. In the high electron density regime, the induced superconductivity evolves with electron density in agreement with our model based on the Hamiltonian of Bernevig, Hughes and Zhang. This agreement provides a quantitative value for g ˜/vF, where g ˜ is the effective gfactor and vF is the Fermi velocity. Our new understanding of the interplay between spin physics and superconductivity introduces a way to spatially engineer the order parameter from singlet to triplet pairing, and in general allows investigation of electronic spin texture at the Fermi surface of materials.
Does there exist a sensible quantum theory of an ``algebravalued'' scalar field\\?
NASA Astrophysics Data System (ADS)
Anco, Stephen C.; Wald, Robert M.
19890401
Consider a scalar field φ in Minkowski spacetime, but let φ be valued in an associative, commutative algebra openA rather than openR. One may view the resulting theory as describing a collection of coupled real scalar fields. At the classical level, theories of this type are completely well behaved and have a global symmetry group which is a nontrivial enlargement of the Poincaré group. (They are analogs of the new class of gauge theories for massless spin2 fields found recently by one of us, whose gauge group is a nontrivial enlargement of the usual diffeomorphism group.) We investigate the quantization of such scalar field theories here by studying the case of a λφ4 field, with φ valued in the twodimensional algebra generated by an identity element e and a nilpotent element v satisfying v2=0. The ColemanMandula theorem, which states that the symmetry group of a nontrivial quantum field theory cannot be a nontrivial enlargement of the Poincaré group, is evaded here because the finite ``extra'' symmetries of the classical theory fail to be implemented in the quantum theory by unitary operators and the infinitesimal symmetries (which can be represented in the quantum theory by quadratic forms) connect the oneparticle Hilbert space to multiparticle states. Nevertheless, we find that the conventional Feynman rules for this theory lead to vacuum decay at the tree level and fail to yield a welldefined S matrix. Some alternative approaches are investigated, but these also appear to fail. Thus, although the classical theory is perfectly well behaved, it seems that there does not exist a sensible quantum theory of an algebravalued scalar field.
BOOK REVIEW: Classical Solutions in Quantum Field Theory Classical Solutions in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Mann, Robert
20130201
Quantum field theory has evolved from its early beginnings as a tool for understanding the interaction of light with matter into a rather formidable technical paradigm, one that has successfully provided the mathematical underpinnings of all nongravitational interactions. Over the eight decades since it was first contemplated the methods have become increasingly more streamlined and sophisticated, yielding new insights into our understanding of the subatomic world and our abilities to make clear and precise predictions. Some of the more elegant methods have to do with nonperturbative and semiclassical approaches to the subject. The chief players here are solitons, instantons, and anomalies. Over the past three decades there has been a steady rise in our understanding of these objects and of our ability to calculate their effects and implications for the rest of quantum field theory. This book is a welcome contribution to this subject. In 12 chapters it provides a clear synthesis of the key developments in these subjects at a level accessible to graduate students that have had an introductory course to quantum field theory. In the author's own words it provides both 'a survey and an overview of this field'. The first half of the book concentrates on solitonskinks, vortices, and magnetic monopolesand their implications for the subject. The reader is led first through the simplest models in one spatial dimension, into more sophisticated cases that required more advanced topological methods. The author does quite a nice job of introducing the various concepts as required, and beginning students should be able to get a good grasp of the subject directly from the text without having to first go through the primary literature. The middle part of the book deals with the implications of these solitons for both cosmology and for duality. While the cosmological discussion is quite nice, the discussion on BPS solitons, supersymmetry and duality is rather condensed. It is
Kondotype transport through a quantum dot under magnetic fields
Dong, Bing; Lei, X. L.
20010615
In this paper, we investigate the Kondo correlation effects on linear and nonlinear transport in a quantum dot connected to reservoirs under finite magnetic fields, using the slaveboson mean field approach suggested by Kotliar and Ruckenstein [Phys. Rev. Lett. >57, 1362 (1986)]. A brief comparison between the present formulation and other slaveboson formulation is presented to justify this approach. The numerical results show that the linear conductance near electronhole symmetry is suppressed by the application of the magnetic fields, but an anomalous enhancement is predicted in the nonsymmetry regime. The effect of external magnetic fields on the nonlinear differential conductances is discussed for the Kondo system. A significant reduction of the peak splitting is observed due to the strong Kondo correlation, which agrees well with experimental data.
Impact of nonlinear effective interactions on group field theory quantum gravity condensates
NASA Astrophysics Data System (ADS)
Pithis, Andreas G. A.; Sakellariadou, Mairi; Tomov, Petar
20160901
We present the numerical analysis of effectively interacting group field theory models in the context of the group field theory quantum gravity condensate analog of the GrossPitaevskii equation for real BoseEinstein condensates including combinatorially local interaction terms. Thus, we go beyond the usually considered construction for free models. More precisely, considering such interactions in a weak regime, we find solutions for which the expectation value of the number operator N is finite, as in the free case. When tuning the interaction to the strongly nonlinear regime, however, we obtain solutions for which N grows and eventually blows up, which is reminiscent of what one observes for real BoseEinstein condensates, where a strong interaction regime can only be realized at high density. This behavior suggests the breakdown of the Bogoliubov ansatz for quantum gravity condensates and the need for nonFock representations to describe the system when the condensate constituents are strongly correlated. Furthermore, we study the expectation values of certain geometric operators imported from loop quantum gravity in the free and interacting cases. In particular, computing solutions around the nontrivial minima of the interaction potentials, one finds, already in the weakly interacting case, a nonvanishing condensate population for which the spectra are dominated by the lowest nontrivial configuration of the quantum geometry. This result indicates that the condensate may indeed consist of many smallest building blocks giving rise to an effectively continuous geometry, thus suggesting the interpretation of the condensate phase to correspond to a geometric phase.
Magnetic field induced mixed level Kondo effect in twolevel quantum dots
NASA Astrophysics Data System (ADS)
Wong, Arturo; Ngo, Anh; Ulloa, Sergio
20120201
Semiconductor quantum dots provide an easily tunable environment in which to investigate the Kondo effect. As it is known, Kondo correlations are suppressed by magnetic fields, showing e.g. a drop in the conductance of a quantum dot device. However, certain systems may exhibit an increasing conductance as a function of an applied magnetic field [1]. In this work we use the numerical renormalization group method to study a twolevel quantum dot system with onlevel and interlevel Coulomb repulsion, coupled to a single channel. When there is a finite detuning between levels, and a local singlet develops in one of them, the linear conductance of the device shows a maximum structure as a function of an inplane magnetic field, which depends on the temperature of the system. This maximum occurs at a magnetic field strength such that the spin up state of one of the levels and spin down of the other are degenerate, allowing a ``mixed level'' Kondo effect. The respective spectral functions feature a resonance at the Fermi energy, commensurate with the Kondo physics. We discuss the properties of this mixed level Kondo state in terms of the detuning and the other parameters of the system. [4pt] [1] R. Sakano and N. Kawakami, PRB 73, 155332 (2006)
Suh, J; Weinstein, A J; Lei, C U; Wollman, E E; Steinke, S K; Meystre, P; Clerk, A A; Schwab, K C
20140613
Quantum fluctuations of the light field used for continuous position detection produce stochastic backaction forces and ultimately limit the sensitivity. To overcome this limit, the backaction forces can be avoided by giving up complete knowledge of the motion, and these types of measurements are called "backaction evading" or "quantum nondemolition" detection. We present continuous twotone backaction evading measurements with a superconducting electromechanical device, realizing three longstanding goals: detection of backaction forces due to the quantum noise of a microwave field, reduction of this quantum backaction noise by 8.5 ± 0.4 decibels (dB), and measurement imprecision of a single quadrature of motion 2.4 ± 0.7 dB below the mechanical zeropoint fluctuations. Measurements of this type will find utility in ultrasensitive measurements of weak forces and nonclassical states of motion.
Singleion microwave nearfield quantum sensor
NASA Astrophysics Data System (ADS)
Wahnschaffe, M.; Hahn, H.; Zarantonello, G.; Dubielzig, T.; Grondkowski, S.; BautistaSalvador, A.; Kohnen, M.; Ospelkaus, C.
20170101
We develop an intuitive model of 2D microwave nearfields in the unusual regime of centimeter waves localized to tens of microns. Close to an intensity minimum, a simple effective description emerges with five parameters that characterize the strength and spatial orientation of the zero and first order terms of the nearfield, as well as the field polarization. Such a field configuration is realized in a microfabricated planar structure with an integrated microwave conductor operating near 1 GHz. We use a single 9 Be+ ion as a highresolution quantum sensor to measure the field distribution through energy shifts in its hyperfine structure. We find agreement with simulations at the submicron and fewdegree level. Our findings give a clear and general picture of the basic properties of oscillatory 2D nearfields with applications in quantum information processing, neutral atom trapping and manipulation, chipscale atomic clocks, and integrated microwave circuits.
IR photodetector based on rectangular quantum wire in magnetic field
Jha, Nandan
20140424
In this paper we study rectangular quantum wire based IR detector with magnetic field applied along the wires. The energy spectrum of a particle in rectangular box shows level repulsions and crossings when external magnetic field is applied. Due to this complex level dynamics, we can tune the spacing between any two levels by varying the magnetic field. This method allows user to change the detector parameters according to his/her requirements. In this paper, we numerically calculate the energy subband levels of the square quantum wire in constant magnetic field along the wire and quantify the possible operating wavelength range that can be obtained by varying the magnetic field. We also calculate the photon absorption probability at different magnetic fields and give the efficiency for different wavelengths if the transition is assumed between two lowest levels.
Universal quantum control in zerofield nuclear magnetic resonance
NASA Astrophysics Data System (ADS)
Bian, Ji; Jiang, Min; Cui, Jiangyu; Liu, Xiaomei; Chen, Botao; Ji, Yunlan; Zhang, Bo; Blanchard, John; Peng, Xinhua; Du, Jiangfeng
20170501
This paper describes a general method for the manipulation of nuclear spins in zero magnetic field. In the absence of magnetic fields, the spins lose the individual information on chemical shifts and inequivalent spins can only be distinguished by nuclear gyromagnetic ratios and spinspin couplings. For spin1/2 nuclei with different gyromagnetic ratios (i.e., different species) in zero magnetic field, we describe the scheme to realize a set of universal quantum logic gates, e.g., arbitrary singlequbit gates and a twoqubit controllednot gate. This method allows for universal quantum control in systems which might provide promising applications in materials science, chemistry, biology, quantum information processing, and fundamental physics.
Magneticfield and quantum confinement asymmetry effects on excitons
Pereyra, P.; Ulloa, S. E.
20000115
A theoretical analysis and calculation of the excitonic states in asymmetric quantum dots is carried out in the presence of magnetic fields. The lack of rotational symmetry, introduced by strains and structural factors, produces splittings of the excitonic states with corresponding consequences on the optical oscillator strengths and polarization dependence. For example, we find that the asymmetry produces Zeeman splittings that are smaller than those for symmetric dots at small fields, which could be used as an additional diagnostic of the geometry of the structure. We focus our calculations on naturally occurring quantum dots due to layer fluctuations in narrow quantum wells. Moreover, we observe that increasing magnetic fields produce an interesting crossover to pure angular momentum states for all the excitonic eigenstates, regardless of the degree of asymmetry of the dots and their size. Explicit calculations of photoluminescence excitation yields are presented and related to the different degrees of freedom of the system. (c) 2000 The American Physical Society.
Fieldemission from quantumdotinperovskite solids
NASA Astrophysics Data System (ADS)
García de Arquer, F. Pelayo; Gong, Xiwen; Sabatini, Randy P.; Liu, Min; Kim, GiHwan; Sutherland, Brandon R.; Voznyy, Oleksandr; Xu, Jixian; Pang, Yuangjie; Hoogland, Sjoerd; Sinton, David; Sargent, Edward
20170301
Quantum dot and well architectures are attractive for infrared optoelectronics, and have led to the realization of compelling light sensors. However, they require welldefined passivated interfaces and rapid charge transport, and this has restricted their efficient implementation to costly vacuumepitaxially grown semiconductors. Here we report solutionprocessed, sensitive infrared fieldemission photodetectors. Using quantumdotsinperovskite, we demonstrate the extraction of photocarriers via field emission, followed by the recirculation of photogenerated carriers. We use in operando ultrafast transient spectroscopy to sense biasdependent photoemission and recapture in fieldemission devices. The resultant photodiodes exploit the superior electronic transport properties of organometal halide perovskites, the quantumsizetuned absorption of the colloidal quantum dots and their matched interface. These fieldemission quantumdotinperovskite photodiodes extend the perovskite response into the shortwavelength infrared and achieve measured specific detectivities that exceed 1012 Jones. The results pave the way towards novel functional photonic devices with applications in photovoltaics and light emission.
Sadeghi, S M
20140901
When a hybrid system consisting of a semiconductor quantum dot and a metallic nanoparticle interacts with a laser field, the plasmonic field of the metallic nanoparticle can be normalized by the quantum coherence generated in the quantum dot. In this Letter, we study the states of polarization of such a coherentplasmonic field and demonstrate how these states can reveal unique aspects of the collective molecular properties of the hybrid system formed via coherent excitonplasmon coupling. We show that transition between the molecular states of this system can lead to ultrafast polarization dynamics, including sudden reversal of the sense of variations of the plasmonic field and formation of circular and elliptical polarization.
Reality, Causality, and Probability, from Quantum Mechanics to Quantum Field Theory
NASA Astrophysics Data System (ADS)
Plotnitsky, Arkady
20151001
These three lectures consider the questions of reality, causality, and probability in quantum theory, from quantum mechanics to quantum field theory. They do so in part by exploring the ideas of the key founding figures of the theory, such N. Bohr, W. Heisenberg, E. Schrödinger, or P. A. M. Dirac. However, while my discussion of these figures aims to be faithful to their thinking and writings, and while these lectures are motivated by my belief in the helpfulness of their thinking for understanding and advancing quantum theory, this project is not driven by loyalty to their ideas. In part for that reason, these lectures also present different and even conflicting ways of thinking in quantum theory, such as that of Bohr or Heisenberg vs. that of Schrödinger. The lectures, most especially the third one, also consider new physical, mathematical, and philosophical complexities brought in by quantum field theory visàvis quantum mechanics. I close by briefly addressing some of the implications of the argument presented here for the current state of fundamental physics.
NonHermitian approach of edge states and quantum transport in a magnetic field
NASA Astrophysics Data System (ADS)
Ostahie, B.; NiÅ£a, M.; Aldea, A.
20161101
We develop a manifest nonHermitian approach of spectral and transport properties of twodimensional mesoscopic systems in a strong magnetic field. The finite system to which several terminals are attached constitutes an open system that can be described by an effective Hamiltonian. The lifetime of the quantum states expressed by the energy imaginary part depends specifically on the leadsystem coupling and makes the difference among three regimes: resonant, integer quantum Hall effect, and superradiant. The discussion is carried on in terms of edge state lifetime in different gaps, channel formation, role of hybridization, and transmission coefficients quantization. A toy model helps in understanding nonHermitian aspects in open systems.
Magnetocaloric effect and magnetic cooling near a fieldinduced quantumcritical point
Wolf, Bernd; Tsui, Yeekin; JaiswalNagar, Deepshikha; Tutsch, Ulrich; Honecker, Andreas; RemovićLanger, Katarina; Hofmann, Georg; Prokofiev, Andrey; Assmus, Wolf; Donath, Guido; Lang, Michael
20110101
The presence of a quantumcritical point (QCP) can significantly affect the thermodynamic properties of a material at finite temperatures T. This is reflected, e.g., in the entropy landscape S(T,r) in the vicinity of a QCP, yielding particularly strong variations for varying the tuning parameter r such as pressure or magnetic field B. Here we report on the determination of the critical enhancement of ∂S/∂B near a Binduced QCP via absolute measurements of the magnetocaloric effect (MCE), (∂T/∂B)S and demonstrate that the accumulation of entropy around the QCP can be used for efficient lowtemperature magnetic cooling. Our proof of principle is based on measurements and theoretical calculations of the MCE and the cooling performance for a Cu2+containing coordination polymer, which is a very good realization of a spin½ antiferromagnetic Heisenberg chain—one of the simplest quantumcritical systems.
Quantum field theory of the Casimir effect for real media
Mostepanenko, V.M.; Trunov, N.N.
19851101
The quantum field theory is developed for the corrections to the Casimir force arising when the field penetrates the material of the plates. A new type of divergence arising from the corresponding modification of the boundary conditions is analyzed. General expressions are obtained for the vacuum energy of the electromagnetic field in the space between nonideal plates, and the actual corrections to the Casimir force are calculated in firstorder perturbation theory in the penetration depth.
An algorithm to design finite field multipliers using a selfdual normal basis
NASA Technical Reports Server (NTRS)
Wang, C. C.
19870101
Finite field multiplication is central in the implementation of some errorcorrecting coders. Massey and Omura have presented a revolutionary design for multiplication in a finite field. In their design, a normal base is utilized to represent the elements of the field. The concept of using a selfdual normal basis to design the MasseyOmura finite field multiplier is presented. Presented first is an algorithm to locate a selfdual normal basis for GF(2 sup m) for odd m. Then a method to construct the product function for designing the MasseyOmura multiplier is developed. It is shown that the construction of the product function base on a selfdual basis is simpler than that based on an arbitrary normal base.
Sudiarta, I. Wayan; Angraini, Lily Maysari
20160419
We have applied the finite difference time domain (FDTD) method with the supersymmetric quantum mechanics (SUSYQM) procedure to determine excited energies of one dimensional quantum systems. The theoretical basis of FDTD, SUSYQM, a numerical algorithm and an illustrative example for a particle in a one dimensional squarewell potential were given in this paper. It was shown that the numerical results were in excellent agreement with theoretical results. Numerical errors produced by the SUSYQM procedure was due to errors in estimations of superpotentials and supersymmetric partner potentials.
Effects of Electric Fields on Quantum Well Intersubband Transitions
NASA Astrophysics Data System (ADS)
Harwit, Alex
A new technique is described to calculate the exact eigenstates of a quantum well superlattice of Gallium Arsenide/Aluminum Gallium Arsenide (GaAs/AlGaAs) in a perpendicular electric field. In the model the sloping potential of the conduction band is approximated by a series of small steps. Plane wave states are propagated across the quantum well structure and the quasieigenstates and quasieigenenergies are found at the transmission resonances of the system. We have used the technique to quantify the tunability of a new infrared modulator utilizing an intraconduction band transition in the quantum well. Two such quantum well samples were grown by Molecular Beam Epitaxy (MBE). They consisted of 92 and 110 Angstrom GaAs quantum wells separated by AlGaAs barriers. Under the application of a perpendicular electric field, shifts were observed in the quantum well intersubband absorption energies, in good agreement with theoretical calculations. These tunable transitions can be applied to far infrared light modulators.
Effects of a scalar scaling field on quantum mechanics
Benioff, Paul
20160418
This paper describes the effects of a complex scalar scaling field on quantum mechanics. The field origin is an extension of the gauge freedom for basis choice in gauge theories to the underlying scalar field. The extension is based on the idea that the value of a number at one space time point does not determine the value at another point. This, combined with the description of mathematical systems as structures of different types, results in the presence of separate number fields and vector spaces as structures, at different space time locations. Complex number structures and vector spaces at each location are scaled by a complex space time dependent scaling factor. The effect of this scaling factor on several physical and geometric quantities has been described in other work. Here the emphasis is on quantum mechanics of one and two particles, their states and properties. Multiparticle states are also briefly described. The effect shows as a complex, nonunitary, scalar field connection on a fiber bundle description of nonrelativistic quantum mechanics. Here, the lack of physical evidence for the presence of this field so far means that the coupling constant of this field to fermions is very small. It also means that the gradient of the field must be very small in a local region of cosmological space and time. Outside this region, there are no restrictions on the field gradient.
Effects of a scalar scaling field on quantum mechanics
Benioff, Paul
20160418
This paper describes the effects of a complex scalar scaling field on quantum mechanics. The field origin is an extension of the gauge freedom for basis choice in gauge theories to the underlying scalar field. The extension is based on the idea that the value of a number at one space time point does not determine the value at another point. This, combined with the description of mathematical systems as structures of different types, results in the presence of separate number fields and vector spaces as structures, at different space time locations. Complex number structures and vector spaces at eachmore » location are scaled by a complex space time dependent scaling factor. The effect of this scaling factor on several physical and geometric quantities has been described in other work. Here the emphasis is on quantum mechanics of one and two particles, their states and properties. Multiparticle states are also briefly described. The effect shows as a complex, nonunitary, scalar field connection on a fiber bundle description of nonrelativistic quantum mechanics. Here, the lack of physical evidence for the presence of this field so far means that the coupling constant of this field to fermions is very small. It also means that the gradient of the field must be very small in a local region of cosmological space and time. Outside this region, there are no restrictions on the field gradient.« less
Effects of a scalar scaling field on quantum mechanics
Benioff, Paul
20160418
This paper describes the effects of a complex scalar scaling field on quantum mechanics. The field origin is an extension of the gauge freedom for basis choice in gauge theories to the underlying scalar field. The extension is based on the idea that the value of a number at one space time point does not determine the value at another point. This, combined with the description of mathematical systems as structures of different types, results in the presence of separate number fields and vector spaces as structures, at different space time locations. Complex number structures and vector spaces at each location are scaled by a complex space time dependent scaling factor. The effect of this scaling factor on several physical and geometric quantities has been described in other work. Here the emphasis is on quantum mechanics of one and two particles, their states and properties. Multiparticle states are also briefly described. The effect shows as a complex, nonunitary, scalar field connection on a fiber bundle description of nonrelativistic quantum mechanics. Here, the lack of physical evidence for the presence of this field so far means that the coupling constant of this field to fermions is very small. It also means that the gradient of the field must be very small in a local region of cosmological space and time. Outside this region, there are no restrictions on the field gradient.
Computational approach for calculating bound states in quantum field theory
NASA Astrophysics Data System (ADS)
Lv, Q. Z.; Norris, S.; Brennan, R.; Stefanovich, E.; Su, Q.; Grobe, R.
20160901
We propose a nonperturbative approach to calculate boundstate energies and wave functions for quantum field theoretical models. It is based on the direct diagonalization of the corresponding quantum field theoretical Hamiltonian in an effectively discretized and truncated Hilbert space. We illustrate this approach for a Yukawalike interaction between fermions and bosons in one spatial dimension and show where it agrees with the traditional method based on the potential picture and where it deviates due to recoil and radiative corrections. This method permits us also to obtain some insight into the spatial characteristics of the distribution of the fermions in the ground state, such as the bremsstrahlunginduced widening.
Field emission from quantum size GaN structures
NASA Astrophysics Data System (ADS)
Yilmazoglu, O.; Pavlidis, D.; Litvin, Yu. M.; Hubbard, S.; Tiginyanu, I. M.; Mutamba, K.; Hartnagel, H. L.; Litovchenko, V. G.; Evtukh, A.
20031201
Whisker structures and quantum dots fabricated by photoelectrochemical (PEC) etching of undoped and doped metalorganic chemical vapor deposition (MOCVD)grown GaN (2×10 17 or 3×10 18 cm 3) are investigated in relation with their fieldemission characteristics. Different surface morphologies, corresponding to different etching time and photocurrent, results in different fieldemission characteristics with low turnon voltage down to 4 V/μm and the appearance of quantumsize effect in the I V curves.
Electric field engineering using quantumsizeeffecttuned heterojunctions
NASA Astrophysics Data System (ADS)
Adinolfi, V.; Ning, Z.; Xu, J.; Masala, S.; Zhitomirsky, D.; Thon, S. M.; Sargent, E. H.
20130701
A quantum junction solar cell architecture was recently reported that employs colloidal quantum dots (CQDs) on each side of the pn junction. This architecture extends the range of design opportunities for CQD photovoltaics, since the bandgap can be tuned across the lightabsorbing semiconductor layer via control over CQD size, employing solutionprocessed, roomtemperature fabricated materials. We exploit this feature by designing and demonstrating a fieldenhanced heterojunction architecture. We optimize the electric field profile within the solar cell through bandgap engineering, thereby improving carrier collection and achieving an increased open circuit voltage, resulting in a 12% improvement in power conversion efficiency.
NASA Astrophysics Data System (ADS)
Droste, Stephanie; Governale, Michele
20160401
We study the finitetime full counting statistics for subgap transport through a singlelevel quantum dot tunnelcoupled to one normal and one superconducting lead. In particular, we determine the factorial and the ordinary cumulants both for finite times and in the longtime limit. We find that the factorial cumulants violate the sign criterion, indicating a nonbinomial distribution, even in absence of Coulomb repulsion due to the presence of superconducting correlations. At short times the cumulants exhibit oscillations which are a signature of the coherent transfer of Cooper pairs between the dot and the superconductor.
Exact Electromagnetic Fields Produced by a Finite Wire with Constant Current
ERIC Educational Resources Information Center
Jimenez, J. L.; Campos, I.; Aquino, N.
20080101
We solve exactly the problem of calculating the electromagnetic fields produced by a finite wire with a constant current, by using two methods: retarded potentials and Jefimenko's formalism. One result in this particular case is that the usual BiotSavart law of magnetostatics gives the correct magnetic field of the problem. We also show…
Review of finite fields: Applications to discrete Fourier, transforms and ReedSolomon coding
NASA Technical Reports Server (NTRS)
Wong, J. S. L.; Truong, T. K.; Benjauthrit, B.; Mulhall, B. D. L.; Reed, I. S.
19770101
An attempt is made to provide a stepbystep approach to the subject of finite fields. Rigorous proofs and highly theoretical materials are avoided. The simple concepts of groups, rings, and fields are discussed and developed more or less heuristically. Examples are used liberally to illustrate the meaning of definitions and theories. Applications include discrete Fourier transforms and ReedSolomon coding.
Exact Electromagnetic Fields Produced by a Finite Wire with Constant Current
ERIC Educational Resources Information Center
Jimenez, J. L.; Campos, I.; Aquino, N.
20080101
We solve exactly the problem of calculating the electromagnetic fields produced by a finite wire with a constant current, by using two methods: retarded potentials and Jefimenko's formalism. One result in this particular case is that the usual BiotSavart law of magnetostatics gives the correct magnetic field of the problem. We also show…
A software framework for solving bioelectrical field problems based on finite elements.
Sachse, F B; Cole, M J; Stinstra, J G
20060101
Computational modeling and simulation can provide important insights into the electrical and electrophysiological properties of cells, tissues, and organs. Commonly, the modeling is based on Maxwell's and Poisson's equations for electromagnetic and electric fields, respectively, and numerical techniques are applied for field calculation such as the finite element and finite differences methods. Focus of this work are finite element methods, which are based on an elementwise discretization of the spatial domain. These methods can be classified on the element's geometry, e.g. triangles, tetrahedrons and hexahedrons, and the underlying interpolation functions, e.g. polynomials of various order. Aim of this work is to describe finite elementbased approaches and their application to extend the problemsolving environment SCIRun/BioPSE. Finite elements of various types were integrated and methods for interpolation and integration were implemented. General methods for creation of finite element system matrices and boundary conditions were incorporated. The extension provides flexible means for geometric modeling, physical simulation, and visualization with particular application in solving bioelectric field problems.
Ionisation of a quantum dot by electric fields
Eminov, P A; Gordeeva, S V
20120831
We have derived analytical formulas for differential and total ionisation probabilities of a twodimensional quantum dot by a constant electric field. In the adiabatic approximation, we have calculated the probability of this process in the field of a plane electromagnetic wave and in a superposition of constant and alternating electric fields. The imaginarytime method is used to obtain the momentum distribution of the ionisation probability of a bound system by an intense field generated by a superposition of parallel constant and alternating electric fields. The total probability of the process per unit time is calculated with exponential accuracy. The dependence of the results obtained on the characteristic parameters of the problem is investigated. (laser applications and other topics in quantum electronics)
Quantum Hall physics: Hierarchies and conformal field theory techniques
NASA Astrophysics Data System (ADS)
Hansson, T. H.; Hermanns, M.; Simon, S. H.; Viefers, S. F.
20170401
The fractional quantum Hall effect, being one of the most studied phenomena in condensed matter physics during the past 30 years, has generated many groundbreaking new ideas and concepts. Very early on it was realized that the zoo of emerging states of matter would need to be understood in a systematic manner. The first attempts to do this, by Haldane and Halperin, set an agenda for further work which has continued to this day. Since that time the idea of hierarchies of quasiparticles condensing to form new states has been a pillar of our understanding of fractional quantum Hall physics. In the 30 years that have passed since then, a number of new directions of thought have advanced our understanding of fractional quantum Hall states and have extended it in new and unexpected ways. Among these directions is the extensive use of topological quantum field theories and conformal field theories, the application of the ideas of composite bosons and fermions, and the study of nonAbelian quantum Hall liquids. This article aims to present a comprehensive overview of this field, including the most recent developments.
PREFACE: Particles and Fields: Classical and Quantum
NASA Astrophysics Data System (ADS)
Asorey, M.; ClementeGallardo, J.; Marmo, G.
20070701
This volume contains some of the contributions to the Conference Particles and Fields: Classical and Quantum, which was held at Jaca (Spain) in September 2006 to honour George Sudarshan on his 75th birthday. Former and current students, associates and friends came to Jaca to share a few wonderful days with George and his family and to present some contributions of their present work as influenced by George's impressive achievements. This book summarizes those scientific contributions which are presented as a modest homage to the master, collaborator and friend. At the social ceremonies various speakers were able to recall instances of his lifelong activity in India, the United States and Europe, adding colourful remarks on the friendly and intense atmosphere which surrounded those collaborations, some of which continued for several decades. This meeting would not have been possible without the financial support of several institutions. We are deeply indebted to Universidad de Zaragoza, Ministerio de Educación y Ciencia de España (CICYT), Departamento de Ciencia, Tecnología y Universidad del Gobierno de Aragón, Universitá di Napoli 'Federico II' and Istituto Nazionale di Fisica Nucleare. Finally, we would like to thank the participants, and particularly George's family, for their contribution to the wonderful atmosphere achieved during the Conference. We would like also to acknowledge the authors of the papers collected in the present volume, the members of the Scientific Committee for their guidance and support and the referees for their generous work. M Asorey, J ClementeGallardo and G Marmo The Local Organizing Committee George Sudarshan
A. Ashtekhar (Pennsylvania State University, USA) 
L. J. Boya (Universidad de Zaragoza, Spain) 
I. Cirac (Max Planck Institute, Garching
Magnetic field effects in fewlevel quantum dots: Theory and application to experiment NASA Astrophysics Data System (ADS) Wright, Christopher J.; Galpin, Martin R.; Logan, David E. 20110901 We examine several effects of an applied magnetic field on Andersontype models for both single and twolevel quantum dots, and we make direct comparison between numerical renormalization group (NRG) calculations and recent conductance measurements. On the theoretical side, the focus is on magnetization, singleparticle dynamics, and zerobias conductance, with emphasis on the universality arising in strongly correlated regimes, including a method to obtain the scaling behavior of fieldinduced Kondo resonance shifts over a very wide field range. NRG is also used to interpret recent experiments on spin(1)/(2) and spin1 quantum dots in a magnetic field, which we argue do not wholly probe universal regimes of behavior, and the calculations are shown to yield good qualitative agreement with essentially all features seen in experiment. The results capture in particular the observed field dependence of the Kondo conductance peak in a spin(1)/(2) dot, with quantitative deviations from experiment occurring at fields in excess of ˜5T, indicating the eventual inadequacy of using the equilibrium singleparticle spectrum to calculate the conductance at finite bias. Finitekey security analysis of quantum key distribution with imperfect light sources Mizutani, Akihiro; Curty, Marcos; Lim, Charles Ci Wen; ... 20150909 In recent years, the gap between theory and practice in quantum key distribution (QKD) has been significantly narrowed, particularly for QKD systems with arbitrarily flawed optical receivers. The status for QKD systems with imperfect light sources is however less satisfactory, in the sense that the resulting secure key rates are often overly dependent on the quality of state preparation. This is especially the case when the channel loss is high. Very recently, to overcome this limitation, Tamaki et al proposed a QKD protocol based on the socalled 'rejected data analysis', and showed that its security in the limit of infinitelymore » long keys is almost independent of any encoding flaw in the qubit space, being this protocol compatible with the decoy state method. Here, as a step towards practical QKD, we show that a similar conclusion is reached in the finitekey regime, even when the intensity of the light source is unstable. More concretely, we derive security bounds for a wide class of realistic light sources and show that the bounds are also efficient in the presence of high channel loss. Our results strongly suggest the feasibility of long distance provably secure communication with imperfect light sources.« less Finitekey security analysis of quantum key distribution with imperfect light sources Mizutani, Akihiro; Curty, Marcos; Lim, Charles Ci Wen; Imoto, Nobuyuki; Tamaki, Kiyoshi 20150909 In recent years, the gap between theory and practice in quantum key distribution (QKD) has been significantly narrowed, particularly for QKD systems with arbitrarily flawed optical receivers. The status for QKD systems with imperfect light sources is however less satisfactory, in the sense that the resulting secure key rates are often overly dependent on the quality of state preparation. This is especially the case when the channel loss is high. Very recently, to overcome this limitation, Tamaki et al proposed a QKD protocol based on the socalled 'rejected data analysis', and showed that its security in the limit of infinitely long keys is almost independent of any encoding flaw in the qubit space, being this protocol compatible with the decoy state method. Here, as a step towards practical QKD, we show that a similar conclusion is reached in the finitekey regime, even when the intensity of the light source is unstable. More concretely, we derive security bounds for a wide class of realistic light sources and show that the bounds are also efficient in the presence of high channel loss. Our results strongly suggest the feasibility of long distance provably secure communication with imperfect light sources. Acceleration of adiabatic quantum dynamics in electromagnetic fields Masuda, Shumpei; Nakamura, Katsuhiro 20111015 We show a method to accelerate quantum adiabatic dynamics of wave functions under electromagnetic field (EMF) by developing the preceding theory [Masuda and Nakamura, Proc. R. Soc. London Ser. A 466, 1135 (2010)]. Treating the orbital dynamics of a charged particle in EMF, we derive the driving field which accelerates quantum adiabatic dynamics in order to obtain the final adiabatic states in any desired short time. The scheme is consolidated by describing a way to overcome possible singularities in both the additional phase and driving potential due to nodes proper to wave functions under EMF. As explicit examples, we exhibit the fast forward of adiabatic squeezing and transport of excited Landau states with nonzero angular momentum, obtaining the result consistent with the transitionless quantum driving applied to the orbital dynamics in EMF. Quantum synchrotron spectra from semirelativistic electrons in teragauss magnetic fields NASA Technical Reports Server (NTRS) Brainerd, J. J. 19870101 Synchrotron spectra are calculated from quantum electrodynamic transition rates for thermal and powerlaw electron distributions. It is shown that quantum effects appear in thermal spectra when the photon energy is greater than the electron temperature, and in powerlaw spectra when the electron energy in units of the electron rest mass times the magnetic field strength in units of the critical field strength is of order unity. These spectra are compared with spectra calculated from the ultrarelativistic approximation for synchrotron emission. It is found that the approximation for the powerlaw spectra is good, and the approximation for thermal spectra produces the shape of the spectrum accurately but fails to give the correct normalization. Single photon pair creation masks the quantum effects for powerlaw distributions, so only modifications to thermal spectra are important for gammaray bursts. Quantum phenomena and the zeropoint radiation field. II NASA Astrophysics Data System (ADS) de La Peña, L.; Cetto, A. M. 19950401 A previous paper was devoted to the discussion of a new version of stochastic electrodynamics (SED) and to the study of the conditions under which quantum mechanics can be derived from it, in the radiationless approximation. In this paper further effects on matter due to the zeropoint field are studied, such as atomic stability, radiative transitions, the Lamb shift, etc., and are shown to be correctly described by the proposed version of SED. Also, a detailed energybalance condition and a fluctuationdissipation relation are established; it is shown in particular that equilibrium is attained only with a field spectrum ˜Ω 3. The proposed approach is shown to suggest an understanding of quantum mechanics as a kind of limitcycle theory. Finally, a brief discussion is included about the nonchaotic behavior of the (bounded) SED system in the quantum regime, as measured by Lyapunov exponents.
