Mesa Pascasio, J.; Fussy, S.; Schwabl, H.; Grössing, G.
2016-03-01
We present our model of an Emergent QuantumMechanics which can be characterized by “realism without pre-determination”. This is illustrated by our analytic description and corresponding computer simulations of Bohmian-like “surreal” trajectories, which are obtained classically, i.e. without the use of any quantummechanical tool such as wavefunctions. However, these trajectories do not necessarily represent ontological paths of particles but rather mappings of the probability density flux in a hydrodynamical sense. Modelling emergent quantummechanics in a high-low intesity double slit scenario gives rise to the “quantum sweeper effect” with a characteristic intensity pattern. This phenomenon should be experimentally testable via weak measurement techniques.
In this Perspective, several developments in the field of quantummechanics/molecular mechanics (QM/MM) approaches are reviewed. Emphasis is placed on the use of correlated wavefunction theory and new state of the art methods for the treatment of large quantumsystems. Until recently, computational chemistry approaches to large/complex chemical problems have seldom been considered as tools for quantitative predictions. However, due to the tremendous development of computational resources and new quantum chemical methods, it is nowadays possible to describe the electronic structure of biomolecules at levels of theory which a decade ago were only possible for system sizes of up to 20 atoms. These advances are here outlined in the context of QM/MM. The article concludes with a short outlook on upcoming developments and possible bottlenecks for future applications.
In the same way as the quantum no-cloning theorem and quantum key distribution in two preceding papers, entanglement-assisted quantum teleportation and Grover's search algorithm are generalized by transferring them to an abstract setting, including usual quantummechanics as a special case. This again shows that a much more general and abstract access to these quantummechanical features is possible than commonly thought. A non-classical extension of conditional probability and, particularly, a very special type of state-independent conditional probability are used instead of Hilbert spaces and wavefunctions.
Based on the stochastic unravelling of the reduced density operator in the Feynman path integral formalism for an open quantumsystem in touch with harmonic environments, a new non-Markovian stochastic Schrödinger equation (NMSSE) has been established that allows for the systematic perturbation expansion in the system-bath coupling to arbitrary order. This NMSSE can be transformed in a facile manner into the other two NMSSEs, i.e., non-Markovian quantum state diffusion and time-dependent wavepacket diffusion method. Benchmarked by numerically exact results, we have conducted a comparative study of the proposed method in its lowest order approximation, with perturbative quantum master equations in the symmetric spin-boson model and the realistic Fenna-Matthews-Olson complex. It is found that our method outperforms the second-order time-convolutionless quantum master equation in the whole parameter regime and even far better than the fourth-order in the slow bath and high temperature cases. Besides, the method is applicable on an equal footing for any kind of spectral density function and is expected to be a powerful tool to explore the quantum dynamics of large-scale systems, benefiting from the wavefunction framework and the time-local appearance within a single stochastic trajectory.
We consider wavefunctions which are non-negative in some tensor product basis. We study what possible teleportation can occur in such wavefunctions, giving a complete answer in some cases (when one system is a qubit) and partial answers elsewhere. We use this to show that a one-dimensional wavefunction which is non-negative and has zero correlation length can be written in a “coherent Gibbs state” form, as explained later. We conjecture that such holds in higher dimensions. Additionally, some results are provided on possible teleportation in general wavefunctions, explaining how Schmidt coefficients before measurement limit the possible Schmidt coefficients after measurement, andmore » on the absence of a “generalized area law” [D. Aharonov et al., in Proceedings of Foundations of Computer Science (FOCS) (IEEE, 2014), p. 246; e-print arXiv.org:1410.0951] even for Hamiltonians with no sign problem. One of the motivations for this work is an attempt to prove a conjecture about ground state wavefunctions which have an “intrinsic” sign problem that cannot be removed by any quantum circuit. We show a weaker version of this, showing that the sign problem is intrinsic for commuting Hamiltonians in the same phase as the double semion model under the technical assumption that TQO-2 holds [S. Bravyi et al., J. Math. Phys. 51, 093512 (2010)].« less
It is a long-standing goal to understand the reaction mechanisms of catalytic metalloenzymes at an entangled many-electron level, but this is hampered by the exponential complexity of quantummechanics. Here, by exploiting the special structure of physical quantum states and using the density matrix renormalization group, we compute near-exact many-electron wavefunctions of the Mn4CaO5 cluster of photosystem II, with more than 1 × 10(18) quantum degrees of freedom. This is the first treatment of photosystem II beyond the single-electron picture of density functional theory. Our calculations support recent modifications to the structure determined by X-ray crystallography. We further identify multiple low-lying energy surfaces associated with the structural distortion seen using X-ray crystallography, highlighting multistate reactivity in the chemistry of the cluster. Direct determination of Mn spin-projections from our wavefunctions suggests that current candidates that have been recently distinguished using parameterized spin models should be reassessed. Through entanglement maps, we reveal rich information contained in the wavefunctions on bonding changes in the cycle.
Clay, Raymond C.; Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94550; Morales, Miguel A., E-mail: moralessilva2@llnl.gov
2015-06-21
Multideterminant wavefunctions, while having a long history in quantum chemistry, are increasingly being used in highly accurate quantum Monte Carlo calculations. Since the accuracy of QMC is ultimately limited by the quality of the trial wavefunction, multi-Slater determinants wavefunctions offer an attractive alternative to Slater-Jastrow and more sophisticated wavefunction ansatz for several reasons. They can be efficiently calculated, straightforwardly optimized, and systematically improved by increasing the number of included determinants. In spite of their potential, however, the convergence properties of multi-Slater determinant wavefunctions with respect to orbital set choice and excited determinant selection are poorly understood, which hinders the applicationmore » of these wavefunctions to large systems and solids. In this paper, by performing QMC calculations on the equilibrium and stretched carbon dimer, we find that convergence of the recovered correlation energy with respect to number of determinants can depend quite strongly on basis set and determinant selection methods, especially where there is strong correlation. We demonstrate that properly chosen orbital sets and determinant selection techniques from quantum chemistry methods can dramatically reduce the required number of determinants (and thus the computational cost) to reach a given accuracy, which we argue shows clear need for an automatic QMC-only method for selecting determinants and generating optimal orbital sets.« less
The combination of quantum effects and interactions in quantum many-body systems can result in exotic phases with fundamentally entangled ground state wavefunctions--topological phases. Topological phases come in two types, both of which will be studied in this thesis. In topologically ordered phases, the pattern of entanglement in the ground state wavefunction encodes the statistics of exotic emergent excitations, a universal indicator of a phase that is robust to all types of perturbations. In symmetry protected topological phases, the entanglement instead encodes a universal response of the system to symmetry defects, an indicator that is robust only to perturbations respecting the protecting symmetry. Finding and creating these phases in physical systems is a motivating challenge that tests all aspects--analytical, numerical, and experimental--of our understanding of the quantum many-body problem. Nearly three decades ago, the creation of simple ansatz wavefunctions--such as the Laughlin fractional quantum hall state, the AKLT state, and the resonating valence bond state--spurred analytical understanding of both the role of entanglement in topological physics and physical mechanisms by which it can arise. However, quantitative understanding of the relevant phase diagrams is still challenging. For this purpose, tensor networks provide a toolbox for systematically improving wavefunction ansatz while still capturing the relevant entanglement properties. In this thesis, we use the tools of entanglement and tensor networks to analyze ansatz states for several proposed new phases. In the first part, we study a featureless phase of bosons on the honeycomb lattice and argue that this phase can be topologically protected under any one of several distinct subsets of the crystalline lattice symmetries. We discuss methods of detecting such phases with entanglement and without. In the second part, we consider the problem of constructing fixed-point wavefunctions for
By assuming that a fermion de-constitutes immediately at source, that its constituents, as bosons, propagate uniformly as scalar vacuum terms with phase (radial) symmetry, and that fermions are unique solutions for specific phase conditions, we find a model that self-quantizes matter from continuous waves, unifying bosons and fermion ontologies in a single basis, in a constitution-invariant process. Vacuum energy has a wavefunction context, as a mass-energy term that enables wave collapse and increases its amplitude, with gravitational field as the gradient of the flux density. Gravitational and charge-based force effects emerge as statistics without special treatment. Confinement, entanglement, vacuum statistics, forces, and wavefunction terms emerge from the model's deterministic foundations.
Alhaidari, A. D., E-mail: haidari@sctp.org.sa; Ismail, M. E. H.
2015-07-15
In the standard formulation of quantummechanics, one starts by proposing a potential function that models the physical system. The potential is then inserted into the Schrödinger equation, which is solved for the wavefunction, bound states energy spectrum, and/or scattering phase shift. In this work, however, we propose an alternative formulation in which the potential function does not appear. The aim is to obtain a set of analytically realizable systems, which is larger than in the standard formulation and may or may not be associated with any given or previously known potential functions. We start with the wavefunction, which ismore » written as a bounded infinite sum of elements of a complete basis with polynomial coefficients that are orthogonal on an appropriate domain in the energy space. Using the asymptotic properties of these polynomials, we obtain the scattering phase shift, bound states, and resonances. This formulation enables one to handle not only the well-known quantumsystems but also previously untreated ones. Illustrative examples are given for two- and three-parameter systems.« less
Quantummechanics (QM) forms the most crucial ingredient of modern-era physical science curricula at undergraduate level. The abstract ideas involved in QM related concepts pose a challenge towards appropriate visualization as a consequence of their counter-intuitive nature and lack of experiment-assisted visualization tools. At the heart of the quantummechanical formulation lies the concept of ‘wavefunction’, which forms the basis for understanding the behavior of physical systems. At undergraduate level, the concept of ‘wavefunction’ is introduced in an abstract framework using mathematical tools and therefore opens up an enormous scope for alternative conceptions and erroneous visualization. The present work is an attempt towards exploring the visualization models constructed by undergraduate students for appreciating the concept of ‘wavefunction’. We present a qualitative analysis of the data obtained from administering a questionnaire containing four visualization based questions on the topic of ‘wavefunction’ to a group of ten undergraduate-level students at an institute in India which excels in teaching and research of basic sciences. Based on the written responses, all ten students were interviewed in detail to unravel the exact areas of difficulty in visualization of ‘wavefunction’. The outcome of present study not only reveals the gray areas in students’ conceptualization, but also provides a plausible route to address the issues at the pedagogical level within the classroom.
We prove that the theorems of TDDFT can be extended to a class of qubit Hamiltonians that are universal for quantum computation. The theorems of TDDFT applied to universal Hamiltonians imply that single-qubit expectation values can be used as the basic variables in quantum computation and information theory, rather than wavefunctions. From a practical standpoint this opens the possibility of approximating observables of interest in quantum computations directly in terms of single-qubit quantities (i.e. as density functionals). Additionally, we also demonstrate that TDDFT provides an exact prescription for simulating universal Hamiltonians with other universal Hamiltonians that have different, and possibly easier-to-realize two-qubit interactions. This establishes the foundations of TDDFT for quantum computation and opens the possibility of developing density functionals for use in quantum algorithms.
Presents an explanation, without mathematical equations, of the basic principles of quantummechanics. Includes wave-particle duality, the probability character of the wavefunction, and the uncertainty relations. (MLH)
Cyclobutadiene has a four-membered carbon ring with two double bonds, but this highly strained molecular configuration is almost square and, via a coordinated motion, the nuclei quantummechanically tunnels through the high-energy square state to a configuration equivalent to the initial configuration under a 90° rotation. This results in a square ground state, comprising a superposition of two molecular configurations, that is driven by quantum tunneling. Using a quantummechanical model, and an effective nuclear potential from density functional theory, we calculate the vibrational energy spectrum and the accompanying wavefunctions. We use the wavefunctions to identify the motions of the molecule and detail how different motions can enhance or suppress the tunneling rate. This is relevant for kinematics of tunneling-driven reactions, and we discuss these implications. We are also able to provide a qualitative account of how the molecule will respond to an external perturbation and how this may enhance or suppress infra-red-active vibrational transitions.
Styer, Daniel F.; Balkin, Miranda S.; Becker, Kathryn M.; Burns, Matthew R.; Dudley, Christopher E.; Forth, Scott T.; Gaumer, Jeremy S.; Kramer, Mark A.; Oertel, David C.; Park, Leonard H.; Rinkoski, Marie T.; Smith, Clait T.; Wotherspoon, Timothy D.
2002-03-01
Nine formulations of nonrelativistic quantummechanics are reviewed. These are the wavefunction, matrix, path integral, phase space, density matrix, second quantization, variational, pilot wave, and Hamilton-Jacobi formulations. Also mentioned are the many-worlds and transactional interpretations. The various formulations differ dramatically in mathematical and conceptual overview, yet each one makes identical predictions for all experimental results.
Nonrelativistic quantummechanics is commonly formulated in terms of wavefunctions (probability amplitudes) obeying the static and the time-dependent Schrödinger equations (SE). Despite the success of this representation of the quantum world a wave–particle duality concept is required to reconcile the theory with observations (experimental measurements). A first solution to this dichotomy was introduced in the de Broglie–Bohm theory according to which a pilot-wave (solution of the SE) is guiding the evolution of particle trajectories. Here, I propose a geometrization of quantummechanics that describes the time evolution of particles as geodesic lines in a curved space, whose curvature is inducedmore » by the quantum potential. This formulation allows therefore the incorporation of all quantum effects into the geometry of space–time, as it is the case for gravitation in the general relativity.« less
Hirschfelder, J. O.; Christoph, A. C.; Palke, W. E.
1974-01-01
Exact numerical calculations are made for scattering of quantummechanical particles hitting a square two-dimensional potential barrier (an exact analog of the Goos-Haenchen optical experiments). Quantummechanical streamlines are plotted and found to be smooth and continuous, to have continuous first derivatives even through the classical forbidden region, and to form quantized vortices around each of the nodal points. A comparison is made between the present numerical calculations and the stationary wave approximation, and good agreement is found between both the Goos-Haenchen shifts and the reflection coefficients. The time-independent Schroedinger equation for real wavefunctions is reduced to solving a nonlinear first-order partial differential equation, leading to a generalization of the Prager-Hirschfelder perturbation scheme. Implications of the hydrodynamical formulation of quantummechanics are discussed, and cases are cited where quantum and classical mechanical motions are identical.
The way to determine the renormalized energy of inhomogeneous systems of a quantum field under an external potential is established for both equilibrium and nonequilibrium scenarios based on thermo field dynamics. The key step is to find an extension of the on-shell concept valid in homogeneous case. In the nonequilibrium case, we expand the field operator by time-dependent wavefunctions that are solutions of the appropriately chosen differential equation, synchronizing with temporal change of thermal situation, and the quantum transport equation is derived from the renormalization procedure. Through numerical calculations of a triple-well model with a reservoir, we show that the number distribution and the time-dependent wavefunctions are relaxed consistently to the correct equilibrium forms at the long-term limit.
Wave-function collapse models are considered to be the modified theories of standard quantummechanics at the macroscopic level. By introducing nonlinear stochastic terms in the Schrödinger equation, these models (different from standard quantummechanics) predict that it is fundamentally impossible to prepare macroscopic systems in macroscopic superpositions. The validity of these models can only be examined by experiments, and hence efficient protocols for these kinds of experiments are greatly needed. Here we provide a protocol that is able to probe the postulated collapse effect by means of the entanglement of the center-of-mass motion of two nanospheres optically trapped in a Fabry-Pérot cavity. We show that the collapse noise results in a large reduction of the steady-state entanglement, and the entanglement, with and without the collapse effect, shows distinguishable scalings with certain system parameters, which can be used to determine unambiguously the effect of these models.
Amaran, Saieswari; Kosloff, Ronnie; Tomza, Michał; Skomorowski, Wojciech; Pawłowski, Filip; Moszynski, Robert; Rybak, Leonid; Levin, Liat; Amitay, Zohar; Berglund, J. Martin; Reich, Daniel M.; Koch, Christiane P.
2013-10-01
Two-photon photoassociation of hot magnesium atoms by femtosecond laser pulses, creating electronically excited magnesium dimer molecules, is studied from first principles, combining ab initio quantum chemistry and molecular quantum dynamics. This theoretical framework allows for rationalizing the generation of molecular rovibrational coherence from thermally hot atoms [L. Rybak, S. Amaran, L. Levin, M. Tomza, R. Moszynski, R. Kosloff, C. P. Koch, and Z. Amitay, Phys. Rev. Lett. 107, 273001 (2011)]. Random phase thermal wavefunctions are employed to model the thermal ensemble of hot colliding atoms. Comparing two different choices of basis functions, random phase wavefunctions built from eigenstates are found to have the fastest convergence for the photoassociation yield. The interaction of the colliding atoms with a femtosecond laser pulse is modeled non-perturbatively to account for strong-field effects.
Sellier, Jean Michel, E-mail: jeanmichel.sellier@parallel.bas.bg
2015-09-15
A formulation of non-relativistic quantummechanics in terms of Newtonian particles is presented in the shape of a set of three postulates. In this new theory, quantumsystems are described by ensembles of signed particles which behave as field-less classical objects which carry a negative or positive sign and interact with an external potential by means of creation and annihilation events only. This approach is shown to be a generalization of the signed particle Wigner Monte Carlo method which reconstructs the time-dependent Wigner quasi-distribution function of a system and, therefore, the corresponding Schrödinger time-dependent wave-function. Its classical limit is discussedmore » and a physical interpretation, based on experimental evidences coming from quantum tomography, is suggested. Moreover, in order to show the advantages brought by this novel formulation, a straightforward extension to relativistic effects is discussed. To conclude, quantum tunnelling numerical experiments are performed to show the validity of the suggested approach.« less
Meyer, Ralf; Pototschnig, Johann V.; Hauser, Andreas W.; Ernst, Wolfgang E.
2016-06-01
Research on ultracold molecules has seen a growing interest recently in the context of high-resolution spectroscopy and quantum computation. The preparation of molecules in low vibrational levels of the ground state is experimentally challenging, and typically achieved by population transfer using excited electronic states. On the theoretical side, highly accurate potential energy surfaces are needed for a correct description of processes such as the coherent de-excitation from the highest and therefore weakly bound vibrational levels in the electronic ground state via couplings to electronically excited states. Particularly problematic is the correct description of potential features at large intermolecular distances. Franck-Condon overlap integrals for nuclear wavefunctions in barely bound vibrational states are extremely sensitive to inaccuracies of the potential at long range. In this study, we compare the predictions of common, wavefunction-based ab initio techniques for a known de-excitation mechanism in alkali-alkaline earth dimers. It is the aim to analyze the predictive power of these methods for a preliminary evaluation of potential cooling mechanisms in heteronuclear open shell systems which offer the experimentalist an electric as well as a magnetic handle for manipulation. The series of X-Sr molecules, with X = Li, Na, K and Rb, has been chosen for a direct comparison. Quantum degenerate mixtures of Rb and Sr have already been produced, making this combination very promising for the production of ultracold molecules. B. Pasquiou, A. Bayerle, S. M. Tzanova, S. Stellmer, J. Szczepkowski, M. Parigger, R. Grimm, and F. Schreck, Phys. Rev. A, 2013, 88, 023601
We discuss a general setup which allows the study of the perturbation theory of an arbitrary, locally harmonic 1D quantummechanical potential as well as its multi-variable (many-body) generalization. The latter may form a prototype for regularized quantum field theory. We first generalize the method of Bender-Wu,and derive exact recursion relations which allow the determination of the perturbative wave-function and energy corrections to an arbitrary order, at least in principle. For 1D systems, we implement these equations in an easy to use MATHEMATICA® package we call BenderWu. Our package enables quick home-computer computation of high orders of perturbation theory (about 100 orders in 10-30 s, and 250 orders in 1-2 h) and enables practical study of a large class of problems in QuantumMechanics. We have two hopes concerning the BenderWu package. One is that due to resurgence, large amount of non-perturbative information, such as non-perturbative energies and wave-functions (e.g. WKB wave functions), can in principle be extracted from the perturbative data. We also hope that the package may be used as a teaching tool, providing an effective bridge between perturbation theory and non-perturbative physics in textbooks. Finally, we show that for the multi-variable case, the recursion relation acquires a geometric character, and has a structure which allows parallelization to computer clusters.
Kent, Paul; McDaniel, Tyler; Li, Ying Wai; D'Azevedo, Ed
Within ab intio Quantum Monte Carlo (QMC) simulations, the leading numerical cost for large systems is the computation of the values of the Slater determinants in the trial wavefunctions. The evaluation of each Monte Carlo move requires finding the determinant of a dense matrix, which is traditionally iteratively evaluated using a rank-1 Sherman-Morrison updating scheme to avoid repeated explicit calculation of the inverse. For calculations with thousands of electrons, this operation dominates the execution profile. We propose a novel rank- k delayed update scheme. This strategy enables probability evaluation for multiple successive Monte Carlo moves, with application of accepted moves to the matrices delayed until after a predetermined number of moves, k. Accepted events grouped in this manner are then applied to the matrices en bloc with enhanced arithmetic intensity and computational efficiency. This procedure does not change the underlying Monte Carlo sampling or the sampling efficiency. For large systems and algorithms such as diffusion Monte Carlo where the acceptance ratio is high, order of magnitude speedups can be obtained on both multi-core CPU and on GPUs, making this algorithm highly advantageous for current petascale and future exascale computations.
In this paper we use numerical simulations to study a two-dimensional (2D) quantum dot (cavity) with two leads for passing currents (electrons, photons, etc.) through the system. By introducing an imaginary potential in each lead the system is made symmetric under parity-time inversion (PT symmetric). This system is experimentally realizable in the form of, e.g., quantum dots in low-dimensional semiconductors, optical and electromagnetic cavities, and other classical wave analogs. The computational model introduced here for studying spectra, exceptional points (EPs), wave-function symmetries and morphology, and current flow includes thousands of interacting states. This supplements previous analytic studies of few interacting states by providing more detail and higher resolution. The Hamiltonian describing the system is non-Hermitian; thus, the eigenvalues are, in general, complex. The structure of the wave functions and probability current densities are studied in detail at and in between EPs. The statistics for EPs is evaluated, and reasons for a gradual dynamical crossover are identified.
Chen, X. J.; Yu, T. J.; Lu, H. M.; Yuan, G. C.; Shen, B.; Zhang, G. Y.
2013-10-01
Using modified k.p perturbation method, the optical polarization properties of Al-rich AlGaN/AlN quantum wells (QWs) are studied. It is found that change of wavefunction overlaps between conduction band and valance subbands of heavy hole, light hole, and crystal-field split off hole is different. Such difference leads to the overturn of polarization degree and modulates optical polarization properties as well width and strain vary. This prompts that changing wavefunction overlaps of electron and hole can lead to a way to modulate optical polarization properties of Al-rich AlGaN/AlN QWs, on no condition that valence band order changes.
A well-known feature of quantummechanics is the secure exchange of secret bit strings which can then be used as keys to encrypt messages transmitted over any classical communication channel. It is demonstrated that this quantum key distribution allows a much more general and abstract access than commonly thought. The results include some generalizations of the Hilbert space version of quantum key distribution, but are based upon a general nonclassical extension of conditional probability. A special state-independent conditional probability is identified as origin of the superior security of quantum key distribution; this is a purely algebraic property of the quantum logic and represents the transition probability between the outcomes of two consecutive quantum measurements.
The Hohenberg-Kohn theorem of Density Functional Theory (DFT), and extensions thereof, tells us that all properties of a system of electrons can be determined through their density, which uniquely determines the many-body wave-function. Given access to the appropriate, universal, functionals of the density we would, in theory, be able to determine all observables of any electronic system, without explicit reference to the wave-function. On the other hand, the wave-function is at the core of Quantum Information (QI), with the wave-function of a set of qubits being the central computational resource in a quantum computer. While there is seemingly little overlap between DFT and QI, reliance upon observables form a key connection. Though the time-evolution of the wave-function and associated phase information is fundamental to quantum computation, the initial and final states of a quantum computer are characterized by observables of the system. While observables can be extracted directly from a system's wave-function, DFT tells us that we may be able to intuit a method for extracting them from its density. In this talk, I will review the fundamentals of DFT and how these principles connect to the world of QI. This will range from DFT's utility in the engineering of physical qubits, to the possibility of using it to efficiently (but approximately) simulate Hamiltonians at the logical level. The apparent paradox of describing algorithms based on the quantummechanical many-body wave-function with a DFT-like theory based on observables will remain a focus throughout. The ultimate goal of this talk is to initiate a dialog about what DFT could do for QI, in theory and in practice. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
The last five years have witnessed an amazing development in the field of nano- and micromechanics. What was widely considered fantasy ten years ago is about to become an experimental reality: the quantum regime of mechanicalsystems is within reach of current experiments. Two factors (among many) have contributed significantly to this situation. As part of the widespread effort into nanoscience and nanofabrication, it is now possible to produce high-quality nanomechanical and micromechanical resonators, spanning length scales of millimetres to nanometres, and frequencies from kilohertz to gigahertz. Researchers coupled these mechanical elements to high-sensitivity actuation and readout systems such as single-electron transistors, quantum dots, atomic point contacts, SQUID loops, high-finesse optical or microwave-cavities etc. Some of these ultra-sensitive readout schemes are in principle capable of detection at the quantum limit and a large part of the experimental effort is at present devoted to achieving this. On the other hand, the fact that the groups working in the field come from various different physics backgrounds—the authors of this editorial are a representative sample—has been a constant source of inspiration for helpful theoretical and experimental tools that have been adapted from other fields to the mechanical realm. To name just one example: ideas from quantum optics have led to the recent demonstration (both in theory and experiment) that coupling a mechanical resonator to a high-finesse optical cavity can be fully analogous to the well-known sideband-resolved laser cooling of ions and hence is capable in principle of cooling a mechanical mode into its quantum ground state. There is no doubt that such interdisciplinarity has been a crucial element for the development of the field. It is interesting to note that a very similar sociological phenomenon occurred earlier in the quantum information community, an area which is deeply enriched by the
Schemmer, M.; Johnson, A.; Photopoulos, R.; Bouchoule, I.
2017-04-01
The effect of atom losses on a homogeneous one-dimensional Bose gas lying within the quasicondensate regime is investigated using a Monte Carlo wave-function approach. The evolution of the system is calculated, conditioned by the loss sequence, namely, the times of individual losses and the position of the removed atoms. We describe the gas within the linearized Bogoliubov approach. For each mode, we find that, for a given quantum trajectory, the state of the system converges towards a coherent state, i.e., the ground state, displaced in phase space. We show that, provided losses are recorded with a temporal and spatially resolved detector, quantum feedback can be implemented and cooling to the ground state of one or several modes can be realized.
We construct the independent bases on the spatial wavefunction of four-identical-particle systems classified under the rotational group SO(3) and the permutation group S{sub 4} with the usage of transformation coefficients that relate wavefunctions described in one set of internal coordinates with those in another. The basis functions for N⩽ 2 are presented in the explicit expressions based on the harmonic oscillator model. Such independent bases are supposed to play a key role in the construction of the wavefunctions of the five-quark states and the variation calculation of four-body systems. Our prescription avoids the spurious states and can be programmed formore » arbitrary N.« less
We give a formula to calculate a matrix element of a conserved current in the effective quantummechanics defined by the wavefunction-equivalent potentials proposed by the HAL QCD collaboration. As a first step, a non-relativistic field theory with two-channel coupling is considered as the original theory, with which a wavefunction-equivalent HAL QCD potential is obtained in a closed analytic form. The external field method is used to derive the formula by demanding that the result should agree with the original theory. With this formula, the matrix element is obtained by sandwiching the effective current operator between the left and right eigenfunctions of the effective Hamiltonian associated with the HAL QCD potential. In addition to the naive one-body current, the effective current operator contains an additional two-body term emerging from the degrees of freedom which has been integrated out.
Conventional quantum chemical solvation theories are based on the mean-field embedding approximation. That is, the electronic wavefunction is calculated in the presence of the mean field of the environment. In this paper a direct quantummechanical/molecular mechanical (QM/MM) analog of such a mean-field theory is formulated based on variational and perturbative frameworks. In the variational framework, an appropriate QM/MM free energy functional is defined and is minimized in terms of the trial wavefunction that best approximates the true QM wavefunction in a statistically averaged sense. Analytical free energy gradient is obtained, which takes the form of the gradient of effective QM energy calculated in the averaged MM potential. In the perturbative framework, the above variational procedure is shown to be equivalent to the first-order expansion of the QM energy (in the exact free energy expression) about the self-consistent reference field. This helps understand the relation between the variational procedure and the exact QM/MM free energy as well as existing QM/MM theories. Based on this, several ways are discussed for evaluating non-mean-field effects (i.e., statistical fluctuations of the QM wavefunction) that are neglected in the mean-field calculation. As an illustration, the method is applied to an S(N)2 Menshutkin reaction in water, NH(3)+CH(3)Cl-->NH(3)CH(3) (+)+Cl(-), for which free energy profiles are obtained at the Hartree-Fock, MP2, B3LYP, and BHHLYP levels by integrating the free energy gradient. Non-mean-field effects are evaluated to be <0.5 kcal/mol using a Gaussian fluctuation model for the environment, which suggests that those effects are rather small for the present reaction in water.
We study the properties of wavefunctions and the wavepacket dynamics in quasiperiodic tight-binding models in one, two, and three dimensions. The atoms in the one-dimensional quasiperiodic chains are coupled by weak and strong bonds aligned according to the Fibonacci sequence. The associated d-dimensional quasiperiodic tilings are constructed from the direct product of d such chains, which yields either the hypercubic tiling or the labyrinth tiling. This approach allows us to consider fairly large systems numerically. We show that the wavefunctions of the system are multifractal and that their properties can be related to the structure of the system in the regime of strong quasiperiodic modulation by a renormalization group (RG) approach. We also study the dynamics of wavepackets to get information about the electronic transport properties. In particular, we investigate the scaling behaviour of the return probability of the wavepacket with time. Applying again the RG approach we show that in the regime of strong quasiperiodic modulation the return probability is governed by the underlying quasiperiodic structure. Further, we also discuss lower bounds for the scaling exponent of the width of the wavepacket and propose a modified lower bound for the absolute continuous regime.
We present a rigorous path integral treatment of free motion on the Poincaré upper half plane. The Poincaré upper half plane, as a riemannian manifold, has recently become important in string theory and in the theory of quantum chaos. The calculation is done by a time-transformation and the use of the canonical method for determining quantum corrections to the classical lagrangian. Furthermore, we shall show that the same method also works for Liouville quantummechanics. In both cases, the energy spectrum and the normalized wavefunctions are determined.
The large dielectric constant and small effective mass in a semiconductor allows a description of its electronic states in terms of envelope wavefunctions whose energy, time, and length scales are mesoscopic, i.e., halfway between those of atomic and those of condensed matter systems. This property makes it possible to demonstrate and investigate many quantummechanical, many-body, and quantum kinetic phenomena with tabletop experiments that would be nearly impossible in other systems. This, along with the ability to custom-design semiconductor nanostructures, makes semiconductors an ideal laboratory for experimental investigations. We present an overview of some of the most exciting results obtained in semiconductors in recent years using the technique of ultrafast nonlinear optical spectrocopy. These results show that Coulomb correlation plays a major role in semiconductors and makes them behave more like a strongly interacting system than like an atomic system. The results provide insights into the physics of strongly interacting systems that are relevant to other condensed matter systems, but not easily accessible in other materials. PMID:10716981
Wavefunction collapse models modify Schrödinger's equation so that it describes the collapse of a superposition of macroscopically distinguishable states as a genuine physical process [PRA 42, 78 (1990)]. This provides a basis for the resolution of the quantum measurement problem. An additional generic consequence of the collapse mechanism is that it causes particles to exhibit a tiny random diffusive motion. Furthermore, the diffusions of two sufficiently nearby particles are positively correlated -- it is more likely that the particles diffuse in the same direction than would happen if they behaved independently [PRA 89, 032713 (2014)]. The use of this effect is proposed as an experimental test of wave function collapse models in which pairs of nanoparticles are simultaneously released from nearby traps and allowed a brief period of free fall. The random displacements of the particles are then measured. The experiment must be carried out at sufficiently low temperature and pressure for the collapse effects to dominate over the ambient environmental noise. It is argued that these constraints can be satisfied by current technologies for a large class of viable wavefunction collapse models. Work supported by the Templeton World Charity Foundation.
We propose partial measurements as a conceptual tool to understand how to operate with counterfactual claims in quantum physics. Indeed, unlike standard von Neumann measurements, partial measurements can be reversed probabilistically. We first analyze the consequences of this rather unusual feature for the principle of superposition, for the complementarity principle, and for the issue of hidden variables. Then we move on to exploring non-local contexts, by reformulating the EPR paradox, the quantum teleportation experiment, and the entanglement-swapping protocol for the situation in which one uses partial measurements followed by their stochastic reversal. This leads to a number of counter-intuitive results, which are shown to be resolved if we give up the idea of attributing reality to the wavefunction of a single quantumsystem.
This document should be considered in its separation; there are three distinct topics contained within and three distinct chapters within the body of works. In a similar fashion, this abstract should be considered in three parts. Firstly, we explored the existence of multiply-charged atomic ions by having developed a new set of dimensional scaling equations as well as a series of relativistic augmentations to the standard dimensional scaling procedure and to the self-consistent field calculations. Secondly, we propose a novel method of predicting drug efficacy in hopes to facilitate the discovery of new small molecule therapeutics by modeling the agonist-protein system as being similar to the process of Inelastic Electron Tunneling Spectroscopy. Finally, we facilitate the instruction in basic quantummechanical topics through the use of quantum games; this method of approach allows for the generation of exercises with the intent of conveying the fundamental concepts within a first year quantummechanics classroom. Furthermore, no to be mentioned within the body of the text, yet presented in appendix form, certain works modeling the proliferation of cells types within the confines of man-made lattices for the purpose of facilitating artificial vascular transplants. In Chapter 2, we present a theoretical framework which describes multiply-charged atomic ions, their stability within super-intense laser fields, also lay corrections to the systems due to relativistic effects. Dimensional scaling calculations with relativistic corrections for systems: H, H-, H 2-, He, He-, He2-, He3- within super-intense laser fields were completed. Also completed were three-dimensional self consistent field calculations to verify the dimensionally scaled quantities. With the aforementioned methods the system's ability to stably bind 'additional' electrons through the development of multiple isolated regions of high potential energy leading to nodes of high electron density is shown
Oliva, Maxime; Kakofengitis, Dimitris; Steuernagel, Ole
2018-07-01
Phase space dynamics in classical mechanics is described by transport along trajectories. Anharmonic quantummechanicalsystems do not allow for a trajectory-based description of their phase space dynamics. This invalidates some approaches to quantum phase space studies. We first demonstrate the absence of trajectories in general terms. We then give an explicit proof for all quantum phase space distributions with negative values: we show that the generation of coherences in anharmonic quantummechanicalsystems is responsible for the occurrence of singularities in their phase space velocity fields, and vice versa. This explains numerical problems repeatedly reported in the literature, and provides deeper insight into the nature of quantum phase space dynamics.
Variational methods in quantummechanics are customarily presented as invaluable techniques to find approximate estimates of ground state energies. In the present paper a short catalogue of different celebrated potential distributions (both 1D and 3D), for which an exact and complete (energy and wavefunction) ground state determination can be achieved in an elementary way, is illustrated. No previous knowledge of calculus of variations is required. Rather, in all presented cases the exact energy functional minimization is achieved by using only a couple of simple mathematical tricks: ‘completion of square’ and integration by parts. This makes our approach particularly suitable for undergraduates. Moreover, the key role played by particle localization is emphasized through the entire analysis. This gentle introduction to the variational method could also be potentially attractive for more expert students as a possible elementary route toward a rather advanced topic on quantummechanics: the factorization method. Such an unexpected connection is outlined in the final part of the paper.
A fully functional quantum computer must contain at least two important components: a quantum memory for storing and manipulating quantum information and a quantum data bus to securely transfer information between quantum memories. Typically, a quantum memory is composed of a matter system, such as an atom or an electron spin, due to their prolonged quantum coherence. Alternatively, a quantum data bus is typically composed of some propagating degree of freedom, such as a photon, which can retain quantum information over long distances. Therefore, a quantum computer will likely be a hybrid quantum device, consisting of two or more disparate quantumsystems. However, there must be a reliable and controllable quantum interface between the memory and bus in order to faithfully interconvert quantum information. The current engineering challenge for quantum computers is scaling the device to large numbers of controllable quantumsystems, which will ultimately depend on the choice of the quantum elements and interfaces utilized in the device. In this thesis, we present and characterize a hybrid quantum device comprised of single nitrogen-vacancy (NV) centers embedded in a high quality factor diamond mechanical oscillator. The electron spin of the NV center is a leading candidate for the realization of a quantum memory due to its exceptional quantum coherence times. On the other hand, mechanical oscillators are highly sensitive to a wide variety of external forces, and have the potential to serve as a long-range quantum bus between quantumsystems of disparate energy scales. These two elements are interfaced through crystal strain generated by vibrations of the mechanical oscillator. Importantly, a strain interface allows for a scalable architecture, and furthermore, opens the door to integration into a larger quantum network through coupling to an optical interface. There are a few important engineering challenges associated with this device. First, there have been no
Goldschleger, I U; Golschleger, I U; van Staveren, M N; Apkarian, V Ara
2013-07-21
We present the moving picture of a molecular bond, in phase-space, in real-time, at resolution limited by quantum uncertainty. The images are tomographically reconstructed Wigner distribution functions (WDF) obtained from four-wave mixing measurements on Br2-doped ice. The WDF completely characterizes the dissipative quantum evolution of the system, which despite coupling to the environment retains quantum coherence, as evidenced by its persistent negative Wigner hole. The spectral decomposition of the WDF allows a direct visualization of wavefunctions and spatiotemporal coherences of the system and the system-bath interaction. The measurements vividly illustrate nonclassical wave mechanics in a many-body system, in ordinary condensed matter.
Time dynamics of isolated many-body quantumsystems has long been an elusive subject, perhaps most urgently needed in the foundations of quantum statistical mechanics. In generic systems, one expects the nonequilibrium dynamics to lead to thermalization: a relaxation to states where the values of macroscopic quantities are stationary, universal with respect to widely differing initial conditions, and predictable through the time-tested recipe of statistical mechanics. The relaxation mechanism is not obvious, however; dynamical chaos cannot play the key role as it does in classical systems since quantum evolution is linear. Here we demonstrateootnotetextM. Rigol, V. Dunjko, and M. Olshanii, to appear in Nature (2008), using the results of an ab initio numerical experiment with 5 hard-core bosons moving in a 5x5 lattice, that in quantumsystems thermalization happens not in course of time evolution but instead at the level of individual eigenstates, as first proposed by DeutschootnotetextJ. M. Deutsch, Phys.Rev. A 43, 2046 (1991) and SrednickiootnotetextM. Srednicki, Phys. Rev. E 50, 888 (1994).
We introduce a generalized ground state variational wavefunction for parabolically confined two-dimensional quantum dots that equally applies to both cases of weak (or zero) and strong magnetic field. The wavefunction has a Laughlin-like form in the limit of infinite magnetic field, but transforms into a Jastrow-Slater wavefunction at zero magnetic field. At intermediate magnetic fields (where a fraction of electrons is spin-reversed) it resembles Halperin's spin-reversed wavefunction for the fractional quantum Hall effect. The properties of this variational wavefunction are illustrated for the case of two-dimensional quantum dot helium (a system of two interacting electrons in a parabolic confinement potential) where we find the description to be an excellent representation of the true ground state for the whole range of magnetic fields.
There is great interest in quantummechanics as an "emergent" phenomenon. The program holds that nonobvious patterns and laws can emerge from complicated physical systems operating by more fundamental rules. We find a new approach where quantummechanics itself should be viewed as an information management tool not derived from physics nor depending on physics. The main accomplishment of quantum-style theory comes in expanding the notion of probability. We construct a map from macroscopic information as data" to quantum probability. The map allows a hidden variable description for quantum states, and efficient use of the helpful tools of quantummechanics in unlimited circumstances. Quantum dynamics via the time-dependent Shroedinger equation or operator methods actually represents a restricted class of classical Hamiltonian or Lagrangian dynamics, albeit with different numbers of degrees of freedom. We show that under wide circumstances such dynamics emerges from structureless dynamical systems. The uses of the quantum information management tools are illustrated by numerical experiments and practical applications
The physical description of all materials is rooted in quantummechanics, which describes how atoms bond and electrons interact at a fundamental level. Although these quantum effects can in many cases be approximated by a classical description at the macroscopic level, in recent years there has been growing interest in material systems where quantum effects remain manifest over a wider range of energy and length scales. Such quantum materials include superconductors, graphene, topological insulators, Weyl semimetals, quantum spin liquids, and spin ices. Many of them derive their properties from reduced dimensionality, in particular from confinement of electrons to two-dimensional sheets. Moreover, they tend to be materials in which electrons cannot be considered as independent particles but interact strongly and give rise to collective excitations known as quasiparticles. In all cases, however, quantum-mechanical effects fundamentally alter properties of the material. This Review surveys the electronic properties of quantum materials through the prism of the electron wavefunction, and examines how its entanglement and topology give rise to a rich variety of quantum states and phases; these are less classically describable than conventional ordered states also driven by quantummechanics, such as ferromagnetism.
Starting from a complex 4-potential A = αdβ we show that the 4-current density in electromagnetism and the probability current density in relativistic quantummechanics are of identical form. With the Dirac-Clifford algebra Cl1,3 as mathematical basis, the given 4-potential allows topological solutions of the fields, quite similar to Bateman's construction, but with a double field solution that was overlooked previously. A more general nullvector condition is found and wave-functions of charged and neutral particles appear as topological configurations of the electromagnetic fields.
We present a method to analyze the wavefunctions of six-vertex models by extending the Izergin-Korepin analysis originally developed for domain wall boundary partition functions. First, we apply the method to the case of the basic wavefunctions of the XXZ-type six-vertex model. By giving the Izergin-Korepin characterization of the wavefunctions, we show that these wavefunctions can be expressed as multiparameter deformations of the quantum group deformed Grothendieck polynomials. As a second example, we show that the Izergin-Korepin analysis is effective for analysis of the wavefunctions for a triangular boundary and present the explicit forms of the symmetric functions representing these wavefunctions. As a third example, we apply the method to the elliptic Felderhof model which is a face-type version and an elliptic extension of the trigonometric Felderhof model. We show that the wavefunctions can be expressed as one-parameter deformations of an elliptic analog of the Vandermonde determinant and elliptic symmetric functions.
Humble, Travis S [Knoxville, TN; Bennink, Ryan S [Knoxville, TN; Grice, Warren P [Oak Ridge, TN
2011-12-13
The use of quantum-mechanically entangled photons for monitoring the integrity of a physical border or a communication link is described. The no-cloning principle of quantum information science is used as protection against an intruder's ability to spoof a sensor receiver using a `classical` intercept-resend attack. Correlated measurement outcomes from polarization-entangled photons are used to protect against quantum intercept-resend attacks, i.e., attacks using quantum teleportation.
Scan QuantumMechanics is a novel interpretation of some aspects of quantummechanics in which the superposition of states is only an approximate effective concept. Quantumsystems scan all possible states in the superposition and switch randomly and very rapidly among them. A crucial property that we postulate is quantum inertia, that increases whenever a constituent is added, or the system is perturbed with all kinds of interactions. Once the quantum inertia Iq reaches a critical value Icr for an observable, the switching among its different eigenvalues stops and the corresponding superposition comes to an end, leaving behind a system with a well defined value of that observable. Consequently, increasing the mass, temperature, gravitational strength, etc. of a quantumsystem increases its quantum inertia until the superposition of states disappears for all the observables and the system transmutes into a classical one. Moreover, the process could be reversible. Entanglement can only occur between quantumsystems because an exact synchronization between the switchings of the systems involved must be established in the first place and classical systems do not have any switchings to start with. Future experiments might determine the critical inertia Icr corresponding to different observables, which translates into a critical mass Mcr for fixed environmental conditions as well as critical temperatures, critical electric and magnetic fields, etc. In addition, this proposal implies a new radiation mechanism from astrophysical objects with strong gravitational fields, giving rise to non-thermal synchrotron emission, that could contribute to neutron star formation. Superconductivity, superfluidity, Bose-Einstein condensates, and any other physical phenomena at very low temperatures must be reanalyzed in the light of this interpretation, as well as mesoscopic systems in general.
We present a theoretical framework for the dynamics of bosonic Bogoliubov quasiparticles. We call it Lorentz quantummechanics because the dynamics is a continuous complex Lorentz transformation in complex Minkowski space. In contrast, in usual quantummechanics, the dynamics is the unitary transformation in Hilbert space. In our Lorentz quantummechanics, three types of state exist: space-like, light-like and time-like. Fundamental aspects are explored in parallel to the usual quantummechanics, such as a matrix form of a Lorentz transformation, and the construction of Pauli-like matrices for spinors. We also investigate the adiabatic evolution in these mechanics, as well as the associated Berry curvature and Chern number. Three typical physical systems, where bosonic Bogoliubov quasi-particles and their Lorentz quantum dynamics can arise, are presented. They are a one-dimensional fermion gas, Bose-Einstein condensate (or superfluid), and one-dimensional antiferromagnet.
The familiar concepts of state vectors and operators in quantummechanics rely on associative products of observables. However, these notions do not apply to some exotic systems such as magnetic monopoles, which have long been known to lead to nonassociative algebras. Their quantum physics has remained obscure. This Letter presents the first derivation of potentially testable physical results in nonassociative quantummechanics, based on effective potentials. They imply new effects which cannot be mimicked in usual quantummechanics with standard magnetic fields.
The Hamiltonian of the quantum Calogero-Sutherland model of N identical particles on the circle with 1/r 2 interactions has eigenfunctions consisting of Jack polynomials times the base state. By use of the generalized Jack polynomials taking values in modules of the symmetric group and the matrix solution of a system of linear differential equations one constructs novel eigenfunctions of the Hamiltonian. Like the usual wavefunctions each eigenfunction determines a symmetric probability density on the N-torus. The construction applies to any irreducible representation of the symmetric group. The methods depend on the theory of generalized Jack polynomials due to Griffeth, and the Yang-Baxter graph approach of Luque and the author.
The main foundational issue for quantum information is: What is quantum information about? What does it refer to? Classical information typically refers to physical properties, and since classical is a subset of quantum information (assuming the world is quantummechanical), quantum information should--and, it will be argued, does--refer to quantum physical properties represented by projectors on appropriate subspaces of a quantum Hilbert space. All sorts of microscopic and macroscopic properties, not just measurement outcomes, can be represented in this way, and are thus a proper subject of quantum information. The Stern-Gerlach experiment illustrates this. When properties are compatible, which is to say their projectors commute, Shannon's classical information theory based on statistical correlations extends without difficulty or change to the quantum case. When projectors do not commute, giving rise to characteristic quantum effects, a foundation for the subject can still be constructed by replacing the ``measurement and wave-function collapse'' found in textbooks--an efficient calculational tool, but one giving rise to numerous conceptual difficulties--with a fully consistent and paradox free stochastic formulation of standard quantummechanics. This formulation is particularly helpful in that it contains no nonlocal superluminal influences; the reason the latter carry no information is that they do not exist.
A 2D Ising model with transverse field on a triangular lattice is studied using exact diagonalization. The quantum entanglement of the system is quantified by the entanglement of formation. The ground state property of the system is studied and the quantified entanglement is shown to be closely related to the ground state wavefunction while the singularity in the entanglement as a function of the transverse field is a reasonable indicator of the quantum phase transition. In order to tune the entanglement, one can either include an impurity in the otherwise homogeneous system whose strength is tunable, or one can vary the external transverse field as a tuner. The latter kind of tuning involves complicated dynamical properties of the system. From the study of the dynamics on a comparatively smaller system, we provide ways to tune the entanglement without triggering any decoherence. The finite temperature effect is also discussed. Besides showing above physical results, the realization of the trace-minimization method in our system is provided; the scalability of such method to larger systems is argued.
It is shown that a periodic emergence and destruction of an additional quantum number leads to an exponential growth of energy of a quantummechanicalsystem subjected to a slow periodic variation of parameters. The main example is given by systems (e.g., quantum billiards and quantum graphs) with periodically divided configuration space. In special cases, the process can also lead to a long period of cooling that precedes the acceleration, and to the desertion of the states with a particular value of the quantum number.
Full-dimensional quantummechanics calculations were performed to determine the vibrational energy levels of HOCO and DOCO based on an accurate potential energy surface. Almost all of the vibrational energy levels up to 3500 cm -1 from the vibrational ground state were assigned, and the calculated energy levels in this work are well in agreement with the reported results by Bowman. The corresponding full dimensional wavefunctions present some special features. When the energy level approaches the barrier height, the trans-HOCO and cis-HOCO states strongly couple through tunneling interactions, and the tunneling interaction and Fermi resonance were observed in the DOCO system. The energy level patterns of trans-HOCO, cis-HOCO and trans-DOCO provide a reasonable fitted barrier height using the fitting formula of Field et al., however, a discrepancy exists for the cis-DOCO species which is considered as a random event. Our full-dimensional calculations give positive evidence for the accuracy of the spectroscopic characterization model of the isomerization transition state reported by Field et al., which was developed from one-dimensional model systems. Furthermore, the special case of cis-DOCO in this work means that the isotopic substitution can solve the problem of the accidental failure of Field's spectroscopic characterization model.
A quantum-mechanical transport equation (QMTE) is derived which should be applicable to a wide range of problems involving the interaction of radiation with atoms or molecules which are also subject to collisions with perturber atoms. The equation follows the time evolution of the macroscopic atomic density matrix elements of atoms located at classical position R and moving with classical velocity v. It is quantummechanical in the sense that all collision kernels or rates which appear have been obtained from a quantum-mechanical theory and, as such, properly take into account the energy-level variations and velocity changes of the active (emitting or absorbing) atom produced in collisions with perturber atoms. The present formulation is better suited to problems involving high-intensity external fields, such as those encountered in laser physics.
A general noncommutative quantummechanicalsystem in a central potential V=V(r) in two dimensions is considered. The spectrum is bounded from below and, for large values of the anticommutative parameter θ, we find an explicit expression for the eigenvalues. In fact, any quantummechanicalsystem with these characteristics is equivalent to a commutative one in such a way that the interaction V(r) is replaced by V=V(HHO,Lz), where HHO is the Hamiltonian of the two-dimensional harmonic oscillator and Lz is the z component of the angular momentum. For other finite values of θ the model can be solved by using perturbation theory.
We introduce an intramolecular energy decomposition scheme for analyzing non-covalent interactions within molecules in the spirit of symmetry-adapted perturbation theory (SAPT). The proposed intra-SAPT approach is based upon the Chemical Hamiltonian of Mayer [Int. J. Quantum Chem. 23(2), 341–363 (1983)] and the recently introduced zeroth-order wavefunction [J. F. Gonthier and C. Corminboeuf, J. Chem. Phys. 140(15), 154107 (2014)]. The scheme decomposes the interaction energy between weakly bound fragments located within the same molecule into physically meaningful components, i.e., electrostatic-exchange, induction, and dispersion. Here, we discuss the key steps of the approach and demonstrate that a single-determinant wavefunction can already delivermore » a detailed and insightful description of a wide range of intramolecular non-covalent phenomena such as hydrogen bonds, dihydrogen contacts, and π − π stacking interactions. Intra-SAPT is also used to shed the light on competing intra- and intermolecular interactions.« less
Strambini, E; Makarenko, K S; Abulizi, G; de Jong, M P; van der Wiel, W G
2016-01-06
Nonlocality is a key feature discriminating quantum and classical physics. Quantum-interference phenomena, such as Young's double slit experiment, are one of the clearest manifestations of nonlocality, recently addressed as dynamical to specify its origin in the quantum equations of motion. It is well known that loss of dynamical nonlocality can occur due to (partial) collapse of the wavefunction due to a measurement, such as which-path detection. However, alternative mechanisms affecting dynamical nonlocality have hardly been considered, although of crucial importance in many schemes for quantum information processing. Here, we present a fundamentally different pathway of losing dynamical nonlocality, demonstrating that the detailed geometry of the detection scheme is crucial to preserve nonlocality. By means of a solid-state quantum-interference experiment we quantify this effect in a diffusive system. We show that interference is not only affected by decoherence, but also by a loss of dynamical nonlocality based on a local reduction of the number of quantum conduction channels of the interferometer. With our measurements and theoretical model we demonstrate that this mechanism is an intrinsic property of quantum dynamics. Understanding the geometrical constraints protecting nonlocality is crucial when designing quantum networks for quantum information processing.
Correa, Alfredo; Reboredo, Fernando; Balseiro, Carlos
2005-03-01
We present a theoretical method for the design and optimization of quantum corrals[1] with specific electronic properties. Taking advantage that spins are subject to a RKKY interaction that is directly controlled by the scattering of the quantum corral, we design corral structures that reproduce spin Hamiltonians with coupling constants determined a priori[2]. We solve exactly the bi-dimensional scattering problem for each corral configuration within the s-wave approximation[3] and subsequently the geometry of the quantum corral is optimized by means of simulated annealing[4] and genetic algorithms[5]. We demonstrate the possibility of automatic design of structures with complicated target electronic properties[6]. This work was performed under the auspices of the US Department of Energy by the University of California at the LLNL under contract no W-7405-Eng-48. [1] M. F. Crommie, C. P. Lutz and D. M. Eigler, Nature 403, 512 (2000) [2] D. P. DiVincenzo et al., Nature 408, 339 (2000) [3] G. A. Fiete and E. J. Heller, Rev. Mod. Phys. 75, 933 (2003) [4] M. R. A. T. N. Metropolis et al., J. Chem. Phys. 1087 (1953) [5] E. Aarts and J. K. Lenstra, eds. Local search in combinatorial problems (Princeton University Press, 1997) [6] A. A. Correa, F. Reboredo and C. Balseiro, Phys. Rev. B (in press).
The argument follows from the viewpoint that quantummechanics is taken not in the usual form involving vectors and linear operators in Hilbert spaces, but as a boundary value problem for a special class of partial differential equations-in the present work, the nonrelativistic Schrodinger equation for motion of a structureless particle in four- dimensional space-time in the presence of a potential energy distribution that can be time-as well as space-dependent. The domain of interest is taken to be one of two semi-infinite boxes, one bounded by two t=constant planes and the other by two t=constant planes. Each gives rise to a characteristic boundary value problem: one in which the initial, input values on one t=constant wall are given, with zero asymptotic wavefunction values in all spatial directions, the output being the values on the second t=constant wall; the second with certain input values given on both z=constant walls, with zero asymptotic values in all directions involving time and the other spatial coordinates, the output being the complementary values on the z=constant walls. The first problem corresponds to ordinary quantummechanics; the second, to a fully time-dependent version of a problem normally considered only for the steady state (time-independent Schrodinger equation). The second problem is formulated in detail. A conserved indefinite metric is associated with space-like propagation, where the sign of the norm of a unidirectional state corresponds to its spatial direction of travel.
This work presents a general model for open quantumsystems using an information game along the lines of Jaynes’ original work. It is shown how an energy based reweighting of propagators provides a novel moment generating function at each time point in the process. Derivatives of the generating function give moments of the time derivatives of observables. Aside from the mathematically helpful properties, the ansatz reproduces key physics of stochastic quantum processes. At high temperature, the average density matrix follows the Caldeira-Leggett equation. Its associated Langevin equation clearly demonstrates the emergence of dissipation and decoherence time scales, as well as an additional diffusion due to quantum confinement. A consistent interpretation of these results is that decoherence and wavefunction collapse during measurement are directly related to the degree of environmental noise, and thus occur because of subjective uncertainty of an observer.
We review selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics. We cover topics such as equilibration and thermalisation in pure state statistical mechanics, the eigenstate thermalisation hypothesis, the equivalence of ensembles, non-equilibration dynamics following global and local quenches as well as ramps. We also address initial state independence, absence of thermalisation, and many-body localisation. We elucidate the role played by key concepts for these phenomena, such as Lieb-Robinson bounds, entanglement growth, typicality arguments, quantum maximum entropy principles and the generalised Gibbs ensembles, and quantum (non-)integrability. We put emphasis on rigorous approaches and present the most important results in a unified language.
We review selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics. We cover topics such as equilibration and thermalisation in pure state statistical mechanics, the eigenstate thermalisation hypothesis, the equivalence of ensembles, non-equilibration dynamics following global and local quenches as well as ramps. We also address initial state independence, absence of thermalisation, and many-body localisation. We elucidate the role played by key concepts for these phenomena, such as Lieb-Robinson bounds, entanglement growth, typicality arguments, quantum maximum entropy principles and the generalised Gibbs ensembles, and quantum (non-)integrability. We put emphasis on rigorous approaches and present the most important results in a unified language.
We present a generally covariant approach to quantummechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime". We show that this covariant starting point makes quantization into a purely geometric flatness condition. This makes quantummechanics purely geometric, and possibly even topological. Our approach is especially useful for time-dependent problems and systems subject to ambiguities in choices of clock or observer. As a byproduct, we give a derivation and generalization of the Wigner functions of standard quantummechanics.
Schwarz, Kathleen; Letchworth Weaver, Kendra; Arias, T. A.; Hennig, Richard G.
2011-03-01
Solvation qualitatively alters the energetics of diverse processes from protein folding to reactions on catalytic surfaces. An explicit description of the solvent in quantum-mechanical calculations requires both a large number of electrons and exploration of a large number of configurations in the phase space of the solvent. These problems can be circumvented by including the effects of solvent through a rigorous classical density-functional description of the liquid environment, thereby yielding free energies and thermodynamic averages directly, while eliminating the need for explicit consideration of the solvent electrons. We have implemented and tested this approach within the CASINO Quantum Monte Carlo code. Our method is suitable for calculations in any basis within CASINO, including b-spline and plane wave trial wavefunctions, and is equally applicable to molecules, surfaces, and crystals. For our preliminary test calculations, we use a simplified description of the solvent in terms of an isodensity continuum dielectric solvation approach, though the method is fully compatible with more reliable descriptions of the solvent we shall employ in the future.
Samosvat, D. M.; Chikalova-Luzina, O. P.; Vyatkin, V. M.; Zegrya, G. G.
2016-11-01
In present work the energy transfer between quantum dots by the exchange (Dexter) mechanism is analysed. The interdot Coulomb interaction is taken into consideration. It is assumed that the quantum dot-donor and the quantum dot-acceptor are made from the same compound A3B5 and embedded in the matrix of other material creating potential barriers for electron and holes. The dependences of the energy transfer rate on the quantum-dot system parameters are found using the Kane model that provides the most adequate description spectra of semiconductors A3B5. Numerical calculations show that the rate of the energy transfer by Dexter mechanism is comparable to the rate of the energy transfer by electrostatic mechanism at the distances approaching to the contact ones.
de Menezes, Miralvo B.; Fernandes, M. C. B.; Martins, Maria das Graças R.; Santana, A. E.; Vianna, J. D. M.
2018-02-01
Symplectic QuantumMechanics SQM considers a non-commutative algebra of functions on a phase space Γ and an associated Hilbert space HΓ to construct a unitary representation for the Galilei group. From this unitary representation the Schrödinger equation is rewritten in phase space variables and the Wigner function can be derived without the use of the Liouville-von Neumann equation. In this article we extend the methods of supersymmetric quantummechanics SUSYQM to SQM. With the purpose of applications in quantumsystems, the factorization method of the quantummechanical formalism is then set within supersymmetric SQM. A hierarchy of simpler hamiltonians is generated leading to new computation tools for solving the eigenvalue problem in SQM. We illustrate the results by computing the states and spectra of the problem of a charged particle in a homogeneous magnetic field as well as the corresponding Wigner function.
Density Matrix Theory is a QuantumMechanical formalism in which the wavefunction is eliminated and its role taken over by reduced density matrices. The interest of this is that, it allows one, in principle, to calculate any electronic property of a physical system, without having to solve the Schrodinger equation, using only two entities much simpler than an N-body wavefunction: first and second -order reduced density matrices. In practice, though, this very promising possibility faces the tremendous theoretical problem of N-representability, which has been solved for the former, but, until now, voids any hope of theoretically determining the latter. However, it has been shown that single determinant reduced density matrices of any order may be recovered from coherent X-ray diffraction data, if one provides a proper QuantumMechanical description of the Crystallography experiment. A deeper investigation of this method is the purpose of this work, where we, first, further study the calculation of X-ray reduced density matrices N-representable by a single Slater determinant. In this context, we independently derive necessary and sufficient conditions for the uniqueness of the method. We then show how to account for electron correlation in this model. For the first time, indeed, we derive highly accurate, yet practical, density matrices approximately N-representable by correlated-determinant wavefunctions. The interest of such a result lies in the QuantumMechanical validity of these density matrices, their property of being entirely obtainable from X-ray coherent diffraction data, their very high accuracy conferred by this known property of the N-representing wavefunction, as well as their definition as explicit functionals of the density. All of these properties are finally used in both a theoretical and a numerical application: in the former, we show that these density matrices may be used in the context of Density Functional Theory to highly accurately determine
A sketch of the quantummechanics for closed systems adequate for cosmology is presented. This framework is an extension and clarification of that of Everett and builds on several aspects of the post-Everett development. It especially builds on the work of Zeh, Zurek, Joos and Zeh, and others on the interactions of quantumsystems with the larger universe and on the ideas of Griffiths, Omnes, and others on the requirements for consistent probabilities of histories.
Ellis, John; Hagelin, John S.; Nanopoulos, D. V.; ...
1984-07-01
The treatment of quantum effects in gravitational fields indicates that pure states may evolve into mixed states, and Hawking has proposed modification of the axioms of field theory which incorporate the corresponding violation of quantummechanics. In this study we propose a modified hamiltonian equation of motion for density matrices and use it to interpret upper bounds on the violation of quantummechanics in different phenomenological situations. We apply our formalism to the K 0-K 0 system and to long baseline neutron interferometry experiments. In both cases we find upper bounds of about 2 × 10 -21 GeV on contributionsmore » to the single particle “hamiltonian” which violate quantummechanical coherence. We discuss how these limits might be improved in the future, and consider the relative significance of other successful tests of quantummechanics. Finally, an appendix contains model estimates of the magnitude of effects violating quantummechanics.« less
Hernandez, Hector H.; Chacon-Acosta, Guillermo; Departamento de Matematicas Aplicadas y Sistemas, Universidad Autonoma Metropolitana-Cuajimalpa, Artificios 40, Mexico D. F. 01120
In this work we study the quantum pendulum within the framework of momentous quantummechanics. This description replaces the Schroedinger equation for the quantum evolution of the system with an infinite set of classical equations for expectation values of configuration variables, and quantum dispersions. We solve numerically the effective equations up to the second order, and describe its evolution.
Quasiparticles in the Fractional Quantum Hall Effect behave qualitatively like electrons confined to the lowest landau level, and can do everything electrons can do, including condense into second generation Fractional Quantum Hall ground states. I review in this paper the reasoning leading to variational wavefunctions for ground state and quasiparticles in the 1/3 effect. I then show how two-quasiparticle eigenstates are uniquely determined from symmetry, and how this leads in a natural way to variational wavefunctions for composite states which have the correct densities (2/5, 2/7, ...). I show in the process that the boson, anyon and fermion representations for the quasiparticles used by Haldane, Halperin, and me are all equivalent. I demonstrate a simple way to derive Halperin`s multiple-valued quasiparticle wavefunction from the correct single-valued electron wavefunction. (auth)
Fritz London's seminal idea of ;quantummechanisms of macroscopic scale;, first articulated in 1946, was the unanticipated result of two decades of research, during which London pursued quantum-mechanical explanations of various kinds of systems of particles at different scales. He started at the microphysical scale with the hydrogen molecule, generalized his approach to chemical bonds and intermolecular forces, then turned to macrophysical systems like superconductors and superfluid helium. Along this path, he formulated a set of concepts-the quantummechanism of exchange, the rigidity of the wave function, the role of quantum statistics in multi-particle systems, the possibility of order in momentum space-that eventually coalesced into a new conception of systems of equal particles. In particular, it was London's clarification of Bose-Einstein condensation that enabled him to formulate the notion of superfluids, and led him to the recognition that quantummechanics was not, as it was commonly assumed, relevant exclusively as a micromechanics.
Li, Zhaokai; Yung, Man-Hong; Chen, Hongwei; Lu, Dawei; Whitfield, James D.; Peng, Xinhua; Aspuru-Guzik, Alán; Du, Jiangfeng
2011-01-01
Quantum ground-state problems are computationally hard problems for general many-body Hamiltonians; there is no classical or quantum algorithm known to be able to solve them efficiently. Nevertheless, if a trial wavefunction approximating the ground state is available, as often happens for many problems in physics and chemistry, a quantum computer could employ this trial wavefunction to project the ground state by means of the phase estimation algorithm (PEA). We performed an experimental realization of this idea by implementing a variational-wavefunction approach to solve the ground-state problem of the Heisenberg spin model with an NMR quantum simulator. Our iterative phase estimation procedure yields a high accuracy for the eigenenergies (to the 10−5 decimal digit). The ground-state fidelity was distilled to be more than 80%, and the singlet-to-triplet switching near the critical field is reliably captured. This result shows that quantum simulators can better leverage classical trial wave functions than classical computers PMID:22355607
The use of an orthogonal wavelet basis set (Optimized Maximum-N Generalized Coiflets) to effectively model physical systems in the time domain, in particular the electromagnetic (EM) pulse and quantummechanical (QM) wavefunction, is examined in this work. Although past research has demonstrated the benefits of wavelet basis sets to handle computationally expensive problems due to their multiresolution properties, the overlapping supports of neighboring wavelet basis functions poses problems when dealing with boundary conditions, especially with material interfaces in the EM case. Specifically, this talk addresses this issue using the idea of derivative matching creating fictitious grid points (T.A. Driscoll and B. Fornberg), but replaces the latter element with fictitious wavelet projections in conjunction with wavelet reconstruction filters. Two-dimensional (2D) systems are analyzed, EM pulse incident on silver cylinders and the QM electron wave packet circling the proton in a hydrogen atom system (reduced to 2D), and the new wavelet method is compared to the popular finite-difference time-domain technique.
A numerical recipe is given for obtaining the density image of an initially compact quantummechanicalwavefunction that has expanded by a large but finite factor under free flight. The recipe given avoids the memory storage problems that plague this type of calculation by reducing the problem to the sum of a number of fast Fourier transforms carried out on the relatively small initial lattice. The final expanded state is given exactly on a coarser magnified grid with the same number of points as the initial state. An important application of this technique is the simulation of measured time-of-flight images in ultracold atom experiments, especially when the initial clouds contain superfluid defects. It is shown that such a finite-time expansion, rather than a far-field approximation is essential to correctly predict images of defect-laden clouds, even for long flight times. Examples shown are: an expanding quasicondensate with soliton defects and a matter-wave interferometer in 3D.
The major title of this dissertation, 'From first principles,' is a phase often heard in the study of thermodynamics and quantummechanics. These words embody a powerful idea in the physical sciences; namely, that it is possible to distill the complexities of nature into a set of simple, well defined mathematical laws from which specific relations can then be derived . In thermodynamics, these fundamental laws are immediately familiar to the physical scientist by their numerical order: the First, Second and Third Laws. However, the subject of the present volume is quantummechanics-specifically, non-relativistic quantummechanics, which is appropriate formore » most systems of chemical interest.« less
We shall argue in this paper that a central piece of modern physics does not really belong to physics at all but to elementary probability theory. Given a joint probability distribution J on a set of random variables containing x and y, define a link between x and y to be the condition x=y on J. Define the {\\it state} D of a link x=y as the joint probability distribution matrix on x and y without the link. The two core laws of quantummechanics are the Born probability rule, and the unitary dynamical law whose best known form is the Schrodinger's equation. Von Neumann formulated these two laws in the language of Hilbert space as prob(P) = trace(PD) and D'T = TD respectively, where P is a projection, D and D' are (von Neumann) density matrices, and T is a unitary transformation. We'll see that if we regard link states as density matrices, the algebraic forms of these two core laws occur as completely general theorems about links. When we extend probability theory by allowing cases to count negatively, we find that the Hilbert space framework of quantummechanics proper emerges from the assumption that all D's are symmetrical in rows and columns. On the other hand, Markovian systems emerge when we assume that one of every linked variable pair has a uniform probability distribution. By representing quantum and Markovian structure in this way, we see clearly both how they differ, and also how they can coexist in natural harmony with each other, as they must in quantum measurement, which we'll examine in some detail. Looking beyond quantummechanics, we see how both structures have their special places in a much larger continuum of formal systems that we have yet to look for in nature.
We review some recent developments in the statistical mechanics of isolated quantumsystems. We provide a brief introduction to quantum thermalization, paying particular attention to the eigenstate thermalization hypothesis (ETH) and the resulting single-eigenstate statistical mechanics. We then focus on a class of systems that fail to quantum thermalize and whose eigenstates violate the ETH: These are the many-body Anderson-localized systems; their long-time properties are not captured by the conventional ensembles of quantum statistical mechanics. These systems can forever locally remember information about their local initial conditions and are thus of interest for possibilities of storing quantum information. We discuss key features of many-body localization (MBL) and review a phenomenology of the MBL phase. Single-eigenstate statistical mechanics within the MBL phase reveal dynamically stable ordered phases, and phase transitions among them, that are invisible to equilibrium statistical mechanics and can occur at high energy and low spatial dimensionality, where equilibrium ordering is forbidden.
Conspectus Ab initio modeling of matter has become a pillar of chemical research: with ever-increasing computational power, simulations can be used to accurately predict, for example, chemical reaction rates, electronic and mechanical properties of materials, and dynamical properties of liquids. Many competing quantummechanical methods have been developed over the years that vary in computational cost, accuracy, and scalability: density functional theory (DFT), the workhorse of solid-state electronic structure calculations, features a good compromise between accuracy and speed. However, approximate exchange-correlation functionals limit DFT's ability to treat certain phenomena or states of matter, such as charge-transfer processes or strongly correlated materials. Furthermore, conventional DFT is purely a ground-state theory: electronic excitations are beyond its scope. Excitations in molecules are routinely calculated using time-dependent DFT linear response; however applications to condensed matter are still limited. By contrast, many-electron wavefunction methods aim for a very accurate treatment of electronic exchange and correlation. Unfortunately, the associated computational cost renders treatment of more than a handful of heavy atoms challenging. On the other side of the accuracy spectrum, parametrized approaches like tight-binding can treat millions of atoms. In view of the different (dis-)advantages of each method, the simulation of complex systems seems to force a compromise: one is limited to the most accurate method that can still handle the problem size. For many interesting problems, however, compromise proves insufficient. A possible solution is to break up the system into manageable subsystems that may be treated by different computational methods. The interaction between subsystems may be handled by an embedding formalism. In this Account, we review embedded correlated wavefunction (CW) approaches and some applications. We first discuss our
In some circles of quantum physicists, a view is maintained that the nonseparability of quantumsystems-i.e., the entanglement-is a characteristic feature of quantummechanics. According to this view, the entanglement plays a crucial role in the solution of quantum measurement problem, the origin of the “classicality” from the quantum physics, the explanation of the EPR paradox by a nonlocal character of the quantum world. Besides, the entanglement is regarded as a cornerstone of such modern disciplines as quantum computation, quantum cryptography, quantum information, etc. At the same time, entangled states are well known and widely used in various physics areas. In particular, this notion is widely used in nuclear, atomic, molecular, solid state physics, in scattering and decay theories as well as in other disciplines, where one has to deal with many-body quantumsystems. One of the methods, how to construct the basis states of a composite many-body quantumsystem, is the so-called genealogical decomposition method. Genealogical decomposition allows one to construct recurrently by particle number the basis states of a composite quantumsystem from the basis states of its forming subsystems. These coupled states have a structure typical for entangled states. If a composite system is stable, the internal structure of its forming basis states does not manifest itself in measurements. However, if a composite system is unstable and decays onto its forming subsystems, then the measurables are the quantum numbers, associated with these subsystems. In such a case, the entangled state has a dynamical origin, determined by the Hamiltonian of the corresponding decay process. Possible correlations between the quantum numbers of resulting subsystems are determined by the symmetries-conservation laws of corresponding dynamical variables, and not by the quantum entanglement feature.
The most significant characteristic of nilpotent quantummechanics is that the quantumsystem (fermion state) and its environment (vacuum) are, in mathematical terms, mirror images of each other. So a change in one automatically leads to corresponding changes in the other. We have used this characteristic as a model for self-organization, which has applications well beyond quantum physics. The nilpotent structure has also been identified as being constructed from two commutative vector spaces. This construction has a number of identifiable characteristics which we can expect to find in systems where self-organization is dominant, and a case presented after the publication of a paper by us on ‘The ‘Logic’ of Self-Organizing Systems’,1 in the organization of the neurons in the visual cortex. We expect to find many more complex systems where our general principles, based, by analogy, on nilpotent quantummechanics, will apply.
Adiabatic processes have found many important applications in modern physics, the distinct merit of which is that accurate control over process timing is not required. However, such processes are slow, which limits their application in quantum computation, due to the limited coherent times of typical quantumsystems. Here, we propose a scheme to implement quantum state conversion in opto-electro-mechanicalsystems via a shortcut to adiabaticity, where the process can be greatly speeded up while precise timing control is still not necessary. In our scheme, by modifying only the coupling strength, we can achieve fast quantum state conversion with high fidelity, where the adiabatic condition does not need to be met. In addition, the population of the unwanted intermediate state can be further suppressed. Therefore, our protocol presents an important step towards practical state conversion between optical and microwave photons, and thus may find many important applications in hybrid quantum information processing.
The interpretation of quantummechanics has been disputed ever since the advent of the theory in the 1920's. Famous are the discussions over long time between Einstein and Bohr. Einstein refused to accept the so-called Copenhagen interpretation, where the wave function collapses at a measurement and where the outcome of the measurement is essentially accidental (``God does not play dice''). Alternative interpretations have appeared, but the Copenhagen school has dominated the thoughts throughout the decades. One interesting interpretation was formulated in 1957 by Hugh Everett at Princeton, a student of John Wheeler, which abandons the wave-function collapse. In this model the universe is governed entirely by the Schrödinger equation, which does not allow for any collapse. In Everett's model after a measurement the wave function is separated into different branches that do not interact. This model was left unnoticed for long time until Bryce DeWitt took it up in 1970 and termed it ``Many-Worlds Interpretation'', a term that in some sense is misleading. Everett's model is incomplete, and it was later supplemented by the theory of decoherence, which explains how the different branches decouple as a result of the interaction with the environment. This extended model has in recent years gained increased respect, and some believe that it is the only model made available so far that is fully consistent with quantummechanics. This interpretation can also shed some light on the development of the universe and, in particular, on the so-called Anthropic principle, which puts human beings at the center of the development.
Quasiparticles of charge 1/m in the Fractional Quantum Hall Effect form excitons, which are collective excitations physically similar to the transverse magnetoplasma oscillations of a Wigner crystal. A variational exciton wavefunction which shows explicitly that the magnetic length is effectively longer for quasiparticles than for electrons is proposed. This wavefunction is used to estimate the dispersion relation of these excitons and the matrix elements to generate them optically out of the ground state. These quantities are then used to describe a type of nonlinear conductivity which may occur in these systems when they are relatively clean.
Linares-García, Gabriel; Meza-Montes, Lilia; Stinaff, Eric; Alsolamy, S M; Ware, M E; Mazur, Y I; Wang, Z M; Lee, Jihoon; Salamo, G J
2016-12-01
Electronic and optical properties of InAs/GaAs nanostructures grown by the droplet epitaxy method are studied. Carrier states were determined by k · p theory including effects of strain and In gradient concentration for a model geometry. Wavefunctions are highly localized in the dots. Coulomb and exchange interactions are studied and we found the system is in the strong confinement regime. Microphotoluminescence spectra and lifetimes were calculated and compared with measurements performed on a set of quantum rings in a single sample. Some features of spectra are in good agreement.
With rapid recent advances in quantum technology, we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources.
With rapid recent advances in quantum technology, we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources. PMID:28674011
With rapid recent advances in quantum technology, we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources.
A new variational method, the principle of least radix economy, is formulated. The mathematical and physical relevance of the radix economy, also called digit capacity, is established, showing how physical laws can be derived from this concept in a unified way. The principle reinterprets and generalizes the principle of least action yielding two classes of physical solutions: least action paths and quantumwavefunctions. A new physical foundation of the Hilbert space of quantummechanics is then accomplished and it is used to derive the Schrödinger and Dirac equations and the breaking of the commutativity of spacetime geometry. The formulation provides an explanation of how determinism and random statistical behavior coexist in spacetime and a framework is developed that allows dynamical processes to be formulated in terms of chains of digits. These methods lead to a new (pre-geometrical) foundation for Lorentz transformations and special relativity. The Parker-Rhodes combinatorial hierarchy is encompassed within our approach and this leads to an estimate of the interaction strength of the electromagnetic and gravitational forces that agrees with the experimental values to an error of less than one thousandth. Finally, it is shown how the principle of least-radix economy naturally gives rise to Boltzmann's principle of classical statistical thermodynamics. A new expression for a general (path-dependent) nonequilibrium entropy is proposed satisfying the Second Law of Thermodynamics.
The multiconfiguration time-dependent Hartree-Fock (MCTDHF) and multiconfiguration time-dependent Hartree (MCTDH) methods are employed to investigate nonperturbative multielectron dynamics in finite quantumsystems. MCTDHF is a powerful tool that allows for the investigation of multielectron dynamics in strongly perturbed quantumsystems. 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 pump-probe experiments on noble gas atoms, the nonlinear effects that have been observed in Ne atoms in the presence of an x-ray free-electron 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 spin-free 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
The block-localized wavefunction (BLW) approach is an ab initio valence bond (VB) method incorporating the efficiency of molecular orbital (MO) theory. It can generate the wavefunction for a resonance structure or diabatic state self-consistently by partitioning the overall electrons and primitive orbitals into several subgroups and expanding each block-localized molecular orbital in only one subspace. Although block-localized molecular orbitals in the same subspace are constrained to be orthogonal (a feature of MO theory), orbitals between different subspaces are generally nonorthogonal (a feature of VB theory). The BLW method is particularly useful in the quantification of the electron delocalization (resonance) effect within a molecule and the charge-transfer effect between molecules. In this paper, we extend the BLW method to the density functional theory (DFT) level and implement the BLW-DFT method to the quantummechanical software GAMESS. Test applications to the pi conjugation in the planar allyl radical and ions with the basis sets of 6-31G(d), 6-31+G(d), 6-311+G(d,p), and cc-pVTZ show that the basis set dependency is insignificant. In addition, the BLW-DFT method can also be used to elucidate the nature of intermolecular interactions. Examples of pi-cation interactions and solute-solvent interactions will be presented and discussed. By expressing each diabatic state with one BLW, the BLW method can be further used to study chemical reactions and electron-transfer processes whose potential energy surfaces are typically described by two or more diabatic states.
Bohm, Arno R.; Gadella, Manuel; Kielanowski, Piotr
2011-09-01
The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1) for states or the Heisenberg equation (6a) for observables are given by a unitary group. Dirac kets require the concept of a RHS (rigged Hilbert space) of Schwartz functions; for this kind of RHS a mathematical theorem also leads to time symmetric group evolution. Scattering theory suggests to distinguish mathematically between states (defined by a preparation apparatus) and observables (defined by a registration apparatus (detector)). If one requires that scattering resonances of width Γ and exponentially decaying states of lifetime τ=h/Γ should be the same physical entities (for which there is sufficient evidence) one is led to a pair of RHS's of Hardy functions and connected with it, to a semigroup time evolution t0≤t<∞, with the puzzling result that there is a quantummechanical beginning of time, just like the big bang time for the universe, when it was a quantumsystem. The decay of quasi-stable particles is used to illustrate this quantummechanical time asymmetry. From the analysis of these processes, we show that the properties of rigged Hilbert spaces of Hardy functions are suitable for a formulation of time asymmetry in quantummechanics.
One of the traditional obstacles to learning quantummechanics is the relatively high level of mathematical proficiency required to solve even routine problems. Modern computer algebra systems are now sufficiently reliable that they can be used as mathematical assistants to alleviate this difficulty. In the quantummechanics course at the University of Lethbridge, the traditional three lecture hours per week have been replaced by two lecture hours and a one-hour computer-aided problem solving session using a computer algebra system (Maple). While this somewhat reduces the number of topics that can be tackled during the term, students have a better opportunity to familiarize themselves with the underlying theory with this course design. Maple is also available to students during examinations. The use of a computer algebra system expands the class of feasible problems during a time-limited exercise such as a midterm or final examination. A modern computer algebra system is a complex piece of software, so some time needs to be devoted to teaching the students its proper use. However, the advantages to the teaching of quantummechanics appear to outweigh the disadvantages.
Sachtleben, Kewin; Mazon, Kahio T.; Rego, Luis G. C.
2017-09-01
We propose the equivalence of superconducting qubits with a pistonlike mechanicalquantum engine. The work reports a study on the nature of the nonequilibrium work exchanged with the quantum-nonadiabatic working medium, which is modeled as a multilevel coupled quantum well system subject to an external control parameter. The quantum dynamics is solved for arbitrary control protocols. It is shown that the work output has two components: one that depends instantaneously on the level populations and another that is due to the quantum coherences built in the system. The nonadiabatic coherent dynamics of the quantum engine gives rise to a resistance (friction) force that decreases the work output. We consider the functional equivalence of such a device and a rf-SQUID flux qubit.
Quantum manifestation of classical chaos has been one of the extensively studied subjects for more than a decade. Yet clear understanding of its nature still remains to be an open question partly due to the lack of a canonical definition of quantum chaos. The classical definition seems to be unsuitable in quantummechanics partly because of the Heisenberg quantum uncertainty. In this regard, quantum chaos is somewhat misleading and needs to be clarified at the very fundamental level of physics. Since it is well known that quantummechanics is more fundamental than classical mechanics, the quantum description of classically chaoticmore » nature should be attainable in the limit of large quantum numbers. The focus of my research, therefore, lies on the correspondence principle for classically chaotic systems. The chaotic damped driven pendulum is mainly studied numerically using the split operator method that solves the time-dependent Schroedinger equation. For classically dissipative chaotic systems in which (multi)fractal strange attractors often emerge, several quantum dissipative mechanisms are also considered. For instance, Hoover`s and Kubo-Fox-Keizer`s approaches are studied with some computational analyses. But the notion of complex energy with non-Hermiticity is extensively applied. Moreover, the Wigner and Husimi distribution functions are examined with an equivalent classical distribution in phase-space, and dynamical properties of the wave packet in configuration and momentum spaces are also explored. The results indicate that quantum dynamics embraces classical dynamics although the classicalquantum correspondence fails to be observed in the classically chaotic regime. Even in the semi-classical limits, classically chaotic phenomena would eventually be suppressed by the quantum uncertainty.« less
Reed, A. P.; Mayer, K. H.; Teufel, J. D.; Burkhart, L. D.; Pfaff, W.; Reagor, M.; Sletten, L.; Ma, X.; Schoelkopf, R. J.; Knill, E.; Lehnert, K. W.
2017-12-01
The motion of micrometre-sized mechanical resonators can now be controlled and measured at the fundamental limits imposed by quantummechanics. These resonators have been prepared in their motional ground state or in squeezed states, measured with quantum-limited precision, and even entangled with microwave fields. Such advances make it possible to process quantum information using the motion of a macroscopic object. In particular, recent experiments have combined mechanical resonators with superconducting quantum circuits to frequency-convert, store and amplify propagating microwave fields. But these systems have not been used to manipulate states that encode quantum bits (qubits), which are required for quantum communication and modular quantum computation. Here we demonstrate the conversion of propagating qubits encoded as superpositions of zero and one photons to the motion of a micromechanical resonator with a fidelity in excess of the classical bound. This ability is necessary for mechanical resonators to convert quantum information between the microwave and optical domains or to act as storage elements in a modular quantum information processor. Additionally, these results are an important step towards testing speculative notions that quantum theory may not be valid for sufficiently massive systems.
Spontaneous transitions between bound states of an atomic system, "Lamb Shift" of energy levels and many other phenomena in real nonrelativistic quantumsystems are connected within the influence of the quantum vacuum fluctuations ( fundamental environment (FE)) which are impossible to consider in the limits of standard quantum-mechanical approaches. The joint system "quantumsystem (QS) + FE" is described in the framework of the stochastic differential equation (SDE) of Langevin-Schrödinger (L-Sch) type, and is defined on the extended space R 3 ⊗ R { ξ}, where R 3 and R { ξ} are the Euclidean and functional spaces, respectively. The density matrix for single QS in FE is defined. The entropy of QS entangled with FE is defined and investigated in detail. It is proved that as a result of interaction of QS with environment there arise structures of various topologies which are a new quantum property of the system.
In the classical dynamics of coupled oscillator systems, nonlinearity leads to the existence of stable solutions in which energy remains localized for all time. Here the quantum-mechanical counterpart of classical self-localization is investigated in the context of two model systems. For these quantum models, the terms corresponding to classical nonlinearities modify a subset of the stationary quantum states to be particularly suited to the creation of nonstationary wavepackets that localize energy for long times. The first model considered here is the Quantized Discrete Self-Trapping model (QDST), a system of anharmonic oscillators with linear dispersive coupling used to model local modes of vibration in polyatomic molecules. A simple formula is derived for a particular symmetry class of QDST systems which gives an analytic connection between quantum self-localization and classical local modes. This formula is also shown to be useful in the interpretation of the vibrational spectra of some molecules. The second model studied is the Frohlich/Einstein Dimer (FED), a two-site system of anharmonically coupled oscillators based on the Frohlich Hamiltonian and motivated by the theory of Davydov solitons in biological protein. The Born-Oppenheimer perturbation method is used to obtain approximate stationary state wavefunctions with error estimates for the FED at the first excited level. A second approach is used to reduce the first excited level FED eigenvalue problem to a system of ordinary differential equations. A simple theory of low-energy self-localization in the FED is discussed. The quantum theories of self-localization in the intrinsic QDST model and the extrinsic FED model are compared.
Since the origin of quantum theory in the 1920's, some of its practitioners (and founders) have been troubled by some of its features, including indeterminacy, nonlocality and entanglement. The 'collapse' process described in the Copenhagen Interpretation is suspect for several reasons, and the act of 'measurement,' which is supposed to delimit its regime of validity, has never been unambiguously defined. In recent decades, nonlocality and entanglement have been studied energetically, both theoretically and experimentally, and the theory has been reinterpreted in imaginative ways, but many mysteries remain. We propose that it is necessary to replace the theory by one thatmore » is explicitly nonlinear and nonlocal, and does not distinguish between measurement and non-measurement regimes. We have constructed such a theory, for which the phase of the wavefunction plays the role of a hidden variable via the process of zitterbewegung. To capture this effect, the theory must be relativistic, even when describing nonrelativistic phenomena. It is formulated as a variational principle, in which Nature attempts to minimize the sum of two spacetime integrals. The first integral tends to drive the solution toward a solution of the standard quantummechanical wave equation, and also enforces the Born rule of outcome probabilities. The second integral drives the collapse process. We demonstrate that the new theory correctly predicts the possible outcomes of the electron two-slit experiment, including the infamous 'delayed-choice' variant. We observe that it appears to resolve some long-standing mysteries, but introduces new ones, including possible retrocausality (a cause later than its effect). It is not clear whether the new theory is deterministic.« less
The Born rule, a foundational axiom used to deduce probabilities of events from wavefunctions, is indispensable in the everyday practice of quantum physics. It is also key in the quest to reconcile the ostensibly inconsistent laws of the quantum and classical realms, as it confers physical significance to reduced density matrices, the essential tools of decoherence theory. Following Bohr's Copenhagen interpretation, textbooks postulate the Born rule outright. But, recent attempts to derive it from other quantum principles have been successful, holding promise for simplifying and clarifying the quantum foundational bedrock. Moreover, a major family of derivations is based on envariance,more » a recently discovered symmetry of entangled quantum states. Here, we identify and experimentally test three premises central to these envariance-based derivations, thus demonstrating, in the microworld, the symmetries from which the Born rule is derived. Furthermore, we demonstrate envariance in a purely local quantumsystem, showing its independence from relativistic causality.« less
Korichi, Z.; Meftah, M. T., E-mail: mewalid@yahoo.com
2014-03-15
The purpose of this work is to study some problems in statistical mechanics based on the fractional classical and quantummechanics. At first stage we have presented the thermodynamical properties of the classical ideal gas and the system of N classical oscillators. In both cases, the Hamiltonian contains fractional exponents of the phase space (position and momentum). At the second stage, in the context of the fractional quantummechanics, we have calculated the thermodynamical properties for the black body radiation, studied the Bose-Einstein statistics with the related problem of the condensation and the Fermi-Dirac statistics.
We present a new approach to study the thermodynamic properties of d-dimensional classical systems by reducing the problem to the computation of ground state properties of a d-dimensional quantum model. This classical-to-quantum mapping allows us to extend the scope of standard optimization methods by unifying them under a general framework. The quantum annealing method is naturally extended to simulate classical systems at finite temperatures. We derive the rates to assure convergence to the optimal thermodynamic state using the adiabatic theorem of quantummechanics. For simulated and quantum annealing, we obtain the asymptotic rates of T(t) approximately (pN)/(k(B)logt) and gamma(t) approximately (Nt)(-c/N), for the temperature and magnetic field, respectively. Other annealing strategies are also discussed.
Brodsky, Stanley J.; /SLAC /Southern Denmark U., CP3-Origins; de Teramond, Guy F.
2012-02-16
Light-Front Holography is one of the most remarkable features of the AdS/CFT correspondence. In spite of its present limitations it provides important physical insights into the nonperturbative regime of QCD and its transition to the perturbative domain. This novel framework allows hadronic amplitudes in a higher dimensional anti-de Sitter (AdS) space to be mapped to frame-independent light-front wavefunctions of hadrons in physical space-time. The model leads to an effective confining light-front QCD Hamiltonian and a single-variable light-front Schroedinger equation which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. The coordinate z inmore » AdS space is uniquely identified with a Lorentz-invariant coordinate {zeta} which measures the separation of the constituents within a hadron at equal light-front time and determines the off-shell dynamics of the bound-state wavefunctions, and thus the fall-off as a function of the invariant mass of the constituents. The soft-wall holographic model modified by a positive-sign dilaton metric, leads to a remarkable one-parameter description of nonperturbative hadron dynamics - a semi-classical frame-independent first approximation to the spectra and light-front wavefunctions of meson and baryons. The model predicts a Regge spectrum of linear trajectories with the same slope in the leading orbital angular momentum L of hadrons and the radial quantum number n. The hadron eigensolutions projected on the free Fock basis provides the complete set of valence and non-valence light-front Fock state wavefunctions {Psi}{sub n/H} (x{sub i}, k{sub {perpendicular}i}, {lambda}{sub i}) which describe the hadron's momentum and spin distributions needed to compute the direct measures of hadron structure at the quark and gluon level, such as elastic and transition form factors, distribution amplitudes, structure functions, generalized parton distributions and
The experimentally observed effect of selective deuterium substitution on the open circuit voltage for a blend of poly(3-hexylthiophene)(P3HT) and [6,6]-phenyl-C 61- butyric acid methyl ester (PCBM) (Nat. Commun. 5:3180, 2014) is explored using a 221-atom model of a polymer-wrapped PCBM molecule. We describe the protonic and deuteronic wavefunctions for the H/D isotopologues of the hexyl side chains within a Quantum Trajectory/Electronic Structure approach where the dynamics is performed with newly developed nonlinear corrections to the quantum forces, necessary to describe the nuclear wavefunctions; the classical forces are generated with a Density Functional Tight Binding method. We used the resulting protonicmore » and deuteronic time-dependent wavefunctions to assess the effects of isotopic substitution (deuteration) on the energy gaps relevant to the charge transfer for the donor and acceptor electronic states. Furthermore, while the isotope effect on the electronic energy levels is found negligible, the quantum-induced fluctuations of the energy gap between the charge transfer and charge separated states due to nuclear wavefunctions may account for experimental trends by promoting charge transfer in P3HT/PCBM and increasing charge recombination on the donor in the deuterium substituted P3HT/PCBM.« less
The experimentally observed effect of selective deuterium substitution on the open circuit voltage for a blend of poly(3-hexylthiophene)(P3HT) and [6,6]-phenyl-C 61- butyric acid methyl ester (PCBM) (Nat. Commun. 5:3180, 2014) is explored using a 221-atom model of a polymer-wrapped PCBM molecule. We describe the protonic and deuteronic wavefunctions for the H/D isotopologues of the hexyl side chains within a Quantum Trajectory/Electronic Structure approach where the dynamics is performed with newly developed nonlinear corrections to the quantum forces, necessary to describe the nuclear wavefunctions; the classical forces are generated with a Density Functional Tight Binding method. We used the resulting protonicmore » and deuteronic time-dependent wavefunctions to assess the effects of isotopic substitution (deuteration) on the energy gaps relevant to the charge transfer for the donor and acceptor electronic states. Furthermore, while the isotope effect on the electronic energy levels is found negligible, the quantum-induced fluctuations of the energy gap between the charge transfer and charge separated states due to nuclear wavefunctions may account for experimental trends by promoting charge transfer in P3HT/PCBM and increasing charge recombination on the donor in the deuterium substituted P3HT/PCBM.« less
We present a novel approach that allows to calculate the dielectric response of periodic systems in the quantum Monte Carlo formalism. We employ a many-body generalization for the electric enthalpy functional, where the coupling with the field is expressed via the Berry-phase formulation for the macroscopic polarization. A self-consistent local Hamiltonian then determines the ground-state wavefunction, allowing for accurate diffusion quantum Monte Carlo calculations where the polarization's fixed point is estimated from the average on an iterative sequence. The polarization is sampled through forward-walking. This approach has been validated for the case of the polarizability of an isolated hydrogen atom, and then applied to a periodic system. We then calculate the linear susceptibility and second-order hyper-susceptibility of molecular-hydrogen chains whith different bond-length alternations, and assess the quality of nodal surfaces derived from density-functional theory or from Hartree-Fock. The results found are in excellent agreement with the best estimates obtained from the extrapolation of quantum-chemistry calculations.P. Umari, A.J. Williamson, G. Galli, and N. MarzariPhys. Rev. Lett. 95, 207602 (2005).
We present a new, very efficient semi-numerical approach for the computation of state-specific nuclear gradients of a generic state-averaged multi-configuration self consistent field wavefunction. Our approach eliminates the costly coupled-perturbed multi-configuration Hartree-Fock step as well as the associated integral transformation stage. The details of the implementation within the Firefly quantum chemistry package are discussed and several sample applications are given. The new approach is routinely applicable to geometry optimization of molecular systems with 1000+ basis functions using a standalone multi-core workstation.
Granovsky, Alexander A., E-mail: alex.granovsky@gmail.com
We present a new, very efficient semi-numerical approach for the computation of state-specific nuclear gradients of a generic state-averaged multi-configuration self consistent field wavefunction. Our approach eliminates the costly coupled-perturbed multi-configuration Hartree-Fock step as well as the associated integral transformation stage. The details of the implementation within the Firefly quantum chemistry package are discussed and several sample applications are given. The new approach is routinely applicable to geometry optimization of molecular systems with 1000+ basis functions using a standalone multi-core workstation.
Bonezzi, R.; Corradini, O.; Latini, E.; Waldron, A.
2017-12-01
Solvability of the ubiquitous quantum harmonic oscillator relies on a spectrum generating osp (1 |2 ) superconformal symmetry. We study the problem of constructing all quantummechanical models with a hidden osp (1 |2 ) symmetry on a given space of states. This problem stems from interacting higher spin models coupled to gravity. In one dimension, we show that the solution to this problem is the Vasiliev-Plyushchay family of quantummechanical models with hidden superconformal symmetry obtained by viewing the harmonic oscillator as a one dimensional Dirac system, so that Grassmann parity equals wave function parity. These models—both oscillator and particlelike—realize all possible unitary irreducible representations of osp (1 |2 ).
We consider the quantum centipede made of N fermionic quantum walkers on the one-dimensional lattice interacting by means of the simplest of all hard-bound constraints: the distance between two consecutive fermions is either one or two lattice spacings. This composite quantum walker spreads ballistically, just as the simple quantum walk. However, because of the interactions between the internal degrees of freedom, the distribution of its center-of-mass velocity displays numerous ballistic fronts in the long-time limit, corresponding to singularities in the empirical velocity distribution. The spectrum of the centipede and the corresponding group velocities are analyzed by direct means for the first few values of N. Some analytical results are obtained for arbitrary N by exploiting an exact mapping of the problem onto a free-fermion system. We thus derive the maximal velocity describing the ballistic spreading of the two extremal fronts of the centipede wavefunction, including its non-trivial value in the large-N limit.
In quantummechanics, the path-dependent geometrical phase associated with a physical system, over and above the familiar dynamical phase, was initially discovered in the context of adiabatically changing environments. Subsequently, Aharonov and Anandan liberated this phase from the original formulation of Berry, which used Hamiltonians, dependent on curves in a classical parameter space, to represent the cyclic variations of the environments. Their purely quantummechanical treatment, independent of Hamiltonians, instead used the non-trivial topological structure of the projective space of one-dimensional subspaces of an appropriate Hilbert space. The geometrical phase, in their treatment, results from a parallel transport of the time-dependent pure quantum states along a curve in this space, which is endowed with an abelian connection. Unlike Berry, they were able to achieve this without resort to an adiabatic approximation or to a time-independent eigenvalue equation. Prima facie, these two approaches are conceptually quite different. After a review of both approaches, an exposition bridging this apparent conceptual gap is given; by rigorously analyzing a model composite system, it is shown that, in an appropriate correspondence limit, the Berry phase can be recovered as a special case from the Aharonov-Anandan phase. Moreover, the model composite system is used to show that Berry's correction to the traditional Born-Oppenheimer energy spectra indeed brings the spectra closer to the exact results. Then, an experimental arrangement to measure geometrical phases associated with cyclic and non-cyclic variations of quantum states of an entangled composite system is proposed, utilizing the fundamental ideas of the recently opened field of two-particle interferometry. This arrangement not only resolves the controversy regarding the true nature of the phases associated with photon states, but also unequivocally predicts experimentally accessible geometrical phases in a
The ability to control and exploit quantum coherence and entanglement drives research across many fields ranging from ultra-cold quantum gases to spin systems in condensed matter. Transcending different physical systems, optical approaches have proven themselves to be particularly powerful, since they profit from the established toolbox of quantum optical techniques, are state-selective, contact-less and can be extremely fast. Here, we demonstrate how a precisely timed sequence of monochromatic ultrafast (~ 2-5 ps) optical pulses, with a well defined polarisation can be used to prepare arbitrary superpositions of exciton spin states in a semiconductor quantum dot, achieve ultrafast control of the spin-wavefunction without an applied magnetic field and make high fidelity read-out the quantum state in an arbitrary basis simply by detecting a strong (~ 2-10 pA) electric current flowing in an external circuit. The results obtained show that the combined quantum state preparation, control and read-out can be performed with a near-unity (≥97%) fidelity.
Non-commutativity appears in physics almost hand in hand with quantummechanics. Non-commuting operators corresponding to observables lead to Heisenberg's Uncertainty Principle, which is often used as a prime example of how quantummechanics transcends 'common sense', while the operators that generate a symmetry group are usually given in terms of their commutation relations. This thesis discusses a number of new developments which go beyond the usual stopping point of non-commuting quantities as matrices with complex elements. Chapter 2 shows how certain generalisations of quantummechanics, from using complex numbers to using other (often non-commutative) algebras, can still be written as linear systems with symplectic phase flows. Chapter 3 deals with Adler's trace dynamics, a non-linear graded generalisation of Hamiltonian dynamics with supersymmetry applications, where the phase space coordinates are (generally non-commuting) operators, and reports on aspects of a demonstration that the statistical averages of the dynamical variables obey the rules of complex quantum field theory. The last two chapters discuss specific aspects of quaternionic quantummechanics. Chapter 4 reports a generalised projective representation theory and presents a structure theorem that categorises quaternionic projective representations. Chapter 5 deals with a generalisation of the coherent states formalism and examines how it may be applied to two commonly used groups.
We introduce a new and conceptually simple interpretation of quantummechanics based on reduced density matrices of sub-systems from which the standard Copenhagen interpretation emerges as an effective description of macroscopically large systems. This interpretation describes a world in which definite measurement results are obtained with probabilities that reproduce the Born rule. Wave function collapse is seen to be a useful but fundamentally unnecessary piece of prudent book keeping which is only valid for macro-systems. The new interpretation lies in a class of modal interpretations in that it applies to quantumsystems that interact with a much larger environment. However, we show that it does not suffer from the problems that have plagued similar modal interpretations like macroscopic superpositions and rapid flipping between macroscopically distinct states. We describe how the interpretation fits neatly together with fully quantum formulations of statistical mechanics and that a measurement process can be viewed as a process of ergodicity breaking analogous to a phase transition. The key feature of the new interpretation is that joint probabilities for the ergodic subsets of states of disjoint macro-systems only arise as emergent quantities. Finally we give an account of the EPR-Bohm thought experiment and show that the interpretation implies the violation of the Bell inequality characteristic of quantummechanics but in a way that is rather novel. The final conclusion is that the Copenhagen interpretation gives a completely satisfactory phenomenology of macro-systems interacting with micro-systems.
List of papers on quantum philosophy by J. S. Bell; Preface; Acknowledgements; Introduction by Alain Aspect; 1. On the problem of hidden variables in quantummechanics; 2. On the Einstein-Rosen-Podolsky paradox; 3. The moral aspects of quantummechanics; 4. Introduction to the hidden-variable question; 5. Subject and object; 6. On wave packet reduction in the Coleman-Hepp model; 7. The theory of local beables; 8. Locality in quantummechanics: reply to critics; 9. How to teach special relativity; 10. Einstein-Podolsky-Rosen experiments; 11. The measurement theory of Everett and de Broglie's pilot wave; 12. Free variables and local causality; 13. Atomic-cascade photons and quantum-mechanical nonlocality; 14. de Broglie-Bohm delayed choice double-slit experiments and density matrix; 15. Quantummechanics for cosmologists; 16. Bertlmann's socks and the nature of reality; 17. On the impossible pilot wave; 18. Speakable and unspeakable in quantummechanics; 19. Beables for quantum field theory; 20. Six possible worlds of quantummechanics; 21. EPR correlations and EPR distributions; 22. Are there quantum jumps?; 23. Against 'measurement'; 24. La Nouvelle cuisine.
Hunt, Diego; Sanchez, Veronica M.; Scherlis, Damián A.
2016-08-01
We introduce and discuss a hybrid quantum-mechanics molecular-mechanics (QM-MM) approach for Car-Parrinello DFT simulations with pseudopotentials and planewaves basis, designed for the treatment of periodic systems. In this implementation the MM atoms are considered as additional QM ions having fractional charges of either sign, which provides conceptual and computational simplicity by exploiting the machinery already existing in planewave codes to deal with electrostatics in periodic boundary conditions. With this strategy, both the QM and MM regions are contained in the same supercell, which determines the periodicity for the whole system. Thus, while this method is not meant to compete with non-periodic QM-MM schemes able to handle extremely large but finite MM regions, it is shown that for periodic systems of a few hundred atoms, our approach provides substantial savings in computational times by treating classically a fraction of the particles. The performance and accuracy of the method is assessed through the study of energetic, structural, and dynamical aspects of the water dimer and of the aqueous bulk phase. Finally, the QM-MM scheme is applied to the computation of the vibrational spectra of water layers adsorbed at the TiO2 anatase (1 0 1) solid-liquid interface. This investigation suggests that the inclusion of a second monolayer of H2O molecules is sufficient to induce on the first adsorbed layer, a vibrational dynamics similar to that taking place in the presence of an aqueous environment. The present QM-MM scheme appears as a very interesting tool to efficiently perform molecular dynamics simulations of complex condensed matter systems, from solutions to nanoconfined fluids to different kind of interfaces.
Hunt, Diego; Sanchez, Veronica M; Scherlis, Damián A
2016-08-24
We introduce and discuss a hybrid quantum-mechanics molecular-mechanics (QM-MM) approach for Car-Parrinello DFT simulations with pseudopotentials and planewaves basis, designed for the treatment of periodic systems. In this implementation the MM atoms are considered as additional QM ions having fractional charges of either sign, which provides conceptual and computational simplicity by exploiting the machinery already existing in planewave codes to deal with electrostatics in periodic boundary conditions. With this strategy, both the QM and MM regions are contained in the same supercell, which determines the periodicity for the whole system. Thus, while this method is not meant to compete with non-periodic QM-MM schemes able to handle extremely large but finite MM regions, it is shown that for periodic systems of a few hundred atoms, our approach provides substantial savings in computational times by treating classically a fraction of the particles. The performance and accuracy of the method is assessed through the study of energetic, structural, and dynamical aspects of the water dimer and of the aqueous bulk phase. Finally, the QM-MM scheme is applied to the computation of the vibrational spectra of water layers adsorbed at the TiO2 anatase (1 0 1) solid-liquid interface. This investigation suggests that the inclusion of a second monolayer of H2O molecules is sufficient to induce on the first adsorbed layer, a vibrational dynamics similar to that taking place in the presence of an aqueous environment. The present QM-MM scheme appears as a very interesting tool to efficiently perform molecular dynamics simulations of complex condensed matter systems, from solutions to nanoconfined fluids to different kind of interfaces.
Numerous molecular systems, including solutions, proteins, and composite materials, can be modeled using mixed-resolution representations, of which the quantummechanics/molecular mechanics (QM/MM) approach has become the most widely used. However, the QM/MM approach often faces a number of challenges, including the high cost of repetitive QM computations, the slow sampling even for the MM part in those cases where a system under investigation has a complex dynamics, and a difficulty in providing a simple, qualitative interpretation of numerical results in terms of the influence of the molecular environment upon the active QM region. In this paper, we address these issues by combining QM/MM modeling with the methodology of "bottom-up" coarse-graining (CG) to provide the theoretical basis for a systematic quantum-mechanical/coarse-grained molecular mechanics (QM/CG-MM) mixed resolution approach. A derivation of the method is presented based on a combination of statistical mechanics and quantummechanics, leading to an equation for the effective Hamiltonian of the QM part, a central concept in the QM/CG-MM theory. A detailed analysis of different contributions to the effective Hamiltonian from electrostatic, induction, dispersion, and exchange interactions between the QM part and the surroundings is provided, serving as a foundation for a potential hierarchy of QM/CG-MM methods varying in their accuracy and computational cost. A relationship of the QM/CG-MM methodology to other mixed resolution approaches is also discussed.
Numerous molecular systems, including solutions, proteins, and composite materials, can be modeled using mixed-resolution representations, of which the quantummechanics/molecular mechanics (QM/MM) approach has become the most widely used. However, the QM/MM approach often faces a number of challenges, including the high cost of repetitive QM computations, the slow sampling even for the MM part in those cases where a system under investigation has a complex dynamics, and a difficulty in providing a simple, qualitative interpretation of numerical results in terms of the influence of the molecular environment upon the active QM region. In this paper, we address these issues by combining QM/MM modeling with the methodology of "bottom-up" coarse-graining (CG) to provide the theoretical basis for a systematic quantum-mechanical/coarse-grained molecular mechanics (QM/CG-MM) mixed resolution approach. A derivation of the method is presented based on a combination of statistical mechanics and quantummechanics, leading to an equation for the effective Hamiltonian of the QM part, a central concept in the QM/CG-MM theory. A detailed analysis of different contributions to the effective Hamiltonian from electrostatic, induction, dispersion, and exchange interactions between the QM part and the surroundings is provided, serving as a foundation for a potential hierarchy of QM/CG-MM methods varying in their accuracy and computational cost. A relationship of the QM/CG-MM methodology to other mixed resolution approaches is also discussed.
During the past decades, quantummechanical methods have undergone an amazing transition from pioneering investigations of experts into a wide range of practical applications, made by a vast community of researchers. First principles calculations of systems containing up to a few hundred atoms have become a standard in many branches of science. The sizes of the systems which can be simulated have increased even further during recent years, and quantum-mechanical calculations of systems up to many thousands of atoms are nowadays possible. This opens up new appealing possibilities, in particular for interdisciplinary work, bridging together communities of different needs andmore » sensibilities. In this review we will present the current status of this topic, and will also give an outlook on the vast multitude of applications, challenges and opportunities stimulated by electronic structure calculations, making this field an important working tool and bringing together researchers of many different domains.« less
A century after its inception, quantummechanics continues to puzzle us with dead-and-alive cats, waves "collapsing" into particles, and "spooky action at a distance." In his first book, What Is Real?, science writer and astrophysicist Adam Becker sets out to explore why the physics community is still arguing today about quantummechanics's true meaning.
In the condensed phase, quantum chemical properties such as many-body effects and intermolecular charge fluctuations are critical determinants of the solvation structure and dynamics. Thus, a quantummechanical (QM) molecular description is required for both solute and solvent to incorporate these properties. However, it is challenging to conduct molecular dynamics (MD) simulations for condensed systems of sufficient scale when adapting QM potentials. To overcome this problem, we recently developed the size-consistent multi-partitioning (SCMP) quantummechanics/molecular mechanics (QM/MM) method and realized stable and accurate MD simulations, using the QM potential to a benchmark system. In the present study, as the first application of the SCMP method, we have investigated the structures and dynamics of Na + , K + , and Ca 2+ solutions based on nanosecond-scale sampling, a sampling 100-times longer than that of conventional QM-based samplings. Furthermore, we have evaluated two dynamic properties, the diffusion coefficient and difference spectra, with high statistical certainty. Furthermore the calculation of these properties has not previously been possible within the conventional QM/MM framework. Based on our analysis, we have quantitatively evaluated the quantum chemical solvation effects, which show distinct differences between the cations.
The bending motion of a linear triatomic molecule has two unique characteristics: the bending mode is doubly degenerate and only positive values of the bending angle, expressed by the bond angle supplement ρ bar , can be observed. The double degeneracy requires the wavefunction to be described as a two-dimensional oscillator. In the present work, we first review the conventional expressions based on two, symmetrically equivalent normal coordinates. Then we discuss an alternative expression for the bending wavefunction in terms of two geometrical coordinates, the bond angle supplement ρ bar (= π - τ ⩾ 0 , where τ is the bond angle) and the rotation angle χ (0 ⩽ χ < 2 π) describing rotation of the molecule around the molecular axis. In this formalism, defined for the (ρ bar , χ) polar-coordinate space with volume element ρ bar d ρ bar dχ , the one-dimensional wavefunction resulted through re-normalization for χ has zero amplitude at ρ bar = 0 , and the ro-vibrational average of the bending angle, i.e., the expectation value 〈 ρ bar 〉 , attains a non-zero, positive value for any ro-vibrational state including the vibrational ground state. This conclusion appears to cause some controversy since much conventional spectroscopic wisdom insists on 〈 ρ bar 〉 having the value zero.
Esposito, Giampiero; Marmo, Giuseppe; Miele, Gennaro; Sudarshan, George
2014-11-01
Preface; 1. Introduction: the need for a quantum theory; 2. Experimental foundations of quantum theory; 3. Waves and particles; 4. Schrödinger picture, Heisenberg picture and probabilistic aspects; 5. Integrating the equations of motion; 6. Elementary applications: 1-dimensional problems; 7. Elementary applications: multidimensional problems; 8. Coherent states and related formalism; 9. Introduction to spin; 10. Symmetries in quantummechanics; 11. Approximation methods; 12. Modern pictures of quantummechanics; 13. Formulations of quantummechanics and their physical implications; 14. Exam problems; Glossary of geometric concepts; References; Index.
Keller, Sebastian; Boguslawski, Katharina; Janowski, Tomasz; Reiher, Markus; Pulay, Peter
2015-06-01
The efficient and accurate description of the electronic structure of strongly correlated systems is still a largely unsolved problem. The usual procedures start with a multiconfigurational (usually a Complete Active Space, CAS) wavefunction which accounts for static correlation and add dynamical correlation by perturbation theory, configuration interaction, or coupled cluster expansion. This procedure requires the correct selection of the active space. Intuitive methods are unreliable for complex systems. The inexpensive black-box unrestricted natural orbital (UNO) criterion postulates that the Unrestricted Hartree-Fock (UHF) charge natural orbitals with fractional occupancy (e.g., between 0.02 and 1.98) constitute the active space. UNOs generally approximate the CAS orbitals so well that the orbital optimization in CAS Self-Consistent Field (CASSCF) may be omitted, resulting in the inexpensive UNO-CAS method. A rigorous testing of the UNO criterion requires comparison with approximate full configuration interaction wavefunctions. This became feasible with the advent of Density Matrix Renormalization Group (DMRG) methods which can approximate highly correlated wavefunctions at affordable cost. We have compared active orbital occupancies in UNO-CAS and CASSCF calculations with DMRG in a number of strongly correlated molecules: compounds of electronegative atoms (F2, ozone, and NO2), polyenes, aromatic molecules (naphthalene, azulene, anthracene, and nitrobenzene), radicals (phenoxy and benzyl), diradicals (o-, m-, and p-benzyne), and transition metal compounds (nickel-acetylene and Cr2). The UNO criterion works well in these cases. Other symmetry breaking solutions, with the possible exception of spatial symmetry, do not appear to be essential to generate the correct active space. In the case of multiple UHF solutions, the natural orbitals of the average UHF density should be used. The problems of the UNO criterion and their potential solutions are discussed
Where does quantummechanics part ways with classical mechanics? How does quantum randomness differ fundamentally from classical randomness? We cannot fully explain how the theories differ until we can derive them within a single axiomatic framework, allowing an unambiguous account of how one theory is the limit of the other. Here we derive non-relativistic quantummechanics and classical statistical mechanics within a common framework. The common axioms include conservation of average energy and conservation of probability current. But two axioms distinguish quantummechanics from classical statistical mechanics: an "ontic extension" defines a nonseparable (global) random variable that generates physical correlations, and an "epistemic restriction" constrains allowed phase space distributions. The ontic extension and epistemic restriction, with strength on the order of Planck's constant, imply quantum entanglement and uncertainty relations. This framework suggests that the wave function is epistemic, yet it does not provide an ontic dynamics for individual systems.
We discuss an explicit realization of the dissipative dynamics anticipated in the proof of 't Hooft's existence theorem, which states that 'For any quantumsystem there exists at least one deterministic model that reproduces all its dynamics after prequantization'. - There is an energy-parity symmetry hidden in the Liouville equation, which mimics the Kaplan-Sundrum protective symmetry for the cosmological constant. This symmetry may be broken by the coarse-graining inherent in physics at scales much larger than the Planck length. We correspondingly modify classical ensemble theory by incorporating dissipative fluctuations (information loss) - which are caused by discrete spacetime continually 'measuring' matter. In this way, aspects of quantummechanics, such as the von Neumann equation, including a Lindblad term, arise dynamically and expectations of observables agree with the Born rule. However, the resulting quantum coherence is accompanied by an intrinsic decoherence and continuous localization mechanism. Our proposal leads towards a theory that is linear and local at the quantummechanical level, but the relation to the underlying classical degrees of freedom is nonlocal.
This report on progress explores recent advances in our theoretical and experimental understanding of the physics of open quantumsystems (OQSs). The study of such systems represents a core problem in modern physics that has evolved to assume an unprecedented interdisciplinary character. OQSs consist of some localized, microscopic, region that is coupled to an external environment by means of an appropriate interaction. Examples of such systems may be found in numerous areas of physics, including atomic and nuclear physics, photonics, biophysics, and mesoscopic physics. It is the latter area that provides the main focus of this review, an emphasis that is driven by the capacity that exists to subject mesoscopic devices to unprecedented control. We thus provide a detailed discussion of the behavior of mesoscopic devices (and other OQSs) in terms of the projection-operator formalism, according to which the system under study is considered to be comprised of a localized region (Q), embedded into a well-defined environment (P) of scattering wavefunctions (with Q + P = 1). The Q subspace must be treated using the concepts of non-Hermitian physics, and of particular interest here is: the capacity of the environment to mediate a coupling between the different states of Q; the role played by the presence of exceptional points (EPs) in the spectra of OQSs; the influence of EPs on the rigidity of the wavefunction phases, and; the ability of EPs to initiate a dynamical phase transition (DPT). EPs are singular points in the continuum, at which two resonance states coalesce, that is where they exhibit a non-avoided crossing. DPTs occur when the quantum dynamics of the open system causes transitions between non-analytically connected states, as a function of some external control parameter. Much like conventional phase transitions, the behavior of the system on one side of the DPT does not serve as a reliable indicator of that on the other. In
We show how a quantum computer can be employed to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical-computer simulations for such problems, to significantly increase their accuracy and enable hitherto intractable simulations. Detailed resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. This demonstrates that quantum computers will realistically be able to tackle important problems in chemistry that are both scientifically and economically significant.
Cooling of matter to the quantum ground state is a primary directive of quantum control. In other words, to extract entropy from a quantumsystem, efficient indirect quantum measurements may be implemented. The main objective is the cooling of the oscillator either to its motional ground state or to non-classical states, such as low-number Fock states, squeezed states or entangled states. It is shown that the use of quantum control procedure is better choice for even experimental realizations because it leads to a squeezed steady state with less than one phonon on average. The steady state of system corresponds tomore » cooling of the system.« less
We advertise the virtues of the Gaussian effective potential (GEP) as a guide to the behavior of quantum field theories. Much superior to the usual one-loop effective potential, the GEP is a natural extension of intuitive notions familiar from quantummechanics. A variety of quantum-mechanical examples are studied here, with an eye to field-theoretic analogies. Quantum restoration of symmetry, dynamical mass generation, and "quantum-mechanical resuscitation" are among the phenomena discussed. We suggest how the GEP could become the basis of a systematic approximation procedure. A companion paper will deal with scalar field theory.
The time evolution of quantum states is arguably one of the more difficult ideas in quantummechanics. In this article, we report on results from an investigation of student understanding of this topic after lecture instruction. We demonstrate specific problems that students have in applying time dependence to quantumsystems and in recognizing…
Lin, Hai; Zhao, Yan; Tishchenko, Oksana; Truhlar, Donald G
2006-09-01
The multiconfiguration molecular mechanics (MCMM) method is a general algorithm for generating potential energy surfaces for chemical reactions by fitting high-level electronic structure data with the help of molecular mechanical (MM) potentials. It was previously developed as an extension of standard MM to reactive systems by inclusion of multidimensional resonance interactions between MM configurations corresponding to specific valence bonding patterns, with the resonance matrix element obtained from quantummechanical (QM) electronic structure calculations. In particular, the resonance matrix element is obtained by multidimensional interpolation employing a finite number of geometries at which electronic-structure calculations of the energy, gradient, and Hessian are carried out. In this paper, we present a strategy for combining MCMM with hybrid quantummechanical molecular mechanical (QM/MM) methods. In the new scheme, electronic-structure information for obtaining the resonance integral is obtained by means of hybrid QM/MM calculations instead of fully QM calculations. As such, the new strategy can be applied to the studies of very large reactive systems. The new MCMM scheme is tested for two hydrogen-transfer reactions. Very encouraging convergence is obtained for rate constants including tunneling, suggesting that the new MCMM method, called QM/MM-MCMM, is a very general, stable, and efficient procedure for generating potential energy surfaces for large reactive systems. The results are found to converge well with respect to the number of Hessians. The results are also compared to calculations in which the resonance integral data are obtained by pure QM, and this illustrates the sensitivity of reaction rate calculations to the treatment of the QM-MM border. For the smaller of the two systems, comparison is also made to direct dynamics calculations in which the potential energies are computed quantummechanically on the fly.
The central part of Everett's formulation of quantummechanics is a quantummechanical model of memory and of observation as the recording of information in a memory. To use this model as an answer to the measurement problem, Everett has to assume that a conscious observer can be in a superposition of such memory states and be unaware of it. This assumption has puzzled generations of readers. The fundamental aim of this dissertation is to find a set of simpler assumptions which are sufficient to show that Everett's model is empirically adequate. I argue that Everett's model needs three assumptions to account for the process of observation: an assumption of decoherence of observers as quantummechanicalsystems; an assumption of supervenience of mental states (qualities) over quantummechanical properties; and an assumption about the interpretation of quantummechanical states in general: quantummechanical states describe ensembles of states of affairs coexisting in the same system. I argue that the only plausible understanding of such ensembles is as ensembles of possibilities, and that all standard no-collapse interpretations agree in this reading of quantummechanical states. Their differences can be understood as different theories about what marks the real state within this ensemble, and Everett's theory as the claim that no additional 'mark of reality' is necessary. Using the three assumptions, I argue that introspection cannot determine the objective quantummechanical state of an observer. Rather, the introspective qualities of a quantummechanical state can be represented by a (classical) statistical ensemble of subjective states. An analysis of these subjective states and their dynamics leads to the conclusion that they suffice to give empirically correct predictions. The argument for the empirical adequacy of the subjective state entails that knowledge of the objective quantummechanical state is impossible in principle. Empirical reality for a conscious
States that the major problem in learning quantummechanics is often the student's ignorance of classical mechanics and that one conceptual hurdle in quantummechanics is its statistical nature, in contrast to the determinism of classical mechanics. (MLH)
Precise control over quantumsystems can enable the realization of fascinating applications such as powerful computers, secure communication devices, and simulators that can elucidate the physics of complex condensed matter systems. However, the fragility of quantum effects makes it very difficult to harness the power of quantummechanics. In this thesis, we present novel systems and tools for gaining fundamental insights into the complex quantum world and for bringing practical applications of quantummechanics closer to reality. We first optimize and show equivalence between a wide range of techniques for storage of photons in atomic ensembles. We describe experiments demonstrating the potential of our optimization algorithms for quantum communication and computation applications. Next, we combine the technique of photon storage with strong atom-atom interactions to propose a robust protocol for implementing the two-qubit photonic phase gate, which is an important ingredient in many quantum computation and communication tasks. In contrast to photon storage, many quantum computation and simulation applications require individual addressing of closely-spaced atoms, ions, quantum dots, or solid state defects. To meet this requirement, we propose a method for coherent optical far-field manipulation of quantumsystems with a resolution that is not limited by the wavelength of radiation. While alkali atoms are currently the system of choice for photon storage and many other applications, we develop new methods for quantum information processing and quantum simulation with ultracold alkaline-earth atoms in optical lattices. We show how multiple qubits can be encoded in individual alkaline-earth atoms and harnessed for quantum computing and precision measurements applications. We also demonstrate that alkaline-earth atoms can be used to simulate highly symmetric systems exhibiting spin-orbital interactions and capable of providing valuable insights into strongly
We investigate the difficulties that undergraduate students in quantummechanics courses have in transferring learning from previous courses or within the same course from one context to another by administering written tests and conducting individual interviews. Quantummechanics is abstract and its paradigm is very different from the classical one. A good grasp of the principles of quantummechanics requires creating and organizing a knowledge structure consistent with the quantum postulates. Previously learned concepts such as the principle of superposition and probability can be useful in quantummechanics if students are given opportunity to build associations between new and prior knowledge. We also discuss the need for better alignment between quantummechanics and modern physics courses taken previously because semi-classical models can impede internalization of the quantum paradigm in more advanced courses.
Dalla Piazza, Bastien; Mourigal, M.; Christensen, N. B.; ...
2014-12-15
Quantum magnets have occupied the fertile ground between many-body theory and low-temperature experiments on real materials since the early days of quantummechanics. However, our understanding of even deceptively simple systems of interacting spins-1/2 is far from complete. The quantum square-lattice Heisenberg antiferromagnet (QSLHAF), for example, exhibits a striking anomaly of hitherto unknown origin in its magnetic excitation spectrum. This quantum effect manifests itself for excitations propagating with the specific wave vector (π, 0). Here, we use polarized neutron spectroscopy to fully characterize the magnetic fluctuations in the metal-organic compound CFTD, a known realization of the QSLHAF model. Our experimentsmore » reveal an isotropic excitation continuum at the anomaly, which we analyse theoretically using Gutzwiller-projected trial wavefunctions. The excitation continuum is accounted for by the existence of spatially-extended pairs of fractional S=1/2 quasiparticles, 2D analogues of 1D spinons. Away from the anomalous wave vector, these fractional excitations are bound and form conventional magnons. Lastly, our results establish the existence of fractional quasiparticles in the high-energy spectrum of a quasi-two-dimensional antiferromagnet, even in the absence of frustration.« less
This paper aims at the development of 't Hooft's quantization proposal to describe composite quantummechanicalsystems. In particular, we show how 't Hooft's method can be utilized to obtain from two classical Bateman oscillators a composite quantumsystem corresponding to a quantum isotonic oscillator. For a suitable range of parameters, the composite system can be also interpreted as a particle in an effective magnetic field interacting through a spin-orbital interaction term. In the limit of a large separation from the interaction region we can identify the irreducible subsystems with two independent quantum oscillators.
Quantum heat engines employ as working agents multilevel systems instead of classical gases. We show that under some conditions quantum heat engines are equivalent to a series of reservoirs at different altitudes containing balls of various weights. A cycle consists of picking up at random a ball from one reservoir and carrying it to the next, thereby performing or absorbing some work. In particular, quantum heat engines, employing two-level atoms as working agents, are modeled by reservoirs containing balls of weight 0 or 1. The mechanical model helps us prove that the maximum efficiency of quantum heat engines is the Carnot efficiency. Heat pumps and negative temperatures are considered.
We prove the uniqueness of the ground state for a supersymmetric quantummechanicalsystem of two fermions and two bosons, which is closely related to theN=1 WZ-model. The proof is constructive and gives detailed information on what the ground state looks like
The purpose of this study was to construct a valid and reliable multiple-choice achievement test to assess students' understanding of core concepts of introductory quantummechanics. Development of the QuantumMechanics Visualization Instrument (QMVI) occurred across four successive semesters in 1999--2001. During this time 213 undergraduate and graduate students attending the Pennsylvania State University (PSU) at University Park and Arizona State University (ASU) participated in this development and validation study. Participating students were enrolled in four distinct groups of courses: Modern Physics, Undergraduate QuantumMechanics, Graduate QuantumMechanics, and Chemistry QuantumMechanics. Expert panels of professors of physics experienced in teaching quantummechanics courses and graduate students in physics and science education established the core content and assisted in the validating of successive versions of the 24-question QMVI. Instrument development was guided by procedures outlined in the Standards for Educational and Psychological Testing (AERA-APA-NCME, 1999). Data gathered in this study provided information used in the development of successive versions of the QMVI. Data gathered in the final phase of administration of the QMVI also provided evidence that the intended score interpretation of the QMVI achievement test is valid and reliable. A moderate positive correlation coefficient of 0.49 was observed between the students' QMVI scores and their confidence levels. Analyses of variance indicated that students' scores in Graduate QuantumMechanics and Undergraduate QuantumMechanics courses were significantly higher than the mean scores of students in Modern Physics and Chemistry QuantumMechanics courses (p < 0.05). That finding is consistent with the additional understanding and experience that should be anticipated in graduate students and junior-senior level students over sophomore physics majors and majors in another field. The moderate
Scanning gate microscopy of quantum point contacts (QPC) in the integer quantum Hall regime is considered in terms of the scattering wave functions with a finite-difference implementation of the quantum transmitting boundary approach. Conductance (G) maps for a clean QPC as well as for a system including an antidot within the QPC constriction are evaluated. The steplike locally flat G maps for clean QPCs turn into circular resonances that are reentrant in an external magnetic field when the antidot is introduced to the constriction. The current circulation around the antidot and the spacing of the resonances at the magnetic field scale react to the probe approaching the QPC. The calculated G maps with a rigid but soft antidot potential reproduce the features detected recently in the electron interferometer [F. Martins et al., Sci. Rep. 3, 1416 (2013), 10.1038/srep01416].
Molecular mechanics methods can efficiently compute the macroscopic properties of a large molecular system but cannot represent the electronic changes that occur during a chemical reaction or an electronic transition. Quantummechanical methods can accurately simulate these processes, but they require considerably greater computational resources. Because electronic changes typically occur in a limited part of the system, such as the solute in a molecular solution or the substrate within the active site of enzymatic reactions, researchers can limit the quantum computation to this part of the system. Researchers take into account the influence of the surroundings by embedding this quantum computation into a calculation of the whole system described at the molecular mechanical level, a strategy known as the mixed quantummechanics/molecular mechanics (QM/MM) approach. The accuracy of this embedding varies according to the types of interactions included, whether they are purely mechanical or classically electrostatic. This embedding can also introduce the induced polarization of the surroundings. The difficulty in QM/MM calculations comes from the splitting of the system into two parts, which requires severing the chemical bonds that link the quantummechanical subsystem to the classical subsystem. Typically, researchers replace the quantoclassical atoms, those at the boundary between the subsystems, with a monovalent link atom. For example, researchers might add a hydrogen atom when a C-C bond is cut. This Account describes another approach, the Local Self Consistent Field (LSCF), which was developed in our laboratory. LSCF links the quantummechanical portion of the molecule to the classical portion using a strictly localized bond orbital extracted from a small model molecule for each bond. In this scenario, the quantoclassical atom has an apparent nuclear charge of +1. To achieve correct bond lengths and force constants, we must take into account the inner shell of
Learning physics is challenging at all levels. Students' difficulties in the introductory level physics courses have been widely studied and many instructional strategies have been developed to help students learn introductory physics. However, research shows that there is a large diversity in students' preparation and skills in the upper-level physics courses and it is necessary to provide scaffolding support to help students learn advanced physics. This thesis explores issues related to students' common difficulties in learning upper-level undergraduate quantummechanics and how these difficulties can be reduced by research-based learning tutorials and peer instruction tools. We investigated students' difficulties in learning quantummechanics by administering written tests and surveys to many classes and conducting individual interviews with a subset of students. Based on these investigations, we developed Quantum Interactive Learning Tutorials (QuILTs) and peer instruction tools to help students build a hierarchical knowledge structure of quantummechanics through a guided approach. Preliminary assessments indicate that students' understanding of quantummechanics is improved after using the research-based learning tools in the junior-senior level quantummechanics courses. We also designed a standardized conceptual survey that can help instructors better probe students' understanding of quantummechanics concepts in one spatial dimension. The validity and reliability of this quantummechanics survey is discussed.
Quantum computation and cryptography both involve scenarios in which a user interacts with an imperfectly modelled or 'untrusted' system. It is therefore of fundamental and practical interest to devise tests that reveal whether the system is behaving as instructed. In 1969, Clauser, Horne, Shimony and Holt proposed an experimental test that can be passed by a quantum-mechanicalsystem but not by a system restricted to classical physics. Here we extend this test to enable the characterization of a large quantumsystem. We describe a scheme that can be used to determine the initial state and to classically command the system to evolve according to desired dynamics. The bipartite system is treated as two black boxes, with no assumptions about their inner workings except that they obey quantum physics. The scheme works even if the system is explicitly designed to undermine it; any misbehaviour is detected. Among its applications, our scheme makes it possible to test whether a claimed quantum computer is truly quantum. It also advances towards a goal of quantum cryptography: namely, the use of 'untrusted' devices to establish a shared random key, with security based on the validity of quantum physics.
In this dissertation, we study the quantummechanics of classically chaotic dynamical systems. We begin by considering the decoherence effects a quantum chaotic system has on a simple quantum few state system. Typical time evolution of a quantumsystem whose classical limit is chaotic generates structures in phase space whose size is much smaller than Planck's constant. A naive application of Heisenberg's uncertainty principle indicates that these structures are not physically relevant. However, if we take the quantum chaotic system in question to be an environment which interacts with a simple two state quantumsystem (qubit), we show that these small phase-space structures cause the qubit to generically lose quantum coherence if and only if the environment has many degrees of freedom, such as a dilute gas. This implies that many-body environments may be crucial for the phenomenon of quantum decoherence. Next, we turn to an analysis of statistical properties of time correlation functions and matrix elements of quantum chaotic systems. A semiclassical evaluation of matrix elements of an operator indicates that the dominant contribution will be related to a classical time correlation function over the energy surface. For a highly chaotic class of dynamics, these correlation functions may be decomposed into sums of Ruelle resonances, which control exponential decay to the ergodic distribution. The theory is illustrated both numerically and theoretically on the Baker map. For this system, we are able to isolate individual Ruelle modes. We further consider dynamical systems whose approach to ergodicity is given by a power law rather than an exponential in time. We propose a billiard with diffusive boundary conditions, whose classical solution may be calculated analytically. We go on to compare the exact solution with an approximation scheme, as well calculate asympotic corrections. Quantum spectral statistics are calculated assuming the validity of the Again, Altshuler
We numerically investigated the optical rectification coefficients (ORCs), transmission coefficient, energy levels and corresponding eigen-functions of GaAs/AlGaAs Fibonacci ordered multiple quantum well systems (FO-MQWs) in the presence of an external electric field. In our calculations, two different methods, including transfer matrix and finite-difference have been used. It has been illustrated that with three types of the FO-MQWs, presented here, localization of the wave-function in any position of the structure is possible. Therefore, managing the electron distribution within the system is easier now. Finally, using the presented structures we could tune the position and amplitude of the ORCs.
This paper presents a minimal formulation of nonrelativistic quantummechanics, by which is meant a formulation which describes the theory in a succinct, self-contained, clear, unambiguous and of course correct manner. The bulk of the presentation is the so-called "microscopic theory", applicable to any closed system S of arbitrary size N, using concepts referring to S alone, without resort to external apparatus or external agents. An example of a similar minimal microscopic theory is the standard formulation of classical mechanics, which serves as the template for a minimal quantum theory. The only substantive assumption required is the replacement of the classical Euclidean phase space by Hilbert space in the quantum case, with the attendant all-important phenomenon of quantum incompatibility. Two fundamental theorems of Hilbert space, the Kochen-Specker-Bell theorem and Gleason's theorem, then lead inevitably to the well-known Born probability rule. For both classical and quantummechanics, questions of physical implementation and experimental verification of the predictions of the theories are the domain of the macroscopic theory, which is argued to be a special case or application of the more general microscopic theory.
In this chapter, we show two fascinating topics lying between quantum information processing and statistical mechanics. First, we introduce an elaborated technique, the surface code, to prepare the particular quantum state with robustness against decoherence. Interestingly, the theoretical limitation of the surface code, accuracy threshold, to restore the quantum state has a close connection with the problem on the phase transition in a special model known as spin glasses, which is one of the most active researches in statistical mechanics. The phase transition in spin glasses is an intractable problem, since we must strive many-body system with complicated interactions with change of their signs depending on the distance between spins. Fortunately, recent progress in spin-glass theory enables us to predict the precise location of the critical point, at which the phase transition occurs. It means that statistical mechanics is available for revealing one of the most interesting parts in quantum information processing. We show how to import the special tool in statistical mechanics into the problem on the accuracy threshold in quantum computation. Second, we show another interesting technique to employ quantum nature, quantum annealing. The purpose of quantum annealing is to search for the most favored solution of a multivariable function, namely optimization problem. The most typical instance is the traveling salesman problem to find the minimum tour while visiting all the cities. In quantum annealing, we introduce quantum fluctuation to drive a particular system with the artificial Hamiltonian, in which the ground state represents the optimal solution of the specific problem we desire to solve. Induction of the quantum fluctuation gives rise to the quantum tunneling effect, which allows nontrivial hopping from state to state. We then sketch a strategy to control the quantum fluctuation efficiently reaching the ground state. Such a generic framework is called
Although time-dependent quantumsystems have been studied since the very beginning of quantummechanics, they continue to attract the attention of many researchers, and almost every decade new important discoveries or new fields of application are made. Among the impressive results or by-products of these studies, one should note the discovery of the path integral method in the 1940s, coherent and squeezed states in the 1960-70s, quantum tunneling in Josephson contacts and SQUIDs in the 1960s, the theory of time-dependent quantum invariants in the 1960-70s, different forms of quantum master equations in the 1960-70s, the Zeno effect in the 1970s, the concept of geometric phase in the 1980s, decoherence of macroscopic superpositions in the 1980s, quantum non-demolition measurements in the 1980s, dynamics of particles in quantum traps and cavity QED in the 1980-90s, and time-dependent processes in mesoscopic quantum devices in the 1990s. All these topics continue to be the subject of many publications. Now we are witnessing a new wave of interest in quantum non-stationary systems in different areas, from cosmology (the very first moments of the Universe) and quantum field theory (particle pair creation in ultra-strong fields) to elementary particle physics (neutrino oscillations). A rapid increase in the number of theoretical and experimental works on time-dependent phenomena is also observed in quantum optics, quantum information theory and condensed matter physics. Time-dependent tunneling and time-dependent transport in nano-structures are examples of such phenomena. Another emerging direction of study, stimulated by impressive progress in experimental techniques, is related to attempts to observe the quantum behavior of macroscopic objects, such as mirrors interacting with quantum fields in nano-resonators. Quantum effects manifest themselves in the dynamics of nano-electromechanical systems; they are dominant in the quite new and very promising field of circuit
Konstantinidis, George; Mahajan, Raghu; Shaghoulian, Edgar
2016-10-01
In this short note we organize a perturbation theory for the Bunch-Davies wavefunction in flat, accelerating cosmologies. The calculational technique avoids the in-in formalism and instead uses an analytic continuation from Euclidean signature. We will consider both massless and conformally coupled self-interacting scalars. These calculations explicitly illustrate two facts. The first is that IR divergences get sharper as the acceleration slows. The second is that UV-divergent contact terms in the Euclidean computation can contribute to the absolute value of the wavefunction in Lorentzian signature. Here UV divergent refers to terms involving inverse powers of the radial cutoff in the Euclidean computation. In Lorentzian signature such terms encode physical time dependence of the wavefunction.
The efficient and accurate description of the electronic structure of strongly correlated systems is still a largely unsolved problem. The usual procedures start with a multiconfigurational (usually a Complete Active Space, CAS) wavefunction which accounts for static correlation and add dynamical correlation by perturbation theory, configuration interaction, or coupled cluster expansion. This procedure requires the correct selection of the active space. Intuitive methods are unreliable for complex systems. The inexpensive black-box unrestricted natural orbital (UNO) criterion postulates that the Unrestricted Hartree-Fock (UHF) charge natural orbitals with fractional occupancy (e.g., between 0.02 and 1.98) constitute the active space. UNOs generally approximatemore » the CAS orbitals so well that the orbital optimization in CAS Self-Consistent Field (CASSCF) may be omitted, resulting in the inexpensive UNO-CAS method. A rigorous testing of the UNO criterion requires comparison with approximate full configuration interaction wavefunctions. This became feasible with the advent of Density Matrix Renormalization Group (DMRG) methods which can approximate highly correlated wavefunctions at affordable cost. We have compared active orbital occupancies in UNO-CAS and CASSCF calculations with DMRG in a number of strongly correlated molecules: compounds of electronegative atoms (F{sub 2}, ozone, and NO{sub 2}), polyenes, aromatic molecules (naphthalene, azulene, anthracene, and nitrobenzene), radicals (phenoxy and benzyl), diradicals (o-, m-, and p-benzyne), and transition metal compounds (nickel-acetylene and Cr{sub 2}). The UNO criterion works well in these cases. Other symmetry breaking solutions, with the possible exception of spatial symmetry, do not appear to be essential to generate the correct active space. In the case of multiple UHF solutions, the natural orbitals of the average UHF density should be used. The problems of the UNO criterion and their potential
The quantum statistics of particles refers to the behavior of a multiparticle wavefunction under adiabatic interchange of two identical particles. While a three dimensional world affords the possibilities of Bosons or Fermions, the two dimensional world has more exotic possibilities such as Fractional and Nonabelian statistics (J. Frölich, in ``Nonperturbative Quantum Field Theory", ed, G. t'Hooft. 1988). The latter is perhaps the most interesting where the wavefunction obeys a ``nonabelian'' representation of the braid group - meaning that braiding A around B then B around C is not the same as braiding B around C then A around B. This property enables one to think about using these exotic systems for robust topological quantum computation (M. Freedman, A. Kitaev, et al, Bull Am Math Soc 40, 31 (2003)). Surprisingly, it is thought that quasiparticles excitations with such nonabelian statistics may actually exist in certain quantum Hall states that have already been observed. The most likely such candidate is the quantum Hall ν=5/2 state(R. L. Willett et al, Phys. Rev. Lett. 59, 1776-1779 (1987)), thought to be a so-called Moore-Read Pfaffian state(G. Moore and N. Read, Nucl Phys. B360 362 (1991)), which can be thought of as a p-wave paired superconducting state of composite fermions(M. Greiter, X. G. Wen, and F. Wilczek, PRL 66, 3205 (1991)). Using this superconducting analogy, we use a Chern-Simons field theory approach to make a number of predictions as to what experimental signatures one should expect for this state if it really is this Moore-Read state(K. Foster, N. Bonesteel, and S. H. Simon, PRL 91 046804 (2003)). We will then discuss how the nonabelian statistics can be explored in detail using a quantum monte-carlo approach (Y. Tserkovnyak and S. H. Simon, PRL 90 106802 (2003)), (I. Finkler, Y. Tserkovnyak, and S. H. Simon, work in progress.) that allows one to explicitly drag one particle around another and observe the change in the wavefunctions
Bell showed that assuming locality leads to a disagreement with quantummechanics. Here the nature of the nonlocality that follows from quantummechanics is investigated. Note by the Editor—Readers will recognize Professor Rosen, author of this paper, as one of the co-authors of the famous EPR paper, Albert Einstein, Boris Podolsky, and Nathan Rosen, ``Can Quantum-Mechanical Description of Physical Reality be considered Complete?'', Phys. Rev. 47, 770-780 (1935). Robert H. Romer, Editor
The focus of this paper is to provide a brief discussion on the quantum measurement process, by reviewing select examples highlighting recent progress towards its understanding. The areas explored include an outline of the measurement problem, the standard interpretation of quantummechanics, quantum to classical transition, types of measurement (including weak and projective measurements) and newly emerging interpretations of quantummechanics (decoherence theory, objective reality, quantum Darwinism and quantum Bayesianism).
We calculate the time taken by a wave packet to travel through a classically forbidden region of space in space fractional quantummechanics. We obtain the close form expression of tunneling time from a rectangular barrier by stationary phase method. We show that tunneling time depends upon the width b of the barrier for b → ∞ and therefore Hartman effect doesn't exist in space fractional quantummechanics. Interestingly we found that the tunneling time monotonically reduces with increasing b. The tunneling time is smaller in space fractional quantummechanics as compared to the case of standard quantummechanics. We recover the Hartman effect of standard quantummechanics as a special case of space fractional quantummechanics.
In recent years, quantum walks have been proposed as promising resources for the simulation of physical quantumsystems. In fact it is widely adopted to simulate quantum dynamics. Up to now single particle quantum walks have been experimentally demonstrated by different approaches, while only few experiments involving many-particle quantum walks have been realized. Here we simulate the 2-particle dynamics on a discrete time quantum walk, built on an array of integrated waveguide beam splitters. The polarization independence of the quantum walk circuit allowed us to exploit the polarization entanglement to encode the symmetry of the two-photon wavefunction, thus the bunching-antibunching behavior of non interacting bosons and fermions has been simulated. We have also characterized the possible distinguishability and decoherence effects arising in such a structure. This study is necessary in view of the realization of a quantum simulator based on an integrated optical array built on a large number of beam splitters.
Kitagawa, Takuya; Broome, Matthew A; Fedrizzi, Alessandro; Rudner, Mark S; Berg, Erez; Kassal, Ivan; Aspuru-Guzik, Alán; Demler, Eugene; White, Andrew G
2012-06-06
Topological phases exhibit some of the most striking phenomena in modern physics. Much of the rich behaviour of quantum Hall systems, topological insulators, and topological superconductors can be traced to the existence of robust bound states at interfaces between different topological phases. This robustness has applications in metrology and holds promise for future uses in quantum computing. Engineered quantumsystems--notably in photonics, where wavefunctions can be observed directly--provide versatile platforms for creating and probing a variety of topological phases. Here we use photonic quantum walks to observe bound states between systems with different bulk topological properties and demonstrate their robustness to perturbations--a signature of topological protection. Although such bound states are usually discussed for static (time-independent) systems, here we demonstrate their existence in an explicitly time-dependent situation. Moreover, we discover a new phenomenon: a topologically protected pair of bound states unique to periodically driven systems.
This paper contains the review of quantum entanglement investigations in living systems, and in the quantummechanically modelled photoactive prebiotic kernel systems. We define our modelled self-assembled supramolecular photoactive centres, composed of one or more sensitizer molecules, precursors of fatty acids and a number of water molecules, as a photoactive prebiotic kernel systems. We propose that life first emerged in the form of such minimal photoactive prebiotic kernel systems and later in the process of evolution these photoactive prebiotic kernel systems would have produced fatty acids and covered themselves with fatty acid envelopes to become the minimal cells of the Fatty Acid World. Specifically, we model self-assembling of photoactive prebiotic systems with observed quantum entanglement phenomena. We address the idea that quantum entanglement was important in the first stages of origins of life and evolution of the biospheres because simultaneously excite two prebiotic kernels in the system by appearance of two additional quantum entangled excited states, leading to faster growth and self-replication of minimal living cells. The quantummechanically modelled possibility of synthesizing artificial self-reproducing quantum entangled prebiotic kernel systems and minimal cells also impacts the possibility of the most probable path of emergence of protocells on the Earth or elsewhere. We also examine the quantum entangled logic gates discovered in the modelled systems composed of two prebiotic kernels. Such logic gates may have application in the destruction of cancer cells or becoming building blocks of new forms of artificial cells including magnetically active ones.
Multiscale modeling has become a popular tool for research applying to different areas including materials science, microelectronics, biology, chemistry, etc. In this tutorial review, we describe a newly developed multiscale computational method, incorporating quantummechanics into electronic device modeling with the electromagnetic environment included through classical electrodynamics. In the quantummechanics/electromagnetics (QM/EM) method, the regions of the system where active electron scattering processes take place are treated quantummechanically, while the surroundings are described by Maxwell's equations and a semiclassical drift-diffusion model. The QM model and the EM model are solved, respectively, in different regions of the system in a self-consistent manner. Potential distributions and current densities at the interface between QM and EM regions are employed as the boundary conditions for the quantummechanical and electromagnetic simulations, respectively. The method is illustrated in the simulation of several realistic systems. In the case of junctionless field-effect transistors, transfer characteristics are obtained and a good agreement between experiments and simulations is achieved. Optical properties of a tandem photovoltaic cell are studied and the simulations demonstrate that multiple QM regions are coupled through the classical EM model. Finally, the study of a carbon nanotube-based molecular device shows the accuracy and efficiency of the QM/EM method.
Newton's mechanics in the 17th century increased the lethality of artillery. Thermodynamics in the 19th led to the steam-powered industrial revolution. Maxwell's unification of electricity, magnetism and light gave us electrical power, the telegraph, radio and television. The discovery of quantummechanics in the 20th century by Planck, Bohr, Einstein, Schrodinger, Heisenberg led to the creation of the atomic and hydrogen bombs as well as computer chips, the world-wide-web and Silicon Valley's multibillion dollar corporations. The lesson is that breakthroughs in fundamental physics, both theoretical and experimental, have always led to profound technological wealth-creating industries and will continue to do so. There is now a new revolution brewing in quantummechanics that can be divided into three periods. The first quantum revolution was from 1900 to about 1975. The second quantum information/computer revolution was from about 1975 to 2015. (The early part of this story is told by Kaiser in his book, How the Hippies Saved Physics, how a small group of Berkeley/San Francisco physicists triggered that second revolution.) The third quantum revolution is how an extension of quantummechanics may lead to the understanding of consciousness as a natural physical phenomenon that can emerge in many material substrates, not only in our carbon-based biochemistry. In particular, this new post-quantummechanics may lead to naturally conscious artificial intelligence in nano-electronic machines, as well as perhaps extending human life spans to hundreds of years and more.
The purpose of this presentation is to assess the status of our understanding of the transition from integrability to thermalizability in isolated quantumsystems. In Classical Mechanics, the boundary stripe between the two is relatively sharp: its integrability edge is marked by the appearance of finite Lyapunov's exponents that further converge to a unique value when the ergodicity edge is reached. Classical ergodicity is a universal property: if a system is ergodic, then every observable attains its microcanonical value in the infinite time average over the trajectory. On the contrary, in QuantumMechanics, Lyapunov's exponents are always zero. Furthermore, since quantum dynamics necessarily invokes coherent superpositions of eigenstates of different energy, projectors to the eigenstates become more relevant; those in turn never thermalize. All of the above indicates that in quantum many-body systems, (a) the integrability-thermalizability transition is smooth, and (b) the degree of thermalizability is not absolute like in classical mechanics, but it is relative to the class of observables of interest. In accordance with these observations, we propose a concrete measure of the degree of quantum thermalizability, consistent with the expected empirical manifestations of it. As a practical application of this measure, we devise a unified recipe for choosing an optimal set of conserved quantities to govern the after-relaxation values of observables, in both integrable quantumsystems and in quantumsystems in between integrable and thermalizable.
the actual data scales with the system dimension for state-vector manipulations, and the square of the dimension for density-operator manipulations. This might easily be GBs, and often the memory of the machine limits the size of the simulated system. Classification: 4.3, 4.13, 6.2, 20 External routines: Boost C++ libraries (http://www.boost.org/), GNU Scientific Library (http://www.gnu.org/software/gsl/), Blitz++ (http://www.oonumerics.org/blitz/), Linear Algebra Package - Flexible Library for Efficient Numerical Solutions (http://flens.sourceforge.net/). Nature of problem: Definition of (open) composite quantumsystems out of elementary building blocks [1]. Manipulation of such systems, with emphasis on dynamical simulations such as Master-equation evolution [2] and Monte Carlo wave-function simulation [3]. Solution method: Master equation, Monte Carlo wave-function method. Restrictions: Total dimensionality of the system. Master equation - few thousands. Monte Carlo wave-function trajectory - several millions. Unusual features: Because of the heavy use of compile-time algorithms, compilation of programs written in the framework may take a long time and much memory (up to several GBs). Additional comments: The framework is not a program, but provides and implements an application-programming interface for developing simulations in the indicated problem domain. Supplementary information: http://cppqed.sourceforge.net/. Running time: Depending on the magnitude of the problem, can vary from a few seconds to weeks.
In the context of nonrelativistic quantummechanics, Gaussian wavepacket solutions of the time-dependent Schrödinger equation provide useful physical insight. This is not the case for relativistic quantummechanics, however, for which both the Klein-Gordon and Dirac wave equations result in strange and counterintuitive wavepacket behaviors, even for free-particle Gaussians. These behaviors include zitterbewegung and other interference effects. As a potential remedy, this paper explores a new trajectory-based formulation of quantummechanics, in which the wavefunction plays no role [Phys. Rev. X, 4, 040002 (2014)]. Quantum states are represented as ensembles of trajectories, whose mutual interaction is the source of all quantum effects observed in nature—suggesting a “many interacting worlds” interpretation. It is shown that the relativistic generalization of the trajectory-based formulation results in well-behaved free-particle Gaussian wavepacket solutions. In particular, probability density is positive and well-localized everywhere, and its spatial integral is conserved over time—in any inertial frame. Finally, the ensemble-averaged wavepacket motion is along a straight line path through spacetime. In this manner, the pathologies of the wave-based relativistic quantum theory, as applied to wavepacket propagation, are avoided.
Macroscopic objects, although quantummechanical by nature, conform to Newtonian mechanics under normal observation. According to the quantummechanical correspondence principle, quantum behavior is indistinguishable from classical behavior in the limit of very large quantum numbers. The purpose of this paper is to provide an example of the…
A method for determining the ground state of a planar interacting many-electron system in a magnetic field perpendicular to the plane is described. The ground state wave-function is expressed as a linear combination of a set of basis functions. Given only the flux and the number of electrons describing an incompressible state, we use the combinatorics of partitioning the flux among the electrons to derive the basis wave-functions as linear combinations of Schur polynomials. The procedure ensures that the basis wave-functions form representations of the angular momentum algebra. We exemplify the method by deriving the basis functions for the 5/2 quantum Hall state with a few particles. We find that one of the basis functions is precisely the Moore-Read Pfaffian wave function.
Bender, Carl M; DeKieviet, Maarten; Klevansky, S. P.
2013-01-01
-symmetric quantummechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on -symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a -symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the phase transition can now be understood intuitively without resorting to sophisticated mathe- matics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter–antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of -synthetic materials are being developed, and the phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of -symmetric quantummechanics. PMID:23509390
An extensively pursued current direction of research in physics aims at the development of practical technologies that exploit the effects of quantummechanics. As part of this ongoing effort, devices for quantum information processing, secure communication, and high-precision sensing are being implemented with diverse systems, ranging from photons, atoms, and spins to mesoscopic superconducting and nanomechanical structures. Their physical properties make some of these systems better suited than others for specific tasks; thus, photons are well suited for transmitting quantum information, weakly interacting spins can serve as long-lived quantum memories, and superconducting elements can rapidly process information encoded in their quantum states. A central goal of the envisaged quantum technologies is to develop devices that can simultaneously perform several of these tasks, namely, reliably store, process, and transmit quantum information. Hybrid quantumsystems composed of different physical components with complementary functionalities may provide precisely such multitasking capabilities. This article reviews some of the driving theoretical ideas and first experimental realizations of hybrid quantumsystems and the opportunities and challenges they present and offers a glance at the near- and long-term perspectives of this fascinating and rapidly expanding field.
An extensively pursued current direction of research in physics aims at the development of practical technologies that exploit the effects of quantummechanics. As part of this ongoing effort, devices for quantum information processing, secure communication, and high-precision sensing are being implemented with diverse systems, ranging from photons, atoms, and spins to mesoscopic superconducting and nanomechanical structures. Their physical properties make some of these systems better suited than others for specific tasks; thus, photons are well suited for transmitting quantum information, weakly interacting spins can serve as long-lived quantum memories, and superconducting elements can rapidly process information encoded in their quantum states. A central goal of the envisaged quantum technologies is to develop devices that can simultaneously perform several of these tasks, namely, reliably store, process, and transmit quantum information. Hybrid quantumsystems composed of different physical components with complementary functionalities may provide precisely such multitasking capabilities. This article reviews some of the driving theoretical ideas and first experimental realizations of hybrid quantumsystems and the opportunities and challenges they present and offers a glance at the near- and long-term perspectives of this fascinating and rapidly expanding field. PMID:25737558
An extensively pursued current direction of research in physics aims at the development of practical technologies that exploit the effects of quantummechanics. As part of this ongoing effort, devices for quantum information processing, secure communication, and high-precision sensing are being implemented with diverse systems, ranging from photons, atoms, and spins to mesoscopic superconducting and nanomechanical structures. Their physical properties make some of these systems better suited than others for specific tasks; thus, photons are well suited for transmitting quantum information, weakly interacting spins can serve as long-lived quantum memories, and superconducting elements can rapidly process information encoded in their quantum states. A central goal of the envisaged quantum technologies is to develop devices that can simultaneously perform several of these tasks, namely, reliably store, process, and transmit quantum information. Hybrid quantumsystems composed of different physical components with complementary functionalities may provide precisely such multitasking capabilities. This article reviews some of the driving theoretical ideas and first experimental realizations of hybrid quantumsystems and the opportunities and challenges they present and offers a glance at the near- and long-term perspectives of this fascinating and rapidly expanding field.
We show that the quantum Jarzynski equality generalizes to PT -symmetric quantummechanics with unbroken PT -symmetry. In the regime of broken PT -symmetry the Jarzynski equality does not hold as also the CPT -norm is not preserved during the dynamics. These findings are illustrated for an experimentally relevant system – two coupled optical waveguides. It turns out that for these systems the phase transition between the regimes of unbroken and broken PT -symmetry is thermodynamically inhibited as the irreversible work diverges at the critical point.
The popular conception of black holes reflects the behavior of the massive black holes found by astronomers and described by classical general relativity. These objects swallow up whatever comes near and emit nothing. Physicists who have tried to understand the behavior of black holes from a quantummechanical point of view, however, have arrived at quite a different picture. The difference is analogous to the difference between thermodynamics and statistical mechanics. The thermodynamic description is a good approximation for a macroscopic system, but statistical mechanics describes what one will see if one looks more closely.
The Horizon QuantumMechanics is an approach that allows one to analyse the gravitational radius of spherically symmetric systems and compute the probability that a given quantum state is a black hole. We first review the (global) formalism and show how it reproduces a gravitationally inspired GUP relation. This results leads to unacceptably large fluctuations in the horizon size of astrophysical black holes if one insists in describing them as (smeared) central singularities. On the other hand, if they are extended systems, like in the corpuscular models, no such issue arises and one can in fact extend the formalism to include asymptotic mass and angular momentum with the harmonic model of rotating corpuscular black holes. The Horizon QuantumMechanics then shows that, in simple configurations, the appearance of the inner horizon is suppressed and extremal (macroscopic) geometries seem disfavoured.
A system for classifying and quantifying entanglement in spin 1/2 pure states is presented based on simple images. From the image point of view, an entangled state can be described as a linear superposition of separable object wavefunction ΨO plus a portion of its own inverse image. Bell states can be defined in this way: \\Psi = 1/\\sqrt 2 (\\Psi _O \\pm \\Psi _I ). Using the method of images, the three-spin 1/2 system is discussed in some detail. This system can exhibit exclusive three-particle ν123 entanglement, two-particle entanglements ν12, ν13, ν23 and/or mixtures of all four. All four image states are orthogonal both to each other and to the object wavefunction. In general, five entanglement parameters ν12, ν13, ν23, ν123 and phi123 are required to define the general entangled state. In addition, it is shown that there is considerable scope for encoding numbers, at least from the classical point of view but using quantum-mechanical principles. Methods are developed for their extraction. It is shown that concurrence can be used to extract even-partite, but not odd-partite information. Additional relationships are also presented which can be helpful in the decoding process. However, in general, numerical methods are mandatory. A simple roulette method for decoding is presented and discussed. But it is shown that if the encoder chooses to use transcendental numbers for the angles defining the target function (α1, β1), etc, the method rapidly turns into the Devil's roulette, requiring finer and finer angular steps.
This article examines some experimental conditions that invite and possibly require recourse to quantum-mechanical-like mathematical models (QMLMs), models based on the key mathematical features of quantummechanics, in scientific fields outside physics, such as biology, cognitive psychology, or economics. In particular, I consider whether the following two correlative features of quantum phenomena that were decisive for establishing the mathematical formalism of quantummechanics play similarly important roles in QMLMs elsewhere. The first is the individuality and discreteness of quantum phenomena, and the second is the irreducibly probabilistic nature of our predictions concerning them, coupled to the particular character of the probabilities involved, as different from the character of probabilities found in classical physics. I also argue that these features could be interpreted in terms of a particular form of epistemology that suspends and even precludes a causal and, in the first place, realist description of quantum objects and processes. This epistemology limits the descriptive capacity of quantum theory to the description, classical in nature, of the observed quantum phenomena manifested in measuring instruments. Quantummechanics itself only provides descriptions, probabilistic in nature, concerning numerical data pertaining to such phenomena, without offering a physical description of quantum objects and processes. While QMLMs share their use of the quantum-mechanical or analogous mathematical formalism, they may differ by the roles, if any, the two features in question play in them and by different ways of interpreting the phenomena they considered and this formalism itself. This article will address those differences as well.
We study certain non-symmetric wavefunctions associated with the quantum nonlinear Schrödinger model, introduced by Komori and Hikami using Gutkin’s propagation operator, which involves representations of the degenerate affine Hecke algebra. We highlight how these functions can be generated using a vertex-type operator formalism similar to the recursion defining the symmetric (Bethe) wavefunction in the quantum inverse scattering method. Furthermore, some of the commutation relations encoded in the Yang-Baxter equation for the relevant monodromy matrix are generalized to the non-symmetric case.
Sinitskiy, Anton V.; Voth, Gregory A., E-mail: gavoth@uchicago.edu
2015-09-07
Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantumsystems at equilibrium has been based on Feynman’s imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionistmore » perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantummechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments.« less
Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantumsystems at equilibrium has been based on Feynman's imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionist perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantummechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments.
We explore quantummechanical theories whose fundamental degrees of freedom are rectangular matrices with Grassmann valued matrix elements. We study particular models where the low energy sector can be described in terms of a bosonic Hermitian matrix quantummechanics. We describe the classical curved phase space that emerges in the low energy sector. The phase space lives on a compact Kähler manifold parameterized by a complex matrix, of the type discovered some time ago by Berezin. The emergence of a semiclassical bosonic matrix quantummechanics at low energies requires that the original Grassmann matrices be in the long rectangular limit.more » In conclusion, we discuss possible holographic interpretations of such matrix models which, by construction, are endowed with a finite dimensional Hilbert space.« less
On the basis of Nelson's stochastic mechanics derivation of the Schrödinger equation, a formal mathematical structure of non-relativistic quantummechanics equivalent to the one in classical analytical mechanics has been established in the literature. We recently were able to augment this structure by deriving quantum Hamilton equations of motion by finding the Nash equilibrium of a stochastic optimal control problem, which is the generalization of Hamilton's principle of classical mechanics to quantumsystems. We showed that these equations allow a description and numerical determination of the ground state of quantum problems without using the Schrödinger equation. We extend this approach here to deliver the complete discrete energy spectrum and related eigenfunctions for bound states of one-dimensional stationary quantumsystems. We exemplify this analytically for the one-dimensional harmonic oscillator and numerically by analyzing a quartic double-well potential, a model of broad importance in many areas of physics. We furthermore point out a relation between the tunnel splitting of such models and mean first passage time concepts applied to Nelson's diffusion paths in the ground state.
When a molecule is subjected to a sufficiently energetic photon it can break apart into fragments through a process called ``photodissociation''. For over 70 years this simple chemical reaction has served as a vital experimental tool for acquiring information about molecular structure, since the character of the photodissociative transition can be inferred by measuring the 3D photofragment angular distribution (PAD). While theoretical understanding of this process has gradually evolved from classical considerations to a fully quantum approach, experiments to date have not yet revealed the full quantum nature of this process. In my talk I will describe recent experiments involving the photodissociation of ultracold, optical lattice-trapped, and fully quantum state-resolved 88Sr2 molecules. Optical absorption images of the PADs produced in these experiments reveal features which are inherently quantummechanical in nature, such as matter-wave interference between output channels, and are sensitive to the quantum statistics of the molecular wavefunctions. The results of these experiments cannot be predicted using quasiclassical methods. Instead, we describe our results with a fully quantummechanical model yielding new intuition about ultracold chemistry.
In proposed quantum computers, electromagnetic pulses are used to implement logic gates on quantum bits (qubits). Gates are unitary transformations applied to coherent qubit wavefunctions and a universal computer can be created using a minimal set of gates. By applying many elementary gates in sequence, desired quantum computations can be performed. This reduced instruction set approach to quantum computing (RISC QC) is characterized by serial application of a few basic pulse shapes and a long coherence time. However, the unitary matrix of the overall computation is ultimately a unitary matrix of the same size as any of the elementary matrices. This suggests that we might replace a sequence of reduced instructions with a single complex instruction using an optimally taylored pulse. We refer to this approach as complex instruction set quantum computing (CISC QC). One trades the requirement for long coherence times for the ability to design and generate potentially more complex pulses. We consider a model system of coupled qubits interacting through nearest neighbor coupling and show that CISC QC can reduce the time required to perform quantum computations.
The internal phase dynamics of a quantumsystem interacting with an electromagnetic field is revealed in details. Theoretical and experimental evidences of a causal relation of the phase of the wave function to the dynamics of the quantumsystem are presented sistematically for the first time. A dynamics-statistical interpretation of the quantummechanics is introduced.
Sodt, Alexander J; Mei, Ye; König, Gerhard; Tao, Peng; Steele, Ryan P; Brooks, Bernard R; Shao, Yihan
2015-03-05
In combined quantummechanical/molecular mechanical (QM/MM) free energy calculations, it is often advantageous to have a frozen geometry for the quantummechanical (QM) region. For such multiple-environment single-system (MESS) cases, two schemes are proposed here for estimating the polarization energy: the first scheme, termed MESS-E, involves a Roothaan step extrapolation of the self-consistent field (SCF) energy; whereas the other scheme, termed MESS-H, employs a Newton-Raphson correction using an approximate inverse electronic Hessian of the QM region (which is constructed only once). Both schemes are extremely efficient, because the expensive Fock updates and SCF iterations in standard QM/MM calculations are completely avoided at each configuration. They produce reasonably accurate QM/MM polarization energies: MESS-E can predict the polarization energy within 0.25 kcal/mol in terms of the mean signed error for two of our test cases, solvated methanol and solvated β-alanine, using the M06-2X or ωB97X-D functionals; MESS-H can reproduce the polarization energy within 0.2 kcal/mol for these two cases and for the oxyluciferin-luciferase complex, if the approximate inverse electronic Hessians are constructed with sufficient accuracy.
We discuss foundational issues of quantum information biology (QIB)—one of the most successful applications of the quantum formalism outside of physics. QIB provides a multi-scale model of information processing in bio-systems: from proteins and cells to cognitive and social systems. This theory has to be sharply distinguished from "traditional quantum biophysics". The latter is about quantum bio-physical processes, e.g., in cells or brains. QIB models the dynamics of information states of bio-systems. We argue that the information interpretation of quantummechanics (its various forms were elaborated by Zeilinger and Brukner, Fuchs and Mermin, and D' Ariano) is the most natural interpretation of QIB. Biologically QIB is based on two principles: (a) adaptivity; (b) openness (bio-systems are fundamentally open). These principles are mathematically represented in the framework of a novel formalism— quantum adaptive dynamics which, in particular, contains the standard theory of open quantumsystems.
When conducting the numerical simulation of quantum transport, the main obstacle is a rapid growth of the dimension of entangled Hilbert subspace. The Quantum Monte Carlo simulation techniques, while being capable of treating the problems of high dimension, are hindered by the so-called "sign problem". In the quantum transport, we have fundamental asymmetry between the processes of emission and absorption of environment excitations: the emitted excitations are rapidly and irreversibly scattered away. Whereas only a small part of these excitations is absorbed back by the open subsystem, thus exercising the non-Markovian self-action of the subsystem onto itself. We were able to devise a method for the exact simulation of the dominant quantum emission processes, while taking into account the small backaction effects in an approximate self-consistent way. Such an approach allows us to efficiently conduct simulations of real-time dynamics of small quantum subsystems immersed in non-Markovian bath for large times, reaching the quasistationary regime. As an example we calculate the spatial quench dynamics of Kondo cloud for a bozonized Kodno impurity model.
I ask the question: What can we infer about the nature and structure of the physical world (a) from experiments already done to test the predictions of quantummechanics (b) from the assumption that all future experiments will agree with those predictions? I discuss existing and projected experiments related to the two classic paradoxes of quantummechanics, named respectively for EPR and Schrödinger's Cat, and show in particular that one natural conclusion from both types of experiment implies the abandonment of the concept of macroscopic counterfactual definiteness.
In a two dimensional free electron gas subjected to a perpendicular spatially varying magnetic field, the classical paths of electrons are snake-like trajectories that weave along the line where the field crosses zero. But quantummechanically this system is described by a symmetric double well potential which, for low excitations, leads to very different electron behavior. We compute the spectrum, as well as the wavefunctions, for states of definite parity in the limit of nearly degenerate states, i.e. for electrons sufficiently far from the B z = 0 line. Transitions between the states are shown to give rise to a tunneling current. If the well is made asymmetrical by a time-dependent parity breaking perturbation then Rabi-like oscillations between parity states occur. Resonances can be excited and used to stimulate the transfer of electrons from one side of the potential barrier to the other through quantum tunneling.
In a two dimensional free electron gas subjected to a perpendicular spatially varying magnetic field, the classical paths of electrons are snake-like trajectories that weave along the line where the field crosses zero. But quantummechanically this system is described by a symmetric double well potential which, for low excitations, leads to very different electron behavior. We compute the spectrum, as well as the wavefunctions, for states of definite parity in the limit of nearly degenerate states, i.e. for electrons sufficiently far from the B z = 0 line. Transitions between the states are shown to give rise to a tunneling current. If the well is made asymmetrical by a time-dependent parity breaking perturbation then Rabi-like oscillations between parity states occur. Resonances can be excited and used to stimulate the transfer of electrons from one side of the potential barrier to the other through quantum tunneling.
We propose a variational wavefunction containing parameters to tune the probabilities of all the possible onsite configurations for the periodic Anderson model. We call it the full onsite-correlation wavefunction (FOWF). This is a simple extension of the Gutzwiller wavefunction (GWF), in which one parameter is included to tune the double occupancy of the f electrons at the same site. We compare the energy of the GWF and the FOWF evaluated by the variational Monte Carlo method and that obtained with the density-matrix renormalization group method. We find that the energy is considerably improved in the FOWF. On the other hand, the physical quantities do not change significantly between these two wavefunctions as long as they describe the same phase, such as the paramagnetic phase. From these results, we not only demonstrate the improvement by the FOWF, but we also gain insights on the applicability and limitation of the GWF to the periodic Anderson model.
In recent times, there is an upsurge of interest in demonstrating the quantum contextuality. In this proceedings, we explore the two different forms of arguments that have been used for showing the contextual character of quantummechanics. First line of study concerns the violations of the noncontextual realist models by quantummechanics, where second line of study that is qualitatively distinct from the earlier one, demonstrates the contextuality within the formalism of quantummechanics.
Critically analyzing the so-called quantum Zeno effect in the measurement problem, we show that observation of this effect does not necessarily mean experimental evidence for the naive notion of wave-function collapse by measurement (the simple projection rule). We also examine what kind of limitation the uncertainty relation and others impose on the observation of the quantum Zeno effect.
Perhaps the most important approximations to the electronic structure problem in quantum chemistry are those based on coupled cluster and density functional theories. Coupled cluster theory has been called the ``gold standard'' of quantum chemistry due to the high accuracy that it achieves for weakly correlated systems. Kohn-Sham density functionals based on semilocal approximations are, without a doubt, the most widely used methods in chemistry and material science because of their high accuracy/cost ratio. The root of the success of coupled cluster and density functionals is their ability to efficiently describe the dynamic part of the electron correlation. However, both traditional coupled cluster and density functional approximations may fail catastrophically when substantial static correlation is present. This severely limits the applicability of these methods to a plethora of important chemical and physical problems such as, e.g., the description of bond breaking, transition states, transition metal-, lanthanide- and actinide-containing compounds, and superconductivity. In an attempt to tackle this problem, nonstandard (single-reference) coupled cluster-based techniques that aim to describe static correlation have been recently developed: pair coupled cluster doubles (pCCD) and singlet-paired coupled cluster doubles (CCD0). The ability to describe static correlation in pCCD and CCD0 comes, however, at the expense of important amounts of dynamic correlation so that the high accuracy of standard coupled cluster becomes unattainable. Thus, the reliable and efficient description of static and dynamic correlation in a simultaneous manner remains an open problem for quantum chemistry and many-body theory in general. In this thesis, different ways to combine pCCD and CCD0 with density functionals in order to describe static and dynamic correlation simultaneously (and efficiently) are explored. The combination of wavefunction and density functional methods has a long
[This paper is part of the Focused Collection on Upper Division Physics Courses.] The time evolution of quantum states is arguably one of the more difficult ideas in quantummechanics. In this article, we report on results from an investigation of student understanding of this topic after lecture instruction. We demonstrate specific problems that students have in applying time dependence to quantumsystems and in recognizing the key role of the energy eigenbasis in determining the time dependence of wave functions. Through analysis of student responses to a set of four interrelated tasks, we categorize some of the difficulties that underlie common errors. The conceptual and reasoning difficulties that have been identified are illustrated through student responses to four sets of questions administered at different points in a junior-level course on quantummechanics. Evidence is also given that the problems persist throughout undergraduate instruction and into the graduate level.
Optical laser fields have been widely used to achieve quantum control over the motional and internal degrees of freedom of atoms and ions, molecules and atomic gases. A route to controlling the quantum states of macroscopic mechanical oscillators in a similar fashion is to exploit the parametric coupling between optical and mechanical degrees of freedom through radiation pressure in suitably engineered optical cavities. If the optomechanical coupling is 'quantum coherent'--that is, if the coherent coupling rate exceeds both the optical and the mechanical decoherence rate--quantum states are transferred from the optical field to the mechanical oscillator and vice versa. This transfer allows control of the mechanical oscillator state using the wide range of available quantum optical techniques. So far, however, quantum-coherent coupling of micromechanical oscillators has only been achieved using microwave fields at millikelvin temperatures. Optical experiments have not attained this regime owing to the large mechanical decoherence rates and the difficulty of overcoming optical dissipation. Here we achieve quantum-coherent coupling between optical photons and a micromechanical oscillator. Simultaneously, coupling to the cold photon bath cools the mechanical oscillator to an average occupancy of 1.7 ± 0.1 motional quanta. Excitation with weak classical light pulses reveals the exchange of energy between the optical light field and the micromechanical oscillator in the time domain at the level of less than one quantum on average. This optomechanical system establishes an efficient quantum interface between mechanical oscillators and optical photons, which can provide decoherence-free transport of quantum states through optical fibres. Our results offer a route towards the use of mechanical oscillators as quantum transducers or in microwave-to-optical quantum links.
Conventional approach to quantummechanics in phase space (q,p), is to take the operator based quantummechanics of Schroedinger, or an equivalent, and assign a c-number function in phase space to it. We propose to begin with a higher level of abstraction, in which the independence and the symmetric role of q and p is maintained throughout, and at once arrive at phase space state functions. Upon reduction to the q- or p-space the proposed formalism gives the conventional quantummechanics, however, with a definite rule for ordering of factors of noncommuting observables. Further conceptual and practical merits of themore » formalism are demonstrated throughout the text.« less
Recently, a new formulation of quantummechanics, based on the concept of signed particles, has been suggested. In this paper, we introduce a cellular automaton which mimics the dynamics of quantum objects in the phase-space in a time-dependent fashion. This is twofold: it provides a simplified and accessible language to non-physicists who wants to simulate quantummechanicalsystems, at the same time it enables a different way to explore the laws of Physics. Moreover, it opens the way towards hybrid simulations of quantumsystems by combining full quantum models with cellular automata when the former fail. In order to show the validity of the suggested cellular automaton and its combination with the signed particle formalism, several numerical experiments are performed, showing very promising results. Being this article a preliminary study on quantum simulations in phase-space by means of cellular automata, some conclusions are drawn about the encouraging results obtained so far and the possible future developments.
Quantum computation is a subject born out of the combination between physics and computer science. It studies how the laws of quantummechanics can be exploited to perform computations much more efficiently than current computers (termed classical computers as oppose to quantum computers). The thesis starts by introducing ideas from quantum physics and theoretical computer science and based on these ideas, introducing the basic concepts in quantum computing. These introductory discussions are intended for non-specialists to obtain the essential knowledge needed for understanding the new results presented in the subsequent chapters. After introducing the basics of quantum computing, we focus on the recently proposed quantum algorithm for linear systems. The new results include i) special instances of quantum circuits that can be implemented using current experimental resources; ii) detailed quantum algorithms that are suitable for a broader class of linear systems. We show that for some particular problems the quantum algorithm is able to achieve exponential speedup over their classical counterparts.
The concept of two (or more) particle entanglement lies at the heart of many fascinating questions concerning the foundations of quantummechanics. The counterintuitive nonlocal behavior of entangled states led Einstein, Podolsky, and Rosen (EPR) to ask their famous 1935 question, "Can quantummechanical description of reality be considered complete?". Although the debate has been raging on for more than 60 years, there is still no absolutely conclusive answer to this question. For if entangled states exist and can be observed, then accepting quantummechanics as a complete theory requires a drastic overhaul of one's physical intuition with regards to the common sense notions of locality and reality put forth by EPR. Contained herein are the results of research investigating various non-classical features of the two-photon entangled states produced in Type-II Spontaneous Parametric Down -Conversion (SPDC). Through a series of experiments we have manifest the nonlocal nature of the quantummechanical "two-photon effective wavefunction" (or Biphoton) realized by certain photon-counting coincidence measurements performed on these states. In particular, we examine a special double entanglement, in which the states are seen to be simultaneously entangled in both spin and space-time variables. The observed phenomena based on this double entanglement lead to many interesting results which defy classical explanation, but are well described within the framework of quantummechanics. The implications provide a unique perspective concerning the nature of the photon, and the concept of quantum entanglement.
Jafarizadeh, M. A.; Heshmati, A.; Karimi, N.; Yahyavi, M.
2018-03-01
Quantum entanglement is the most famous type of quantum correlation between elements of a quantumsystem that has a basic role in quantum communication protocols like quantum cryptography, teleportation and Bell inequality detection. However, it has already been shown that various applications in quantum information theory do not require entanglement. Quantum discord as a new kind of quantum correlations beyond entanglement, is the most popular candidate for general quantum correlations. In this paper, first we find the entanglement witness in a particular multipartite quantumsystem which consists of a N-partite system in 2 n -dimensional space. Then we give an exact analytical formula for the quantum discord of this system. At the end of the paper, we investigate the additivity relation of the quantum correlation and show that this relation is satisfied for a N-partite system with 2 n -dimensional space.
We examine how geometry-dependent normalisation freedom of electronic wave-functions affects extraction of a meaningful diagonal Born-Oppenheimer correction (DBOC) to the ground-state Born-Oppenheimer potential energy surface (PES). By viewing this freedom as a kind of gauge-freedom, it is shown that DBOC and the resulting associated mass-dependent adiabatic PES are gauge-invariant quantities. A sum-over-states (SOS) formula for DBOC which explicitly exhibits this invariance is derived. A biorthogonal formulation suitable for DBOC computations using standard unnormalised coupled-cluster (CC) wave-functions is presented. This is shown to lead to a biorthogonal version of SOS formula with similar properties. On this basis, different computational schemes for evaluating DBOC using approximate CC wave-functions are derived. One of this agrees with the formula used in the current literature. The connection to adiabatic-to-diabatic transformations in non-adiabatic dynamics is explored and complications arising from biorthogonal nature of CC theory are identified.
Chikalova-Luzina, O. P.; Samosvat, D. M.; Vyatkin, V. M.; Zegrya, G. G.
2017-11-01
A microscopic theory of nonradiative resonance energy transfer between spherical A3B5 semiconductor quantum dots by the exchange mechanism is suggested. The interdot Coulomb interaction is taken into consideration. It is assumed that the quantum dot-donor and the quantum dot-acceptor are made from the same A3B5 compound and are embedded in the matrix of another material that produces potential barriers for electrons and holes. The dependences of the energy transfer rate on the quantum-dot system parameters are found in the frame of the Kane model that provides the most adequate description of the real spectra of A3B5 semiconductors. The analytical treatment is carried out with using the density matrix method, which enabled us to perform an energy transfer analysis both in the weak-interaction approximation and in the strong-interaction approximation. The numerical calculations showed the saturation of the energy transfer rate at the distances between the donor and the acceptor approaching the contact one. The contributions of the exchange and direct Coulomb intractions can be of the same order at the small distances and can have the same value in the saturation range.
Quantummechanics is widely recognised as an important and difficult subject, and many studies have been published focusing on students’ conceptual difficulties. However, the sociocultural aspects of studying such an emblematic subject have not been researched to any large extent. This study explores students’ experiences of undergraduate quantummechanics using qualitative analysis of semi-structured interview data. The results inform discussions about the teaching of quantummechanics by adding a sociocultural dimension. Students pictured quantummechanics as an intriguing subject that inspired them to study physics. The study environment they encountered when taking their first quantummechanics course was however not always as inspiring as expected. Quantummechanics instruction has commonly focused on the mathematical framework of quantummechanics, and this kind of teaching was also what the interviewees had experienced. Two ways of handling the encounter with a traditional quantummechanics course were identified in the interviews; either students accept the practice of studying quantummechanics in a mathematical, exercise-centred way or they distance themselves from these practices and the subject. The students who responded by distancing themselves experienced a crisis and disappointment, where their experiences did not match the way they imagined themselves engaging with quantummechanics. The implications of these findings are discussed in relation to efforts to reform the teaching of undergraduate quantummechanics.
Presents a new research-based course on quantummechanics in which the conceptual issues of quantummechanics are taught at an introductory level. Involves students in the discovery of how quantum phenomena deviate from classical everyday experiences. (Contains 31 references.) (Author/YDS)
In combined quantummechanical/molecular mechanical (QM/MM) free energy calculations, it is often advantageous to have a frozen geometry for the quantummechanical (QM) region. For such multiple-environment single-system (MESS) cases, two schemes are proposed here for estimating the polarization energy: the first scheme, termed MESS-E, involves a Roothaan step extrapolation of the self-consistent field (SCF) energy; whereas the other scheme, termed MESS-H, employs a Newton–Raphson correction using an approximate inverse electronic Hessian of the QM region (which is constructed only once). Both schemes are extremely efficient, because the expensive Fock updates and SCF iterations in standard QM/MM calculations are completely avoided at each configuration. They produce reasonably accurate QM/MM polarization energies: MESS-E can predict the polarization energy within 0.25 kcal/mol in terms of the mean signed error for two of our test cases, solvated methanol and solvated β-alanine, using the M06-2X or ωB97X-D functionals; MESS-H can reproduce the polarization energy within 0.2 kcal/mol for these two cases and for the oxyluciferin–luciferase complex, if the approximate inverse electronic Hessians are constructed with sufficient accuracy. PMID:25321186
In combined quantummechanical/molecular mechanical (QM/MM) free energy calculations, it is often advantageous to have a frozen geometry for the quantummechanical (QM) region. For such multiple-environment single-system (MESS) cases, two schemes are proposed here for estimating the polarization energy: the first scheme, termed MESS-E, involves a Roothaan step extrapolation of the self-consistent field (SCF) energy; whereas the other scheme, termed MESS-H, employs a Newton–Raphson correction using an approximate inverse electronic Hessian of the QM region (which is constructed only once). Both schemes are extremely efficient, because the expensive Fock updates and SCF iterations in standard QM/MM calculations are completelymore » avoided at each configuration. Here, they produce reasonably accurate QM/MM polarization energies: MESS-E can predict the polarization energy within 0.25 kcal/mol in terms of the mean signed error for two of our test cases, solvated methanol and solvated β-alanine, using the M06-2X or ωB97X-D functionals; MESS-H can reproduce the polarization energy within 0.2 kcal/mol for these two cases and for the oxyluciferin–luciferase complex, if the approximate inverse electronic Hessians are constructed with sufficient accuracy.« less
This review is of three books, all published by Springer, all on quantum theory at a level above introductory, but very different in content, style and intended audience. That of Gottfried and Yan is of exceptional interest, historical and otherwise. It is a second edition of Gottfried’s well-known book published by Benjamin in 1966. This was written as a text for a graduate quantummechanics course, and has become one of the most used and respected accounts of quantum theory, at a level mathematically respectable but not rigorous. Quantummechanics was already solidly established by 1966, but this second edition gives an indication of progress made and changes in perspective over the last thirty-five years, and also recognises the very substantial increase in knowledge of quantum theory obtained at the undergraduate level. Topics absent from the first edition but included in the second include the Feynman path integral, seen in 1966 as an imaginative but not very useful formulation of quantum theory. Feynman methods were given only a cursory mention by Gottfried. Their practical importance has now been fully recognised, and a substantial account of them is provided in the new book. Other new topics include semiclassical quantummechanics, motion in a magnetic field, the S matrix and inelastic collisions, radiation and scattering of light, identical particle systems and the Dirac equation. A topic that was all but totally neglected in 1966, but which has flourished increasingly since, is that of the foundations of quantum theory. John Bell’s work of the mid-1960s has led to genuine theoretical and experimental achievement, which has facilitated the development of quantum optics and quantum information theory. Gottfried’s 1966 book played a modest part in this development. When Bell became increasingly irritated with the standard theoretical approach to quantum measurement, Viki Weisskopf repeatedly directed him to Gottfried’s book. Gottfried had devoted a
Many systems under control with an applied field also interact with the surrounding environment. Understanding the control mechanisms has remained a challenge, especially the role played by the interaction between the field and the environment. In order to address this need, here we expand the scope of the Hamiltonian-encoding and observable-decoding (HE-OD) technique. HE-OD was originally introduced as a theoretical and experimental tool for revealing the mechanism induced by control fields in closed quantumsystems. The results of open-system HE-OD analysis presented here provide quantitative mechanistic insights into the roles played by a Markovian environment. Two model open quantumsystems are considered for illustration. In these systems, transitions are induced by either an applied field linked to a dipole operator or Lindblad operators coupled to the system. For modest control yields, the HE-OD results clearly show distinct cooperation between the dynamics induced by the optimal field and the environment. Although the HE-OD methodology introduced here is considered in simulations, it has an analogous direct experimental formulation, which we suggest may be applied to open systems in the laboratory to reveal mechanistic insights.
Lahini, Yoav; Steinbrecher, Gregory R.; Bookatz, Adam D.; Englund, Dirk
2018-01-01
Quantum Walks are unitary processes describing the evolution of an initially localized wavefunction on a lattice potential. The complexity of the dynamics increases significantly when several indistinguishable quantum walkers propagate on the same lattice simultaneously, as these develop non-trivial spatial correlations that depend on the particle's quantum statistics, mutual interactions, initial positions, and the lattice potential. We show that even in the simplest case of a quantum walk on a one dimensional graph, these correlations can be shaped to yield a complete set of compact quantum logic operations. We provide detailed recipes for implementing quantum logic on one-dimensional quantum walks in two general cases. For non-interacting bosons—such as photons in waveguide lattices—we find high-fidelity probabilistic quantum gates that could be integrated into linear optics quantum computation schemes. For interacting quantum-walkers on a one-dimensional lattice—a situation that has recently been demonstrated using ultra-cold atoms—we find deterministic logic operations that are universal for quantum information processing. The suggested implementation requires minimal resources and a level of control that is within reach using recently demonstrated techniques. Further work is required to address error-correction.
Gul, Y.; Holmes, S. N.; Myronov, M.; Kumar, S.; Pepper, M.
2018-03-01
We have investigated hole transport in quantum wires formed by electrostatic confinement in strained germanium two-dimensional layers. The ballistic conductance characteristics show the regular staircase of quantum levels with plateaux at n2e 2/h, where n is an integer, e is the fundamental unit of charge and h is Planck’s constant. However as the carrier concentration is reduced, the quantised levels show a behaviour that is indicative of the formation of a zig-zag structure and new quantised plateaux appear at low temperatures. In units of 2e 2/h the new quantised levels correspond to values of n = 1/4 reducing to 1/8 in the presence of a strong parallel magnetic field which lifts the spin degeneracy but does not quantise the wavefunction. A further plateau is observed corresponding to n = 1/32 which does not change in the presence of a parallel magnetic field. These values indicate that the system is behaving as if charge was fractionalised with values e/2 and e/4, possible mechanisms are discussed.
The 2015 Planck data release has placed tight constraints on the class of inflationary models allowed. The current best fit region favors concave downwards inflationary potentials, since they produce a suppressed tensor to scalar index ratio r. Concave downward potentials have a negative curvature {{V}\\prime \\prime} , therefore a tachyonic mass square that drives fluctuations. Furthermore, their use can become problematic if the field rolls in a part of the potential away from the extrema, since the semiclassical approximation of quantum cosmology, used for deriving the most probable wavefunction of the universe from the landscape and for addressing the quantum to classical transition, breaks down away from the steepest descent region. We here propose a way of dealing with such potentials by inverting the metric signature and solving for the wavefunction of the universe in the Euclidean sector. This method allows us to extend our theory of the origin of the universe from a quantum multiverse, to a more general class of concave inflationary potentials where a straightforward application of the semiclassical approximation fails. The work here completes the derivation of modifications to the Newtonian potential and to the inflationary potential, which originate from the quantum entanglement of our universe with all others in the quantum landscape multiverse, leading to predictions of observational signatures for both types of inflationary models, concave and convex potentials.
A strategy for increasing the square of an overlap integral of electron and hole wavefunctions (I 2) in polar c-plane Al x Ga1- x N multiple quantum wells (MQWs) is proposed. By applying quadratic modulation to AlN mole fractions along the c-axis, local bandgap energies and concentrations of immobile charges induced by polarization discontinuity are simultaneously controlled throughout the MQW structure, and optimized band profiles are eventually achieved. The I 2 value can be substantially increased to 94% when the well width (L w) is smaller than 4.0 nm. In addition, I 2 greater than 80% is predicted even for thick MQWs with L w of 10 nm.
We ask the question of how the (weak) equivalence principle established in classical gravitational physics should be reformulated and interpreted for massive quantum objects that may also have internal degrees of freedom (dof). This inquiry is necessary because even elementary concepts like a classical trajectory are not well defined in quantum physics—trajectories originating from quantum histories become viable entities only under stringent decoherence conditions. From this investigation we posit two logically and operationally distinct statements of the equivalence principle for quantumsystems. Version A: the probability distribution of position for a free-falling particle is the same as the probability distribution of a free particle, modulo a mass-independent shift of its mean. Version B: any two particles with the same velocity wave-function behave identically in free fall, irrespective of their masses. Both statements apply to all quantum states, including those without a classical correspondence, and also for composite particles with quantum internal dof. We also investigate the consequences of the interaction between internal and external dof induced by free fall. For a class of initial states, we find dephasing occurs for the translational dof, namely, the suppression of the off-diagonal terms of the density matrix, in the position basis. We also find a gravitational phase shift in the reduced density matrix of the internal dof that does not depend on the particle’s mass. For classical states, the phase shift has a natural classical interpretation in terms of gravitational red-shift and special relativistic time-dilation.
Teaching physics implies making choices. In the case of teaching quantum physics, besides an educational choice - the didactic strategy - another choice must be made, an epistemological one, concerning the interpretation of quantum theory itself. These two choices are closely connected. We have chosen a didactic strategy that privileges the phenomenological-conceptual approach, with emphasis upon quantum features of the systems, instead of searching for classical analogies. This choice has led us to present quantum theory associated with an orthodox, yet realistic, interpretation of the concept of quantum state, considered as the key concept of quantum theory, representing the physical reality of a system, independent of measurement processes. The results of the mplementation of this strategy, with three groups of engineering students, showed that more than a half of them attained a reasonable understanding of the basics of quantummechanics (QM) for this level. In addition, a high degree of satisfaction was attained with the classes as 80% of the students of the experimental groups claimed to have liked it and to be interested in learning more about QM.
Bender, Carl M; DeKieviet, Maarten; Klevansky, S P
2013-04-28
PT-symmetric quantummechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on PT-symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a PT-symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the PT phase transition can now be understood intuitively without resorting to sophisticated mathematics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter-antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of PT-synthetic materials are being developed, and the PT phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of PT-symmetric quantummechanics.
Here, we present a silver atomic-scale device fabricated and operated by a combined technique of electrochemical control (EC) and mechanically controllable break junction (MCBJ). With this EC-MCBJ technique, we can perform mechanically controllable bistable quantum conductance switching of a silver quantum point contact (QPC) in an electrochemical environment at room temperature. Furthermore, the silver QPC of the device can be controlled both mechanically and electrochemically, and the operating mode can be changed from 'electrochemical' to 'mechanical', which expands the operating mode for controlling QPCs. These experimental results offer the perspective that a silver QPC may be used as a contact for a nanoelectromechanical relay.
We realize a simple and robust optomechanical system with a multitude of long-lived (Q > 107) mechanical modes in a phononic-bandgap shielded membrane resonator. An optical mode of a compact Fabry-Perot resonator detects these modes’ motion with a measurement rate (96 kHz) that exceeds the mechanical decoherence rates already at moderate cryogenic temperatures (10 K). Reaching this quantum regime entails, inter alia, quantum measurement backaction exceeding thermal forces and thus strong optomechanical quantum correlations. In particular, we observe ponderomotive squeezing of the output light mediated by a multitude of mechanical resonator modes, with quantum noise suppression up to -2.4 dB (-3.6 dB if corrected for detection losses) and bandwidths ≲90 kHz. The multimode nature of the membrane and Fabry-Perot resonators will allow multimode entanglement involving electromagnetic, mechanical, and spin degrees of freedom.
Quantummechanics is often taken to be necessarily probabilistic. However, this view of quantummechanics appears to be more the result of historical accident than of careful analysis. Moreover, quantummechanics in its usual form faces serious problems. Although the mathematical core of quantummechanics--quantum probability theory- -does not face conceptual difficulties, the application of quantum probability to the physical world leads to problems. In particular, quantummechanics seems incapable of describing our everyday macroscopic experience. Therefore, several authors have proposed new interpretations --including (but not limited to) modal interpretations, spontaneous localization interpretations, the consistent histories approach, and the Bohm theory--each of which deals with quantum-mechanical probabilities differently. Each of these interpretations promises to describe our macroscopic experience and, arguably, each succeeds. Is there any way to compare them? Perhaps, if we turn to another troubling aspect of quantummechanics, non-locality. Non -locality is troubling because prima facie it threatens the compatibility of quantummechanics with special relativity. This prima facie threat is mitigated by the no-signalling theorems in quantummechanics, but nonetheless one may find a 'conflict of spirit' between nonlocality in quantummechanics and special relativity. Do any of these interpretations resolve this conflict of spirit?. There is a strong relation between how an interpretation deals with quantum-mechanical probabilities and how it deals with non-locality. The main argument here is that only a completely deterministic interpretation can be completely local. That is, locality together with the empirical predictions of quantummechanics (specifically, its strict correlations) entails determinism. But even with this entailment in hand, comparison of the various interpretations requires a look at each, to see how non-locality arises, or in the case of
Han, Jaebeom; Mazack, Michael J M; Zhang, Peng; Truhlar, Donald G; Gao, Jiali
2013-08-07
A quantummechanical force field (QMFF) for water is described. Unlike traditional approaches that use quantummechanical results and experimental data to parameterize empirical potential energy functions, the present QMFF uses a quantummechanical framework to represent intramolecular and intermolecular interactions in an entire condensed-phase system. In particular, the internal energy terms used in molecular mechanics are replaced by a quantummechanical formalism that naturally includes electronic polarization due to intermolecular interactions and its effects on the force constants of the intramolecular force field. As a quantummechanical force field, both intermolecular interactions and the Hamiltonian describing the individual molecular fragments can be parameterized to strive for accuracy and computational efficiency. In this work, we introduce a polarizable molecular orbital model Hamiltonian for water and for oxygen- and hydrogen-containing compounds, whereas the electrostatic potential responsible for intermolecular interactions in the liquid and in solution is modeled by a three-point charge representation that realistically reproduces the total molecular dipole moment and the local hybridization contributions. The present QMFF for water, which is called the XP3P (explicit polarization with three-point-charge potential) model, is suitable for modeling both gas-phase clusters and liquid water. The paper demonstrates the performance of the XP3P model for water and proton clusters and the properties of the pure liquid from about 900 × 10(6) self-consistent-field calculations on a periodic system consisting of 267 water molecules. The unusual dipole derivative behavior of water, which is incorrectly modeled in molecular mechanics, is naturally reproduced as a result of an electronic structural treatment of chemical bonding by XP3P. We anticipate that the XP3P model will be useful for studying proton transport in solution and solid phases as well as across
Self-interference embodies the essence of the particle-wave formulation of quantummechanics (QM). According to the Copenhagen interpretation of QM, self-interference by a double-slit requires a large transverse coherence of the incident wavepacket such that it covers the separation between the slits. Bohmian dynamics provides a first step in the separation of the particle-wave character of matter by introducing deterministic trajectories guided by a pilot wave that follows the time-dependent Schrödinger equation. In this work, I present a new description of the phenomenon of self-interference using the geometrical formulation of QM introduced in Tavernelli (2016). In particular, this formalism removes the need for the concept of wavefunction collapse in the interpretation of the act of measurement i.e., the emergence of the classical world. The three QM formulations (Schrödinger, Bohmian, and geometrical) are applied to the description of the scattering of a free electron by a hydrogen atom and a double-slit. The corresponding interpretations of self-interference are compared and discussed.
The transactional interpretation of quantummechanics [1] was originally published in 1986 and is now about 14 years old. It is an explicitly nonlocal and Lorentz invariant alternative to the Copenhagen interpretation. It interprets the formalism for a quantum interaction as describing a "handshake" between retarded waves (ψ) and advanced waves (ψ*) for each quantum event or "transaction" in which energy, momentum, angular momentum, and other conserved quantities are transferred. The transactional interpretation offers the advantages that (1) it is actually "visible" in the formalism of quantummechanics, (2) it is economical, involving fewer independent assumptions than its rivals, (3) it is paradox-free, resolving all of the paradoxes of standard quantum theory including nonlocality and wave function collapse, (4) it does not give a privileged role to observers or measurements, and (5) it permits the visualization of quantum events. We will review the transactional interpretation and some of its applications to "quantum paradoxes."
In the first part of this dissertation, recent efforts to understand quantummechanical effects in biological systems are discussed. Especially, long-lived quantum coherences observed during the electronic energy transfer process in the Fenna-Matthews-Olson complex at physiological condition are studied extensively using theories of open quantumsystems. In addition to the usual master equation based approaches, the effect of the protein structure is investigated in atomistic detail through the combined application of quantum chemistry and molecular dynamics simulations. To evaluate the thermalized reduced density matrix, a path-integral Monte Carlo method with a novel importance sampling approach is developed for excitons coupled to an arbitrary phonon bath at a finite temperature. In the second part of the thesis, simulations of molecular systems and applications to vibrational spectra are discussed. First, the quantum dynamics of a molecule is simulated by combining semiclassical initial value representation and density funcitonal theory with analytic derivatives. A computationally-tractable approximation to the sum-of-states formalism of Raman spectra is subsequently discussed.
We discuss the question of the dynamical meaning of the second law of thermodynamics in the framework of quantummechanics. Previous discussion of the problem in the framework of classical dynamics has shown that the second law can be given a dynamical meaning in terms of the existence of so-called Lyapounov variables—i.e., dynamical variables varying monotonically in time without becoming contradictory. It has been found that such variables can exist in an extended framework of classical dynamics, provided that the dynamical motion is suitably unstable. In this paper we begin to extend these results to quantummechanics. It is found that no dynamical variable with the characteristic properties of nonequilibrium entropy can be defined in the standard formulation of quantummechanics. However, if the Hamiltonian has certain well-defined spectral properties, such variables can be defined but only as a nonfactorizable superoperator. Necessary nonfactorizability of such entropy operators M has the consequence that they cannot preserve the class of pure states. Physically, this means that the distinguishability between pure states and corresponding mixtures must be lost in the case of a quantal system for which the algebra of observables can be extended to include a new dynamical variable representing nonequilibrium entropy. We discuss how this result leads to a solution of the quantum measurement problem. It is also found that the question of existence of entropy of superoperators M is closely linked to the problem of defining an operator of time in quantummechanics. PMID:16578757
A brief introduction to discrete quantummechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation operators and dynamical symmetry algebras, including the q-oscillator algebra and the Askey-Wilson algebra. A simple recipe to construct exactly and quasi-exactly solvable (QES) Hamiltonians in one-dimensional 'discrete' quantummechanics is presented. It reproduces all the known Hamiltonians whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. Several new exactly and QES Hamiltonians are constructed. The sinusoidal coordinate plays an essential role.
Owing to the extreme smallness of any noncommutative scale that may exist in nature, both in the spatial and momentum sector of the quantum phase space, a credible possibility of their detection lies in the gravitational wave (GW) detection scenario, where one effectively probes the relative length-scale variations ˜O [10-20-10-23] . With this motivation, we have theoretically constructed how a free particle and a harmonic oscillator will respond to linearly and circularly polarized gravitational waves if their quantummechanical phase space has a noncommutative structure. We critically analyze the formal solutions which show resonance behavior in the responses of both free particle and HO systems to GW with both kind of polarizations. We discuss the possible implications of these solutions in detecting noncommutativity in a GW detection experiment. We use the currently available upper-bound estimates on various noncommutative parameters to anticipate the relative importance of various terms in the solutions. We also argue how the quantum harmonic oscillator system we considered here can be very relevant in the context of the resonant bar detectors of GW which are already operational.
Raedt, H. D.; Hams, A. H.; Michielsen, K.; Miyashita, S.; Saito, K.
We describe a quantum algorithm to compute the density of states and thermal equilibrium properties of quantum many-body systems. We present results obtained by running this algorithm on a software implementation of a 21-qubit quantum computer for the case of an antiferromagnetic Heisenberg model on triangular lattices of different size.
Quantum tunneling is a ubiquitous phenomenon in nature and crucial for many technological applications. It allows quantum particles to reach regions in space which are energetically not accessible according to classical mechanics. In this “tunneling region,” the particle density is known to decay exponentially. This behavior is universal across all energy scales from nuclear physics to chemistry and solid state systems. Although typically only a small fraction of a particle wavefunction extends into the tunneling region, we present here an extreme quantumsystem: a gigantic molecule consisting of two helium atoms, with an 80% probability that its two nuclei will be found in this classical forbidden region. This circumstance allows us to directly image the exponentially decaying density of a tunneling particle, which we achieved for over two orders of magnitude. Imaging a tunneling particle shows one of the few features of our world that is truly universal: the probability to find one of the constituents of bound matter far away is never zero but decreases exponentially. The results were obtained by Coulomb explosion imaging using a free electron laser and furthermore yielded He2’s binding energy of 151.9±13.3 neV, which is in agreement with most recent calculations. PMID:27930299
The fractional dynamic process of a quantumsystem is a novel and complicated problem. The establishment of a fractional dynamic model is a significant attempt that is expected to reveal the mechanism of fractional quantumsystem. In this paper, a generalized time fractional Schrödinger equation is proposed. To study the fractional dynamics of quantumsystems, we take the two-level system as an example and derive the time fractional equations of motion. The basic properties of the system are investigated by solving this set of equations in the absence of light field analytically. Then, when the system is subject to the light field, the equations are solved numerically. It shows that the two-level system described by the time fractional Schrödinger equation we proposed is a confirmable system.
In this poster, we will show our results from measurements of a hybrid quantumsystem composed of a superconducting transmon qubit-coupled and ultra-high frequency nano-mechanical resonator, embedded in a superconducting cavity. The transmon is capacitively coupled to a 3.4GHz nanoresonator and a T-filter-biased high-Q transmission line cavity. Single-tone and two-tone transmission spectroscopy measurements are used to probe the interactions between the cavity, qubit and mechanical resonator. These measurements are in good agreement with numerical simulations based upon a master equation for the tripartite system including dissipation. The results indicate that this system may be developed to serve as a platform for more advanced measurements with nanoresonators, including quantum state measurement, the exploration of nanoresonator quantum noise, and reservoir engineering.
Preface; Notation; 1. Historical introduction; 2. Particle states in a central potential; 3. General principles of quantummechanics; 4. Spin; 5. Approximations for energy eigenstates; 6. Approximations for time-dependent problems; 7. Potential scattering; 8. General scattering theory; 9. The canonical formalism; 10. Charged particles in electromagnetic fields; 11. The quantum theory of radiation; 12. Entanglement; Author index; Subject index.
Nielsen, William Hvidtfelt Padkær; Tsaturyan, Yeghishe; Møller, Christoffer Bo; Polzik, Eugene S.; Schliesser, Albert
2017-01-01
We realize a simple and robust optomechanical system with a multitude of long-lived (Q > 107) mechanical modes in a phononic-bandgap shielded membrane resonator. An optical mode of a compact Fabry–Perot resonator detects these modes’ motion with a measurement rate (96 kHz) that exceeds the mechanical decoherence rates already at moderate cryogenic temperatures (10 K). Reaching this quantum regime entails, inter alia, quantum measurement backaction exceeding thermal forces and thus strong optomechanical quantum correlations. In particular, we observe ponderomotive squeezing of the output light mediated by a multitude of mechanical resonator modes, with quantum noise suppression up to −2.4 dB (−3.6 dB if corrected for detection losses) and bandwidths ≲90 kHz. The multimode nature of the membrane and Fabry–Perot resonators will allow multimode entanglement involving electromagnetic, mechanical, and spin degrees of freedom. PMID:27999182
Nielsen, William Hvidtfelt Padkær; Tsaturyan, Yeghishe; Møller, Christoffer Bo; Polzik, Eugene S; Schliesser, Albert
2017-01-03
We realize a simple and robust optomechanical system with a multitude of long-lived (Q > 10 7 ) mechanical modes in a phononic-bandgap shielded membrane resonator. An optical mode of a compact Fabry-Perot resonator detects these modes' motion with a measurement rate (96 kHz) that exceeds the mechanical decoherence rates already at moderate cryogenic temperatures (10 K). Reaching this quantum regime entails, inter alia, quantum measurement backaction exceeding thermal forces and thus strong optomechanical quantum correlations. In particular, we observe ponderomotive squeezing of the output light mediated by a multitude of mechanical resonator modes, with quantum noise suppression up to -2.4 dB (-3.6 dB if corrected for detection losses) and bandwidths ≲90 kHz. The multimode nature of the membrane and Fabry-Perot resonators will allow multimode entanglement involving electromagnetic, mechanical, and spin degrees of freedom.
Nucleic acids theoretically possess a Szilard engine function that can convert the energy associated with the Shannon entropy of molecules for which they have coded recognition, into the useful work of geometric reconfiguration of the nucleic acid molecule. This function is logically reversible because its mechanism is literally and physically constructed out of the information necessary to reduce the Shannon entropy of such molecules, which means that this information exists on both sides of the theoretical engine, and because information is retained in the geometric degrees of freedom of the nucleic acid molecule, a quantum gate is formed through whichmore » multi-state nucleic acid qubits can interact. Entangled biophotons emitted as a consequence of symmetry breaking nucleic acid Szilard engine (NASE) function can be used to coordinate relative positioning of different nucleic acid locations, both within and between cells, thus providing the potential for quantum coherence of an entire biological system. Theoretical implications of understanding biological systems as such 'quantum adaptive systems' include the potential for multi-agent based quantum computing, and a better understanding of systemic pathologies such as cancer, as being related to a loss of systemicquantum coherence.« less
Nucleic acids theoretically possess a Szilard engine function that can convert the energy associated with the Shannon entropy of molecules for which they have coded recognition, into the useful work of geometric reconfiguration of the nucleic acid molecule. This function is logically reversible because its mechanism is literally and physically constructed out of the information necessary to reduce the Shannon entropy of such molecules, which means that this information exists on both sides of the theoretical engine, and because information is retained in the geometric degrees of freedom of the nucleic acid molecule, a quantum gate is formed through which multi-state nucleic acid qubits can interact. Entangled biophotons emitted as a consequence of symmetry breaking nucleic acid Szilard engine (NASE) function can be used to coordinate relative positioning of different nucleic acid locations, both within and between cells, thus providing the potential for quantum coherence of an entire biological system. Theoretical implications of understanding biological systems as such "quantum adaptive systems" include the potential for multi-agent based quantum computing, and a better understanding of systemic pathologies such as cancer, as being related to a loss of systemicquantum coherence.
Procopio, Lorenzo M; Rozema, Lee A; Wong, Zi Jing; Hamel, Deny R; O'Brien, Kevin; Zhang, Xiang; Dakić, Borivoje; Walther, Philip
2017-04-21
In standard quantummechanics, complex numbers are used to describe the wavefunction. Although this has so far proven sufficient to predict experimental results, there is no theoretical reason to choose them over real numbers or generalizations of complex numbers, that is, hyper-complex numbers. Experiments performed to date have proven that real numbers are insufficient, but the need for hyper-complex numbers remains an open question. Here we experimentally probe hyper-complex quantum theories, studying one of their deviations from complex quantum theory: the non-commutativity of phases. We do so by passing single photons through a Sagnac interferometer containing both a metamaterial with a negative refractive index, and a positive phase shifter. To accomplish this we engineered a fishnet metamaterial to have a negative refractive index at 780 nm. We show that the metamaterial phase commutes with other phases with high precision, allowing us to place limits on a particular prediction of hyper-complex quantum theories.
Procopio, Lorenzo M.; Rozema, Lee A.; Wong, Zi Jing
In standard quantummechanics, complex numbers are used to describe the wavefunction. Although this has so far proven sufficient to predict experimental results, there is no theoretical reason to choose them over real numbers or generalizations of complex numbers, that is, hyper-complex numbers. Experiments performed to date have proven that real numbers are insufficient, but the need for hyper-complex numbers remains an open question. Here we experimentally probe hyper-complex quantum theories, studying one of their deviations from complex quantum theory: the non-commutativity of phases. We do so by passing single photons through a Sagnac interferometer containing both a metamaterial withmore » a negative refractive index, and a positive phase shifter. In order to accomplish this we engineered a fishnet metamaterial to have a negative refractive index at 780 nm. Here, we show that the metamaterial phase commutes with other phases with high precision, allowing us to place limits on a particular prediction of hyper-complex quantum theories.« less
Procopio, Lorenzo M.; Rozema, Lee A.; Wong, Zi Jing; ...
2017-04-21
In standard quantummechanics, complex numbers are used to describe the wavefunction. Although this has so far proven sufficient to predict experimental results, there is no theoretical reason to choose them over real numbers or generalizations of complex numbers, that is, hyper-complex numbers. Experiments performed to date have proven that real numbers are insufficient, but the need for hyper-complex numbers remains an open question. Here we experimentally probe hyper-complex quantum theories, studying one of their deviations from complex quantum theory: the non-commutativity of phases. We do so by passing single photons through a Sagnac interferometer containing both a metamaterial withmore » a negative refractive index, and a positive phase shifter. In order to accomplish this we engineered a fishnet metamaterial to have a negative refractive index at 780 nm. Here, we show that the metamaterial phase commutes with other phases with high precision, allowing us to place limits on a particular prediction of hyper-complex quantum theories.« less
Procopio, Lorenzo M.; Rozema, Lee A.; Wong, Zi Jing; Hamel, Deny R.; O'Brien, Kevin; Zhang, Xiang; Dakić, Borivoje; Walther, Philip
2017-01-01
In standard quantummechanics, complex numbers are used to describe the wavefunction. Although this has so far proven sufficient to predict experimental results, there is no theoretical reason to choose them over real numbers or generalizations of complex numbers, that is, hyper-complex numbers. Experiments performed to date have proven that real numbers are insufficient, but the need for hyper-complex numbers remains an open question. Here we experimentally probe hyper-complex quantum theories, studying one of their deviations from complex quantum theory: the non-commutativity of phases. We do so by passing single photons through a Sagnac interferometer containing both a metamaterial with a negative refractive index, and a positive phase shifter. To accomplish this we engineered a fishnet metamaterial to have a negative refractive index at 780 nm. We show that the metamaterial phase commutes with other phases with high precision, allowing us to place limits on a particular prediction of hyper-complex quantum theories. PMID:28429711
Bertolami, Orfeu; Bernardini, Alex E.; Leal, Pedro
2018-01-01
Some fundamental aspects related with the construction of Robertson-Schrödinger-like uncertainty-principle inequalities are reported in order to provide an overall description of quantumness, separability and nonlocality of quantumsystems in the noncommutative phase-space. Some consequences of the deformed noncommutative algebra are also considered in physical systems of interest.
Recognizing that syntactic and semantic structures of classical logic are not sufficient to understand the meaning of quantum phenomena, we propose in this paper a new interpretation of quantummechanics based on evidence theory. The connection between these two theories is obtained through a new language, quantum set theory, built on a suggestion by J. Bell. Further, we give a modal logic interpretation of quantummechanics and quantum set theory by using Kripke's semantics of modal logic based on the concept of possible worlds. This is grounded on previous work of a number of researchers (Resconi, Klir, Harmanec) who showed how to represent evidence theory and other uncertainty theories in terms of modal logic. Moreover, we also propose a reformulation of the many-worlds interpretation of quantummechanics in terms of Kripke's semantics. We thus show how three different theories — quantummechanics, evidence theory, and modal logic — are interrelated. This opens, on one hand, the way to new applications of quantummechanics within domains different from the traditional ones, and, on the other hand, the possibility of building new generalizations of quantummechanics itself.
The generalized uncertainty relation applicable to quantum and stochastic systems is derived within the stochastic variational method. This relation not only reproduces the well-known inequality in quantummechanics but also is applicable to the Gross-Pitaevskii equation and the Navier-Stokes-Fourier equation, showing that the finite minimum uncertainty between the position and the momentum is not an inherent property of quantummechanics but a common feature of stochastic systems. We further discuss the possible implication of the present study in discussing the application of the hydrodynamic picture to microscopic systems, like relativistic heavy-ion collisions.
We propose giving the mathematical concept of the pseudospectrum a central role in quantummechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT -symmetric quantummechanics.
The v2 Milestone 10 release of C++QED is primarily a feature release, which also corrects some problems of the previous release, especially as regards the build system. The adoption of C++11 features has led to many simplifications in the codebase. A full doxygen-based API manual [1] is now provided together with updated user guides. A largely automated, versatile new testsuite directed both towards computational and physics features allows for quickly spotting arising errors. The states of trajectories are now savable and recoverable with full binary precision, allowing for trajectory continuation regardless of evolution method (single/ensemble Monte Carlo wave-function or Master equation trajectory). As the main new feature, the framework now presents Python bindings to the highest-level programming interface, so that actual simulations for given composite quantumsystems can now be performed from Python. Catalogue identifier: AELU_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELU_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: yes No. of lines in distributed program, including test data, etc.: 492422 No. of bytes in distributed program, including test data, etc.: 8070987 Distribution format: tar.gz Programming language: C++/Python. Computer: i386-i686, x86 64. Operating system: In principle cross-platform, as yet tested only on UNIX-like systems (including Mac OS X). RAM: The framework itself takes about 60MB, which is fully shared. The additional memory taken by the program which defines the actual physical system (script) is typically less than 1MB. The memory storing the actual data scales with the system dimension for state-vector manipulations, and the square of the dimension for density-operator manipulations. This might easily be GBs, and often the memory of the machine limits the size of the simulated system. Classification: 4.3, 4.13, 6.2. External routines: Boost C
Ultrafast electron and X-ray imaging and spectroscopy are the basis for an ongoing revolution in the understanding of dynamical atomic-scale processes in matter. The underlying technology relies heavily on laser science for the generation and characterization of ever shorter pulses. Recent findings suggest that ultrafast electron microscopy with attosecond-structured wavefunctions may be feasible. However, such future technologies call for means to both prepare and fully analyse the corresponding free-electron quantum states. Here, we introduce a framework for the preparation, coherent manipulation and characterization of free-electron quantum states, experimentally demonstrating attosecond electron pulse trains. Phase-locked optical fields coherently control the electron wavefunction along the beam direction. We establish a new variant of quantum state tomography—`SQUIRRELS'—for free-electron ensembles. The ability to tailor and quantitatively map electron quantum states will promote the nanoscale study of electron-matter entanglement and new forms of ultrafast electron microscopy down to the attosecond regime.
Preface; 1. Introduction; Part I. The Emergence of QuantumMechanics: 2. Quantummechanics and the principle of observability; 3. The problem of interpretation; Part II. The Heisenberg-Bohr Dialogue: 4. The wave-particle duality; 5. Indeterminacy and the limits of classical concepts: the turning point in Heisenberg's thought; 6. Heisenberg and Bohr: divergent viewpoints of complementarity; Part III. Heisenberg's Epistemology and Ontology of QuantumMechanics: 7. The transformation of Kantian philosophy; 8. The linguistic turn in Heisenberg's thought; Conclusion; References; Index.
Preface; 1. Introduction; Part I. The Emergence of QuantumMechanics: 2. Quantummechanics and the principle of observability; 3. The problem of interpretation; Part II. The Heisenberg-Bohr Dialogue: 4. The wave-particle duality; 5. Indeterminacy and the limits of classical concepts: the turning point in Heisenberg's thought; 6. Heisenberg and Bohr: divergent viewpoints of complementarity; Part III. Heisenberg's Epistemology and Ontology of QuantumMechanics: 7. The transformation of Kantian philosophy; 8. The linguistic turn in Heisenberg's thought; Conclusion; References; Index.
Wang, Bo; Yang, Ke R; Xu, Xuefei; Isegawa, Miho; Leverentz, Hannah R; Truhlar, Donald G
2014-09-16
Conspectus The development of more efficient and more accurate ways to represent reactive potential energy surfaces is a requirement for extending the simulation of large systems to more complex systems, longer-time dynamical processes, and more complete statistical mechanical sampling. One way to treat large systems is by direct dynamics fragment methods. Another way is by fitting system-specific analytic potential energy functions with methods adapted to large systems. Here we consider both approaches. First we consider three fragment methods that allow a given monomer to appear in more than one fragment. The first two approaches are the electrostatically embedded many-body (EE-MB) expansion and the electrostatically embedded many-body expansion of the correlation energy (EE-MB-CE), which we have shown to yield quite accurate results even when one restricts the calculations to include only electrostatically embedded dimers. The third fragment method is the electrostatically embedded molecular tailoring approach (EE-MTA), which is more flexible than EE-MB and EE-MB-CE. We show that electrostatic embedding greatly improves the accuracy of these approaches compared with the original unembedded approaches. Quantummechanical fragment methods share with combined quantummechanical/molecular mechanical (QM/MM) methods the need to treat a quantummechanical fragment in the presence of the rest of the system, which is especially challenging for those parts of the rest of the system that are close to the boundary of the quantummechanical fragment. This is a delicate matter even for fragments that are not covalently bonded to the rest of the system, but it becomes even more difficult when the boundary of the quantummechanical fragment cuts a bond. We have developed a suite of methods for more realistically treating interactions across such boundaries. These methods include redistributing and balancing the external partial atomic charges and the use of tuned fluorine
We show that there exist spurious states for the sector two tensor Hamiltonian in multidimensional supersymmetric quantummechanics. For one-dimensional supersymmetric quantummechanics on an infinite domain, the sector one and two Hamiltonians have identical spectra with the exception of the ground state of the sector one. For tensorial multidimensional supersymmetric quantummechanics, there exist normalizable spurious states for the sector two Hamiltonian with energy equal to the ground state energy of the sector one. These spurious states are annihilated by the adjoint charge operator, and hence, they do not correspond to physical states for the original Hamiltonian. The Hermitian property of the sector two Hamiltonian implies the orthogonality between spurious and physical states. In addition, we develop a method for construction of a specific form of the spurious states for any quantumsystem and also generate several spurious states for a two-dimensional anharmonic oscillator system and for the hydrogen atom.
Anninos, Dionysios; Anous, Tarek; Freedman, Daniel Z.
2015-11-30
We examine the late time behavior of the Bunch-Davies wavefunction for interacting light fields in a de Sitter background. We use perturbative techniques developed in the framework of AdS/CFT, and analytically continue to compute tree and loop level contributions to the Bunch-Davies wavefunction. We consider self-interacting scalars of general mass, but focus especially on the massless and conformally coupled cases. We show that certain contributions grow logarithmically in conformal time both at tree and loop level. We also consider gauge fields and gravitons. The four-dimensional Fefferman-Graham expansion of classical asymptotically de Sitter solutions is used to show that the wavefunctionmore » contains no logarithmic growth in the pure graviton sector at tree level. Finally, assuming a holographic relation between the wavefunction and the partition function of a conformal field theory, we interpret the logarithmic growths in the language of conformal field theory.« less
Here, we consider gapped fractional quantum Hall states on the lowest Landau level when the Coulomb energy is much smaller than the cyclotron energy. We introduce two spectral densities, ρ T(ω) andmore » $$\\bar{p}$$ T(ω), which are proportional to the probabilities of absorption of circularly polarized gravitons by the quantum Hall system. We prove three sum rules relating these spectral densities with the shift S, the q 4 coefficient of the static structure factor S 4, and the high-frequency shear modulus of the ground state μ ∞, which is precisely defined. We confirm an inequality, first suggested by Haldane, that S 4 is bounded from below by |S–1|/8. The Laughlin wavefunction saturates this bound, which we argue to imply that systems with ground state wavefunctions close to Laughlin’s absorb gravitons of predominantly one circular polarization. We consider a nonlinear model where the sum rules are saturated by a single magneto-roton mode. In this model, the magneto-roton arises from the mixing between oscillations of an internal metric and the hydrodynamic motion. Implications for experiments are briefly discussed.« less
The sialyltransferase is an enzyme that transfers the sialic acid moiety from cytidine 5'-monophospho-N-acetyl-neuraminic acid (CMP-NeuAc) to the terminal position of glycans. To elucidate the catalytic mechanism of sialyltransferase, we explored the potential energy surface along the sialic acid transfer reaction coordinates by the hybrid quantummechanics/molecular mechanics method on the basis of the crystal structure of sialyltransferase CstII. Our calculation demonstrated that CstII employed an S N 1-like reaction mechanism via the formation of a short-lived oxocarbenium ion intermediate. The computational barrier height was 19.5 kcal/mol, which reasonably corresponded with the experimental reaction rate. We also found that two tyrosine residues (Tyr156 and Tyr162) played a vital role in stabilizing the intermediate and the transition states by quantummechanical interaction with CMP.
In this study we have investigated the electronic structure of the hydrogenic quantum dot with two electrons inside an impenetrable potential surface. The energy eigenvalues and wavefunctions of the ground and excited states of spherical quantum dot have been calculated by using the Quantum Genetic Algorithm (QGA) and Hartree-Fock Roothaan (HFR) method, and the energies are investigated as a function of dot radius. The results show that as dot radius increases, the energy of quantum dot decreases.
Here, we present a silver atomic-scale device fabricated and operated by a combined technique of electrochemical control (EC) and mechanically controllable break junction (MCBJ). With this EC-MCBJ technique, we can perform mechanically controllable bistable quantum conductance switching of a silver quantum point contact (QPC) in an electrochemical environment at room temperature. Furthermore, the silver QPC of the device can be controlled both mechanically and electrochemically, and the operating mode can be changed from ‘electrochemical’ to ‘mechanical’, which expands the operating mode for controlling QPCs. These experimental results offer the perspective that a silver QPC may be used as a contact for a nanoelectromechanical relay.
The article considers the implications of the experiment of A. Einstein, B. Podolsky, and N. Rosen (EPR), and of the exchange (concerning this experiment) between EPR and Bohr concerning the incompleteness, or else nonlocality, of quantummechanics for our understanding of quantum phenomena and quantum probability. The article specifically argues that in the case of quantum phenomena, including those involved in the experiments of the EPR type, the probabilistic considerations are important even when the predictions concerned can be made with certainty, due to the impossibility, in general, to repeat any given quantum experiment with the same outcome. The article argue that this fact, not properly considered or taken into account by EPR, makes it difficult and ultimately impossible to sustain their argument, which it is consistent with Bohr's counterargument to EPR and with his view of quantum phenomena and quantummechanics.
We extend our prior work on the construction of variational wave functions ψ that are functionals of functions χ:ψ=ψ[χ] rather than simply being functions. In this manner, the space of variations is expanded over those of traditional variational wave functions. In this article we perform the constrained search over the functions χ chosen such that the functional ψ[χ] satisfies simultaneously the constraints of normalization and the exact expectation value of an arbitrary single- or two-particle Hermitian operator, while also leading to a rigorous upper bound to the energy. As such the wave function functional is accurate not only in the region of space in which the principal contributions to the energy arise but also in the other region of the space represented by the Hermitian operator. To demonstrate the efficacy of these ideas, we apply such a constrained search to the ground state of the negative ion of atomic hydrogen H-, the helium atom He, and its positive ions Li+ and Be2+. The operators W whose expectations are obtained exactly are the sum of the single-particle operators W=∑irin,n=-2,-1,1,2, W=∑iδ(ri), W=-(1)/(2)∑i∇i2, and the two-particle operators W=∑nun,n=-2,-1,1,2, where u=|ri-rj|. Comparisons with the method of Lagrangian multipliers and of other constructions of wave-function functionals are made. Finally, we present further insights into the construction of wave-function functionals by studying a previously proposed construction of functionals ψ[χ] that lead to the exact expectation of arbitrary Hermitian operators. We discover that analogous to the solutions of the Schrödinger equation, there exist ψ[χ] that are unphysical in that they lead to singular values for the expectations. We also explain the origin of the singularity.
Provided a quantum superconducting condensate is allowed to occupy a curved hyper-plane of space-time, a geometric potential from the kinetic term arises. An energy conservation relation involving the geometric field at every material point in the superconductor can be demonstrated. The induced three-dimensional scalar curvature is directly related to the wavefunction/order parameter of the quantum condensate thus pointing the way to a possible experimental procedure to artificially induce curvature of space-time via change in the electric/probability current density.
Tangles of string typically become knotted, from macroscopic twine down to long-chain macromolecules such as DNA. Here, we demonstrate that knotting also occurs in quantumwavefunctions, where the tangled filaments are vortices (nodal lines/phase singularities). The probability that a vortex loop is knotted is found to increase with its length, and a wide gamut of knots from standard tabulations occur. The results follow from computer simulations of random superpositions of degenerate eigenstates of three simple quantumsystems: a cube with periodic boundaries, the isotropic three-dimensional harmonic oscillator and the 3-sphere. In the latter two cases, vortex knots occur frequently, even in random eigenfunctions at relatively low energy, and are constrained by the spatial symmetries of the modes. The results suggest that knotted vortex structures are generic in complex three-dimensional wave systems, establishing a topological commonality between wave chaos, polymers and turbulent Bose–Einstein condensates. PMID:27468801
These three lectures consider the questions of reality, causality, and probability in quantum theory, from quantummechanics 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 vis-à-vis quantummechanics. I close by briefly addressing some of the implications of the argument presented here for the current state of fundamental physics.
We present hybrid symbolic-numerical tools to generate optimized numerical code for rapid prototyping and fast numerical computation starting from a computer algebra system (CAS) and tailored to any given quantummechanical problem. Although a major focus concerns the quantum chemistry methods of H. Nakatsuji which has yielded successful and very accurate eigensolutions for small atoms and molecules, the tools are general and may be applied to any basis set calculation with a variational principle applied to its linear and non-linear parameters.
In contrast to classical physics, quantum theory demands that not all properties can be simultaneously well defined; the Heisenberg uncertainty principle is a manifestation of this fact. Alternatives have been explored--notably theories relying on joint probability distributions or non-contextual hidden-variable models, in which the properties of a system are defined independently of their own measurement and any other measurements that are made. Various deep theoretical results imply that such theories are in conflict with quantummechanics. Simpler cases demonstrating this conflict have been found and tested experimentally with pairs of quantum bits (qubits). Recently, an inequality satisfied by non-contextual hidden-variable models and violated by quantummechanics for all states of two qubits was introduced and tested experimentally. A single three-state system (a qutrit) is the simplest system in which such a contradiction is possible; moreover, the contradiction cannot result from entanglement between subsystems, because such a three-state system is indivisible. Here we report an experiment with single photonic qutrits which provides evidence that no joint probability distribution describing the outcomes of all possible measurements--and, therefore, no non-contextual theory--can exist. Specifically, we observe a violation of the Bell-type inequality found by Klyachko, Can, Binicioğlu and Shumovsky. Our results illustrate a deep incompatibility between quantummechanics and classical physics that cannot in any way result from entanglement.
Following previous works by E. Prugovečki [Physica A 91A, 202 (1978) and Stochastic QuantumMechanics and Quantum Space-time (Reidel, Dordrecht, 1986)] on common features of classical and quantummechanics, we develop a unified mathematical framework for classical and quantummechanics (based on L2-spaces over classical phase space), in order to investigate to what extent quantummechanics can be obtained as a simple modification of classical mechanics (on both logical and analytical levels). To obtain this unified framework, we split quantum theory in two parts: (i) general quantum axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoints operators, and so on) and (ii) quantummechanics proper that specifies the Hilbert space as L2(Rn); the Heisenberg rule [pi,qj]=-iℏδij with p=-iℏ∇, the free Hamiltonian H=-ℏ2Δ/2m and so on. We show that general quantum axiomatics (up to a supplementary "axiom of classicity") can be used as a nonstandard mathematical ground to formulate physical ideas and equations of ordinary classical statistical mechanics. So, the question of a "true quantization" with "ℏ" must be seen as an independent physical problem not directly related with quantum formalism. At this stage, we show that this nonstandard formulation of classical mechanics exhibits a new kind of operation that has no classical counterpart: this operation is related to the "quantization process," and we show why quantization physically depends on group theory (the Galilei group). This analytical procedure of quantization replaces the "correspondence principle" (or canonical quantization) and allows us to map classical mechanics into quantummechanics, giving all operators of quantum dynamics and the Schrödinger equation. The great advantage of this point of view is that quantization is based on concrete physical arguments and not derived from some "pure algebraic rule" (we exhibit also some limit of the correspondence
We introduce a method to evaluate the relative populations of different conformers of molecular species in solution, aiming at quantummechanical accuracy, while keeping the computational cost at a nearly molecular-mechanics level. This goal is achieved by combining long classical molecular-dynamics simulations to sample the free-energy landscape of the system, advanced clustering techniques to identify the most relevant conformers, and thermodynamic perturbation theory to correct the resulting populations, using quantum-mechanical energies from density functional theory. A quantitative criterion for assessing the accuracy thus achieved is proposed. The resulting methodology is demonstrated in the specific case of cyanin (cyanidin-3-glucoside) in water solution.
Graphene has brought forward a lot of new physics. One of them is the emergence of massless Dirac fermions in addition to the electrons and these features are new to physics. In this theoretical study, the signatures for quantum scar and the breakdown of universality in graphene are investigated with reference to the presence of these two types of fermions. Taking the graphene quantum dot (QD) potential as the confining potential, the radial part of Dirac equations are solved numerically. Concentrations of the two component eigen-wavefunctions about classical periodic orbits emerge as the signatures for the quantum scar. The sudden variations, in the ratio of the radial wave-functions (large and small components), R(g/f), with mass ratio κ are the signatures for breakdown of universality in graphene. The breakdown of universality occurs for the states k = -1 and k = 1, and the state k = -1 is more susceptible to the breakdown of universality.
Although the usual way of representing Markov processes is time asymmetric, there is a way of describing Markov processes, due to Schrodinger, which is time symmetric. This observation provides a link between quantummechanics and the layered Bayesian networks that are often used in automated pattern recognition systems. In particular, there is a striking formal similarity between quantummechanics and a particular type of Bayesian network, the Helmholtz machine, which provides a plausible model for how the mammalian brain recognizes important environmental situations. One interesting aspect of this relationship is that the "wake-sleep" algorithm for training a Helmholtz machine is very similar to the problem of finding the potential for the multi-channel Schrodinger equation. As a practical application of this insight it may be possible to use inverse scattering techniques to study the relationship between human brain wave patterns, pattern recognition, and learning. We also comment on whether there is a relationship between quantum measurements and consciousness.
The action of the quantummechanical volume operator, introduced in connection with a symmetric representation of the three-body problem and recently recognized to play a fundamental role in discretized quantum gravity models, can be given as a second-order difference equation which, by a complex phase change, we turn into a discrete Schrödinger-like equation. The introduction of discrete potential-like functions reveals the surprising crucial role here of hidden symmetries, first discovered by Regge for the quantummechanical 6j symbols; insight is provided into the underlying geometric features. The spectrum and wavefunctions of the volume operator are discussed from the viewpoint of the Hamiltonian evolution of an elementary ‘quantum of space’, and a transparent asymptotic picture of the semiclassical and classical regimes emerges. The definition of coordinates adapted to the Regge symmetry is exploited for the construction of a novel set of discrete orthogonal polynomials, characterizing the oscillatory components of torsion-like modes.
Gullans, Michael; Taylor, Jacob; Ghaemi, Pouyan; Hafezi, Mohammad
Quantum Hall systems exhibit topologically protected edge states, which can have a macroscopic spatial extent. Such edge states provide a unique opportunity to study a quantum emitter whose size far exceeds the wavelength of emitted light. To better understand this limit, we theoretically characterize the optical radiation from integer quantum Hall states in two-dimensional Dirac materials. We show that the scattered light from the bulk reflects the spatial profile of the wavefunctions, enabling spatial imaging of the disorder landscape. We find that the radiation from the edge states are characterized by the presence of large multipole moments in the far-field. This multipole radiation arises from the transfer of angular momentum from the electrons into the scattered light, enabling the generation of coherent light with high orbital angular momentum.
ödinger's equation for non-conservative systems; 46. Pertubation theory; 47. Orthogonality, normalization and Hermitian conjugacy; 48. General matrix elements; Part IV. The Principle of Correspondence: 49. Contact transformations in classical mechanics; 50. Point transformations; 51. Contact transformations in quantummechanics; 52. Constants of motion and angular co-ordinates; 53. Periodic orbits; 54. De Broglie and Schrödinger function; correspondence to classical mechanics; 55. Packets of probability; 56. Correspondence to hydrodynamics; 57. Motion and scattering of wave packets; 58. Formal correspondence between classical and quantummechanics; Part V. Mathematical Appendix: Principle of Invariance: 59. The general theorem of transformation; 60. Operator calculus; 61. Exchange relations; three criteria for conjugacy; 62. First method of canonical transformation; 63. Second method of canonical transformation; 64. Proof of the transformation theorem; 65. Invariance of the matrix elements against unitary transformations; 66. Matrix mechanics; Index of literature; Index of names and subjects.
In this study, for the first time, the energies of two-electron Hulthen quantum dots (TEHQdots) embedded in Debye and quantum plasmas modeled by the more general exponential cosine screened Coulomb (MGECSC) potential under the combined influence of electric and magnetic fields are investigated by numerically solving the Schrödinger equation using the asymptotic iteration method. To do this, the four different forms of the MGECSC potential, which set through the different cases of the potential parameters, are taken into consideration. We propose that plasma environments form considerable quantummechanical effects for quantum dots and other atomic systems and that plasmas are important experimental arguments. In this study, by considering the quantum dot parameters, the external field parameters, and the plasma screening parameters, a control mechanism of the confinement on energies of TEHQdots and the frequency of the radiation emitted by TEHQdots as a result of any excitation is discussed. In this mechanism, the behaviors, similarities, the functionalities of the control parameters, and the influences of plasmas on these quantities are explored.
The application of quantummechanics 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.
We study the quantum-mechanical generalization of force or pressure, and then we extend the classical thermodynamic isobaric process to quantum-mechanicalsystems. Based on these efforts, we are able to study the quantum version of thermodynamic cycles that consist of quantum isobaric processes, such as the quantum Brayton cycle and quantum Diesel cycle. We also consider the implementation of the quantum Brayton cycle and quantum Diesel cycle with some model systems, such as single particle in a one-dimensional box and single-mode radiation field in a cavity. These studies lay the microscopic (quantum-mechanical) foundation for Szilard-Zurek single-molecule engine.
In models of QM over finite fields (e.g., Schumacher's ``modal quantum theory'' MQT), one finite field stands out, Z2, since Z2 vectors represent sets. QM (finite-dimensional) mathematics can be transported to sets resulting in quantummechanics over sets or QM/sets. This gives a full probability calculus (unlike MQT with only zero-one modalities) that leads to a fulsome theory of QM/sets including ``logical'' models of the double-slit experiment, Bell's Theorem, QIT, and QC. In QC over Z2 (where gates are non-singular matrices as in MQT), a simple quantum algorithm (one gate plus one function evaluation) solves the Parity SAT problem (finding the parity of the sum of all values of an n-ary Boolean function). Classically, the Parity SAT problem requires 2n function evaluations in contrast to the one function evaluation required in the quantum algorithm. This is quantum speedup but with all the calculations over Z2 just like classical computing. This shows definitively that the source of quantum speedup is not in the greater power of computing over the complex numbers, and confirms the idea that the source is in superposition.
Quantummechanics holds a fascination for many students, but its mathematical complexity and counterintuitive results can present major barriers. The QuVis QuantumMechanics Visualization Project (www.st-andrews.ac.uk/physics/quvis) aims to overcome these issues through the development and evaluation of interactive simulations with accompanying activities for the learning and teaching of quantummechanics. Over 90 simulations are now available on the QuVis website. One collection of simulations is embedded in the Institute of Physics Quantum Physics website (quantumphysics.iop.org), which consists of freely available resources for an introductory course in quantummechanics starting from two-level systems. Simulations support model-building by reducing complexity, focusing on fundamental ideas and making the invisible visible. They promote engaged exploration, sense-making and linking of multiple representations, and include high levels of interactivity and direct feedback. Simulations are research-based and evaluation with students informs all stages of the development process. Simulations are iteratively refined using student feedback in individual observation sessions and in-class trials. Evaluation has shown that the simulations can help students learn quantummechanics concepts at both the introductory and advanced undergraduate level and that students perceive simulations to be beneficial to their learning. Recent activity includes the launch of a new collection of HTML5 simulations that run on both desktop and tablet-based devices and the introduction of a goal and reward structure in simulations through the inclusion of challenges. This presentation will give an overview of the QuVis resources, highlight recent work and outline future plans. QuVis is supported by the UK Institute of Physics, the UK Higher Education Academy and the University of St Andrews.
Two physical approaches—as distinct, under the classification of Mittelstaedt, from formal approaches—to the problem of individuation of quantum objects are considered, one formulated in spatiotemporal terms and one in quantummechanical terms. The spatiotemporal approach itself has two forms: one attributed to Einstein and based on the ontology of space-time points, and the other proposed by Howard and based on intersections of world lines. The quantummechanical approach is also provided here in two forms, one based on interference and another based on a new Quantum Principle of Individuation (QPI). It is argued that the space-time approach to individuation fails and that the quantum approach offers several advantages over it, including consistency with Leibniz’s Principle of Identity of Indiscernibles.
The dynamical behavior of open quantumsystems plays a key role in many applications of quantummechanics, examples ranging from fundamental problems, such as the environment-induced decay of quantum coherence and relaxation in many-body systems, to applications in condensed matter theory, quantum transport, quantum chemistry, and quantum information. In close analogy to a classical Markovian stochastic process, the interaction of an open quantumsystem with a noisy environment is often modeled phenomenologically by means of a dynamical semigroup with a corresponding time-independent generator in Lindblad form, which describes a memoryless dynamics of the open system typically leading to an irreversible loss of characteristic quantum features. However, in many applications open systems exhibit pronounced memory effects and a revival of genuine quantum properties such as quantum coherence, correlations, and entanglement. Here recent theoretical results on the rich non-Markovian quantum dynamics of open systems are discussed, paying particular attention to the rigorous mathematical definition, to the physical interpretation and classification, as well as to the quantification of quantum memory effects. The general theory is illustrated by a series of physical examples. The analysis reveals that memory effects of the open system dynamics reflect characteristic features of the environment which opens a new perspective for applications, namely, to exploit a small open system as a quantum probe signifying nontrivial features of the environment it is interacting with. This Colloquium further explores the various physical sources of non-Markovian quantum dynamics, such as structured environmental spectral densities, nonlocal correlations between environmental degrees of freedom, and correlations in the initial system-environment state, in addition to developing schemes for their local detection. Recent experiments addressing the detection, quantification, and control of
Chowdhury, S. Hasibul Hassan, E-mail: shhchowdhury@gmail.com; Department of Mathematics and Statistics, Concordia University, Montréal, Québec H3G 1M8; Ali, S. Twareque, E-mail: twareque.ali@concordia.ca
This paper is devoted to the construction and analysis of the Wigner functions for noncommutative quantummechanics, their marginal distributions, and star-products, following a technique developed earlier, viz, using the unitary irreducible representations of the group G{sub NC}, which is the three fold central extension of the Abelian group of ℝ{sup 4}. These representations have been exhaustively studied in earlier papers. The group G{sub NC} is identified with the kinematical symmetry group of noncommutative quantummechanics of a system with two degrees of freedom. The Wigner functions studied here reflect different levels of non-commutativity—both the operators of position and thosemore » of momentum not commuting, the position operators not commuting and finally, the case of standard quantummechanics, obeying the canonical commutation relations only.« less
For a long time microscopic physical descriptions of biological processes have been based on quantummechanical concepts and tools, and routinely employed by chemical physicists and quantum chemists. However, the last ten years have witnessed new developments on these studies from a different perspective, rooted in the framework of quantum information theory. The process that more, than others, has been subject of intense research is the transfer of excitation energy in photosynthetic light-harvesting complexes, a consequence of the unexpected experimental discovery of oscillating signals in such highly noisy systems. The fundamental interdisciplinary nature of this research makes it extremely fascinating, but can also constitute an obstacle to its advance. Here in this review our objective is to provide an essential summary of the progress made in the theoretical description of excitation energy dynamics in photosynthetic systems from a quantummechanical perspective, with the goal of unifying the language employed by the different communities. This is initially realized through a stepwise presentation of the fundamental building blocks used to model excitation transfer, including protein dynamics and the theory of open quantumsystem. Afterwards, we shall review how these models have evolved as a consequence of experimental discoveries; this will lead us to present the numerical techniques that have been introduced to quantitatively describe photo-absorbed energy dynamics. Finally, we shall discuss which mechanisms have been proposed to explain the unusual coherent nature of excitation transport and what insights have been gathered so far on the potential functional role of such quantum features.
The known methods, due for instance to G.W. Mackey and T.F. Jordan, which exploit the transformation properties with respect to the Euclidean and Galileian group to determine the formalism of the Quantum Theory of a localizable particle, fail in the case that the considered transformations are not symmetries of the physical system. In the present work we show that the formalism of standard QuantumMechanics for a particle without spin can be completely recovered by exploiting the covariance properties with respect to the group of Euclidean transformations, without requiring that these transformations are symmetries of the physical system.
We discuss common features in mechanical, electromagnetic and quantumsystems, supporting identical results for the transmission and reflection coefficients of waves arriving perpendicularly at a plane interface. Also, we briefly discuss the origin of special notions such as refractive index in quantummechanics, massive photons in wave guides and…
The gravitational equivalence principle in quantummechanics is of considerable importance, but it is generally not included in physics textbooks. In this note, we present a precise quantum formulation of this principle and comment on its verification in a neutron diffraction experiment. The solution of the time dependent Schrödinger equation for this problem also gives the wave function for the motion of a charged particle in a homogeneous electric field, which is also usually ignored in textbooks on quantummechanics.
We find the covariant deformed Heisenberg algebra and the Laplace-Beltrami operator on the extended h-deformed quantum plane and solve the Schrödinger equations explicitly for some physical systems on the quantum plane. In the commutative limit the behaviour of a quantum particle on the quantum plane becomes that of the quantum particle on the Poincaré half-plane, a surface of constant negative Gaussian curvature. We show that the bound state energy spectra for particles under specific potentials depend explicitly on the deformation parameter h. Moreover, it is shown that bound states can survive on the quantum plane in a limiting case where bound states on the Poincaré half-plane disappear.
Eichelkraut, Toni; Vetter, Christian; Perez-Leija, Armando; Christodoulides, Demetrios; Szameit, Alexander
2014-05-01
We show theoretically and experimentally that two-dimensional continuous time coherent random walks are possible in free space, that is, in the absence of any external potential, by properly tailoring the associated initial wave function. These effects are experimentally demonstrated using classical paraxial light. Evidently, the usage of classical beams to explore the dynamics of point-like quantum particles is possible since both phenomena are mathematically equivalent. This in turn makes our approach suitable for the realization of random walks using different quantum particles, including electrons and photons. To study the spatial evolution of a wavefunction theoretically, we consider the one-dimensional paraxial wave equation (i∂z +1/2 ∂x2) Ψ = 0 . Starting with the initially localized wavefunction Ψ (x , 0) = exp [ -x2 / 2σ2 ] J0 (αx) , one can show that the evolution of such Gaussian-apodized Bessel envelopes within a region of validity resembles the probability pattern of a quantum walker traversing a uniform lattice. In order to generate the desired input-field in our experimental setting we shape the amplitude and phase of a collimated light beam originating from a classical HeNe-Laser (633 nm) utilizing a spatial light modulator.
Multiple observers who interact with environmental encodings of the states of a macroscopic quantumsystem S as required by quantum Darwinism cannot demonstrate that they are jointly observing S without a joint a priori assumption of a classical boundary separating S from its environment E. Quantum Darwinism cannot, therefore, be regarded as providing a purely quantum-mechanical explanation of the "emergence" of classicality.
Wang, Chun-Hung; Duster, Adam W; Aydintug, Baris O; Zarecki, MacKenzie G; Lin, Hai
2018-01-01
We performed steered molecular dynamics (SMD) and umbrella sampling simulations of Cl - ion migration through the transmembrane domain of a prototypical E. coli CLC Cl - /H + antiporter by employing combined quantum-mechanical (QM) and molecular-mechanical (MM) calculations. The SMD simulations revealed interesting conformational changes of the protein. While no large-amplitude motions of the protein were observed during pore opening, the side chain rotation of the protonated external gating residue Glu148 was found to be critical for full access of the channel entrance by Cl - . Moving the anion into the external binding site (S ext ) induced small-amplitude shifting of the protein backbone at the N-terminal end of helix F. As Cl - traveled through the pore, rigid-body swinging motions of helix R separated it from helix D. Helix R returned to its original position once Cl - exited the channel. Population analysis based on polarized wavefunction from QM/MM calculations discovered significant (up to 20%) charge loss for Cl - along the ion translocation pathway inside the pore. The delocalized charge was redistributed onto the pore residues, especially the functional groups containing π bonds (e.g., the Tyr445 side chain), while the charges of the H atoms coordinating Cl - changed almost negligibly. Potentials of mean force computed from umbrella sampling at the QM/MM and MM levels both displayed barriers at the same locations near the pore entrance and exit. However, the QM/MM PMF showed higher barriers (~10 kcal/mol) than the MM PMF (~2 kcal/mol). Binding energy calculations indicated that the interactions between Cl - and certain pore residues were overestimated by the semi-empirical PM3 Hamiltonian and underestimated by the CHARMM36 force fields, both of which were employed in the umbrella sampling simulations. In particular, CHARMM36 underestimated binding interactions for the functional groups containing π bonds, missing the stabilizations of the Cl - ion due
Wang, Chun-Hung; Duster, Adam W.; Aydintug, Baris O.; Zarecki, MacKenzie G.; Lin, Hai
2018-01-01
We performed steered molecular dynamics (SMD) and umbrella sampling simulations of Cl− ion migration through the transmembrane domain of a prototypical E. coli CLC Cl−/H+ antiporter by employing combined quantum-mechanical (QM) and molecular-mechanical (MM) calculations. The SMD simulations revealed interesting conformational changes of the protein. While no large-amplitude motions of the protein were observed during pore opening, the side chain rotation of the protonated external gating residue Glu148 was found to be critical for full access of the channel entrance by Cl−. Moving the anion into the external binding site (Sext) induced small-amplitude shifting of the protein backbone at the N-terminal end of helix F. As Cl− traveled through the pore, rigid-body swinging motions of helix R separated it from helix D. Helix R returned to its original position once Cl− exited the channel. Population analysis based on polarized wavefunction from QM/MM calculations discovered significant (up to 20%) charge loss for Cl− along the ion translocation pathway inside the pore. The delocalized charge was redistributed onto the pore residues, especially the functional groups containing π bonds (e.g., the Tyr445 side chain), while the charges of the H atoms coordinating Cl− changed almost negligibly. Potentials of mean force computed from umbrella sampling at the QM/MM and MM levels both displayed barriers at the same locations near the pore entrance and exit. However, the QM/MM PMF showed higher barriers (~10 kcal/mol) than the MM PMF (~2 kcal/mol). Binding energy calculations indicated that the interactions between Cl− and certain pore residues were overestimated by the semi-empirical PM3 Hamiltonian and underestimated by the CHARMM36 force fields, both of which were employed in the umbrella sampling simulations. In particular, CHARMM36 underestimated binding interactions for the functional groups containing π bonds, missing the stabilizations of the Cl− ion
Wang, Chun-Hung; Duster, Adam W.; Aydintug, Baris O.; Zarecki, MacKenzie G.; Lin, Hai
2018-03-01
We performed steered molecular dynamics (SMD) and umbrella sampling simulations of Cl– ion migration through the transmembrane domain of a prototypical E. coli CLC Cl–/H+ antiporter employing combined quantum-mechanical (QM) and molecular-mechanical (MM) calculations. The SMD simulations revealed interesting conformational changes of the protein. While no large-amplitude motions of the protein were observed during pore opening, the side chain rotation of the protonated external gating residue Glu148 was found critical to full access of the channel entrance by Cl–. Moving the anion into the external binding site (Sext) induced small-amplitude shifting of the protein backbone at the N-terminal end of helix F. As Cl– travelled through the pore, rigid-body swinging motions of helix R separated it from helix D. Helix R returned to its original position once Cl– exited the channel. Population analysis based on polarized wavefunction from QM/MM calculations discovered significant (up to 20%) charge loss for Cl– along the ion translocation pathway inside the pore. The delocalized charge was redistributed onto the pore residues, especially the functional groups containing pi bonds (e.g. the Tyr445 side chain), while the charges of the H atoms coordinating Cl– changed almost negligibly. Potentials of mean force computed from umbrella sampling at the QM/MM and MM levels both displayed barriers at the same locations near the pore entrance and exit. However, the QM/MM PMF showed higher barriers ( 10 kcal/mol) than the MM PMF ( 2 kcal/mol). Binding energy calculations indicated that the interactions between Cl– and certain pore residues were overestimated by the semi-empirical PM3 Hamiltonian and underestimated by the CHARMM36 force fields, both of which were employed in the umbrella sampling simulations. In particular, CHARMM36 underestimated binding interactions for the functional groups containing pi bonds, missing the stabilizations of the Cl– ion due to
emit many photons, which allows for differential quantum efficiencies greater than unity and hence higher power output. QCLs have been successfully...maintained. The step in the well allows for high injection efficiency due to the spatial separation of the wavefunctions. A step quantum well, in which at...III.D.34), the photon density is determined to be ( )thiphotonphoton IILeAn − Γ = ητ (III.D.35) where the internal quantum efficiency
Criteria of measure quantifying quantum coherence, a unique property of quantumsystem, are proposed recently. In this paper, we first give an uncertainty-like expression relating the coherence and the entropy of quantumsystem. This finding allows us to discuss the relations between the entanglement and the coherence. Further, we discuss in detail the relations among the coherence, the discord and the deficit in the bipartite quantumsystem. We show that, the one-way quantum deficit is equal to the sum between quantum discord and the relative entropy of coherence of measured subsystem. PMID:26094795
Assuming a background in basic classical physics, multivariable calculus, and differential equations, A Concise Introduction to QuantumMechanics provides a self-contained presentation of the mathematics and physics of quantummechanics. The relevant aspects of classical mechanics and electrodynamics are reviewed, and the basic concepts of wave-particle duality are developed as a logical outgrowth of experiments involving blackbody radiation, the photoelectric effect, and electron diffraction. The Copenhagen interpretation of the wave function and its relation to the particle probability density is presented in conjunction with Fourier analysis and its generalization to function spaces. These concepts are combined to analyze the system consisting of a particle confined to a box, developing the probabilistic interpretation of observations and their associated expectation values. The Schrödinger equation is then derived by using these results and demanding both Galilean invariance of the probability density and Newtonian energy-momentum relations. The general properties of the Schrödinger equation and its solutions are analyzed, and the theory of observables is developed along with the associated Heisenberg uncertainty principle. Basic applications of wave mechanics are made to free wave packet spreading, barrier penetration, the simple harmonic oscillator, the Hydrogen atom, and an electric charge in a uniform magnetic field. In addition, Dirac notation, elements of Hilbert space theory, operator techniques, and matrix algebra are presented and used to analyze coherent states, the linear potential, two state oscillations, and electron diffraction. Applications are made to photon and electron spin and the addition of angular momentum, and direct product multiparticle states are used to formulate both the Pauli exclusion principle and quantum decoherence. The book concludes with an introduction to the rotation group and the general properties of angular momentum.
The perspective presented here is that modern genetics is at a similar stage of development as were early formulations of quantummechanics theory in the 1920s and that in 2010 we are at the dawn of a new revolution in genetics that promises to enrich and deepen our understanding of the gene and the genome. The interrelationships and interdependence of two views of the gene – the molecular biological view and the epigenetic view – are explored, and it is argued that the classical molecular biological view is incomplete without incorporation of the epigenetic perspective and that in a sense the molecular biological view has been evolving to include the epigenetic view. Intriguingly, this evolution of the molecular view toward the broader and more inclusive epigenetic view of the gene has an intriguing, if not precise, parallel in the evolution of concepts of atomic physics from Newtonian mechanics to quantummechanics that are interesting to consider. PMID:22639577
Because of inevitable coupling with the environment, nearly all practical quantumsystems are open system, where the evolution is not necessarily unitary. In this paper, we propose a duality quantum algorithm for simulating Hamiltonian evolution of an open quantumsystem. In contrast to unitary evolution in a usual quantum computer, the evolution operator in a duality quantum computer is a linear combination of unitary operators. In this duality quantum algorithm, the time evolution of the open quantumsystem is realized by using Kraus operators which is naturally implemented in duality quantum computer. This duality quantum algorithm has two distinct advantages compared to existing quantum simulation algorithms with unitary evolution operations. Firstly, the query complexity of the algorithm is O(d3) in contrast to O(d4) in existing unitary simulation algorithm, where d is the dimension of the open quantumsystem. Secondly, By using a truncated Taylor series of the evolution operators, this duality quantum algorithm provides an exponential improvement in precision compared with previous unitary simulation algorithm. PMID:27464855
Wong, T. G.; Foster, M.; Colgan, J.; Madison, D. H.
2009-01-01
We present calculations of ion-atom collisions using a partial-wave expansion of the projectile wavefunction. Most calculations of ion-atom collisions have typically used classical or plane-wave approximations for the projectile wavefunction, since partial-wave expansions are expected to require prohibitively large numbers of terms to converge…
Methods of solution of the inverse scattering problem at fixed energy in quantummechanics are presented. Scattering experiments of a beam of particles at a nonrelativisitic energy by a target made up of particles are analyzed. The Schroedinger equation is used to develop the quantummechanical description of the system and one of several functions depending on the relative distance of the particles. The inverse problem is the construction of the potentials from experimental measurements.
Duque, C. M.; Acosta, Ruben E.; Morales, A. L.; Mora-Ramos, M. E.; Restrepo, R. L.; Ojeda, J. H.; Kasapoglu, E.; Duque, C. A.
2016-10-01
The electron states in a two-dimensional quantum dot ring are calculated in the presence of a donor impurity atom under the effective mass and parabolic band approximations. The effect of an externally applied electric field is also taken into account. The wavefunctions are obtained via the exact diagonalization of the problem Hamiltonian using a 2D expansion within the adiabatic approximation. The impurity-related optical response is analyzed via the optical absorption, relative refractive index change and the second harmonics generation. The dependencies of the electron states and these optical coefficients with the changes in the configuration of the quantum ring system are discussed in detail.
The Weyl-Wigner map yields the entire structure of Moyal quantummechanics directly from the standard operator formulation. The covariant generalization of Moyal theory, also known as Vey quantummechanics, was presented in the literature many years ago. However, a derivation of the formalism directly from standard operator quantummechanics, clarifying the relation between the two formulations, is still missing. In this article we present a covariant generalization of the Weyl order prescription and of the Weyl-Wigner map and use them to derive Vey quantummechanics directly from the standard operator formulation. The procedure displays some interesting features: it yields all the key ingredients and provides a more straightforward interpretation of the Vey theory including a direct implementation of unitary operator transformations as phase space coordinate transformations in the Vey idiom. These features are illustrated through a simple example.
Data clustering is provided according to a dynamical framework based on quantummechanical time evolution of states corresponding to data points. To expedite computations, we can approximate the time-dependent Hamiltonian formalism by a truncated calculation within a set of Gaussian wave-functions (coherent states) centered around the original points. This allows for analytic evaluation of the time evolution of all such states, opening up the possibility of exploration of relationships among data-points through observation of varying dynamical-distances among points and convergence of points into clusters. This formalism may be further supplemented by preprocessing, such as dimensional reduction through singular value decomposition and/or feature filtering.
Data clustering is provided according to a dynamical framework based on quantummechanical time evolution of states corresponding to data points. To expedite computations, we can approximate the time-dependent Hamiltonian formalism by a truncated calculation within a set of Gaussian wave-functions (coherent states) centered around the original points. This allows for analytic evaluation of the time evolution of all such states, opening up the possibility of exploration of relationships among data-points through observation of varying dynamical-distances among points and convergence of points into clusters. This formalism may be further supplemented by preprocessing, such as dimensional reduction through singular value decomposition and/or feature filtering.
Pogosyan, George S.; Salto-Alegre, Cristina; Wolf, Kurt Bernardo; Yakhno, Alexander
2017-07-01
We consider the differential equation that Zernike proposed to classify aberrations of wavefronts in a circular pupil, whose value at the boundary can be nonzero. On this account, the quantum Zernike system, where that differential equation is seen as a Schrödinger equation with a potential, is special in that it has a potential and a boundary condition that are not standard in quantummechanics. We project the disk on a half-sphere and there we find that, in addition to polar coordinates, this system separates into two additional coordinate systems (non-orthogonal on the pupil disk), which lead to Schrödinger-type equations with Pöschl-Teller potentials, whose eigen-solutions involve Legendre, Gegenbauer, and Jacobi polynomials. This provides new expressions for separated polynomial solutions of the original Zernike system that are real. The operators which provide the separation constants are found to participate in a superintegrable cubic Higgs algebra.
Pöschl-Teller-driven solutions for quantummechanical fluctuations are triggered off by single scalar field theories obtained through a systematic perturbative procedure for generating deformed defects. The analytical properties concerning the quantum fluctuations in one-dimension, zero-mode states, first- and second-excited states, and energy density profiles are all obtained from deformed topological and non-topological structures supported by real scalar fields. Results are firstly derived from an integrated λϕ4 theory, with corresponding generalizations applied to starting λχ4 and sine-Gordon theories. By focusing our calculations on structures supported by the λϕ4 theory, the outcome of our study suggests an exact quantitative correspondence to Pöschl-Teller-driven systems. Embedded into the perturbative quantummechanics framework, such a correspondence turns into a helpful tool for computing excited states and continuous mode solutions, as well as their associated energy spectrum, for quantum fluctuations of perturbatively deformed structures. Perturbative deformations create distinct physical scenarios in the context of exactly solvable quantumsystems and may also work as an analytical support for describing novel braneworld universes embedded into a 5-dimensional gravity bulk.
We calculate the non-equilibrium current driven by a voltage drop across a quantum dot. The system is described by the two lead Anderson model at zero temperature with on-site Coulomb repulsion and non-interacting, linearized leads. We prepare the system in an initial state consisting of a free Fermi sea in each lead with the voltage drop given as the difference between the two Fermi levels. We quench the system by coupling the dot to the leads at t =0 and following the time evolution of the wavefunction. In the long time limit a new type of Bethe Ansatz wavefunction emerges, which satisfies the Lippmann-Schwinger equation with the two Fermi seas serving as the boundary conditions. The solution describes the non-equilibrium steady state of the system. We use this solution to compute the infinite time limit of the expectation value of the current operator at a given voltage, yielding the I-V characteristic. The calculation is non-perturbative and exact. Research supported by NSF Grant DMR 1410583.
We present an exact method of calculating the non-equilibrium current driven by a voltage drop across a quantum dot. The system is described by the two lead Anderson model at zero temperature with on-site Coulomb repulsion and non-interacting, linearized leads. We prepare the system in an initial state consisting of a free Fermi sea in each lead with the voltage drop given as the difference between the two Fermi levels. We quench the system by coupling the dot to the leads at t = 0 and following the time evolution of the wavefunction. In the long time limit a new type of Bethe Ansatz wavefunction emerges, which satisfies the Lippmann-Schwinger equation with the two Fermi seas serving as the boundary conditions. This exact, non-perturbative solution describes the non-equilibrium steady state of the system. We describe how to use this solution to compute the infinite time limit of the expectation value of the current operator at a given voltage, which would yield the I-V characteristic of the dot. Research supported by NSF Grant DMR 1410583.
Vela, Sergi; Verot, Martin; Fromager, Emmanuel; Robert, Vincent
2017-02-01
The present paper reports the application of a computational framework, based on the quantum master equation, the Fermi's golden Rule, and conventional wavefunction-based methods, to describe electron transport through a spin crossover molecular junction (Fe(bapbpy) (NCS)2, 1, bapbpy = N-(6-(6-(Pyridin-2-ylamino)pyridin-2-yl)pyridin-2-yl)-pyridin-2-amine). This scheme is an alternative to the standard approaches based on the relative position and nature of the frontier orbitals, as it evaluates the junction's Green's function by means of accurate state energies and wavefunctions. In the present work, those elements are calculated for the relevant states of the high- and low-spin species of 1, and they are used to evaluate the output conductance within a given range of bias- and gate-voltages. The contribution of the ground and low-lying excited states to the current is analyzed, and inspected in terms of their 2S + 1 Ms-states. In doing so, it is shown the relevance of treating not only the ground state in its maximum-Ms projection, as usually done in most computational-chemistry packages, but the whole spectrum of low-energy states of the molecule. Such improved representation of the junction has a notable impact on the total conductivity and, more importantly, it restores the equivalence between alpha and beta transport, which means that no spin polarization is observed in the absence of Zeeman splitting. Finally, this work inspects the strong- and weak-points of the suggested theoretical framework to understand electron transport through molecular switchable materials, identifies a pathway for future improvement, and offers a new insight into concepts that play a key role in spintronics.
A comparison is made between two alternative definitions for covalent bond orders: one derived from the exchange part of the two-particle density matrix and the other expressed as the correlation of fluctuations (covariance) of the number of electrons between the atomic centers. Although these definitions lead to identical formulae for mono-determinantal SCF wavefunctions, they predict different bond orders for correlated wavefunctions. It is shown that, in this case, the fluctuation-based definition leads to slightly lower values of the bond order than does the exchange-based definition, provided one uses an appropriate space-partitioning technique like that of Bader's topological theory of atoms in a molecule; however, use of Mulliken partitioning in this context leads to unphysical behaviour. The example of H 2 is discussed in detail.
A two- (nondegenerate) level quantumsystem interacting with a classical monochromatic radiation field is described. The existing work on this problem is reviewed and some novel aspects of the problems are presented.
Quantum Finance represents the synthesis of the techniques of quantum theory (quantummechanics and quantum field theory) to theoretical and applied finance. After a brief overview of the connection between these fields, we illustrate some of the methods of lattice simulations of path integrals for the pricing of options. The ideas are sketched out for simple models, such as the Black-Scholes model, where analytical and numerical results are compared. Application of the method to nonlinear systems is also briefly overviewed. More general models, for exotic or path-dependent options are discussed.
While historically many quantum-mechanical simulations of molecular dynamics have relied on the Born-Oppenheimer approximation to separate electronic and nuclear behavior, recently a great deal of interest has arisen in quantum effects in nuclear dynamics as well. Due to the computational difficulty of solving the Schrödinger equation in full, these effects are often treated with approximate methods. In this paper, we present an algorithm to tackle these problems using an extension to the many-interacting-worlds approach to quantummechanics. This technique uses a kernel function to rebuild the probability density, and therefore, in contrast with the approximation presented in the original paper, it can be naturally extended to n-dimensional systems. This opens up the possibility of performing quantum ground-state searches with steepest-descent methods, and it could potentially lead to real-time quantum molecular-dynamics simulations. The behavior of the algorithm is studied in different potentials and numbers of dimensions and compared both to the original approach and to exact Schrödinger equation solutions whenever possible.
In this paper the effects of size, hydrostatic pressure and temperature on electromagnetically induced transparency, as well as on absorption and the dispersion properties of multilayered spherical quantum dot with hydrogenic impurity are theoretically investigated. Energy eigenvalues and wavefunctions of quantumsystems in three-level and four-level configurations are calculated using the shooting method, while optical properties are obtained using the density matrix formalism and master equations. It is shown that peaks of the optical properties experience a blue-shift with increasing hydrostatic pressure and red-shift with increasing temperature. The changes of optical properties as a consequence of changes in barrier wells widths are non-monotonic, and these changes are discussed in detail.
Gao, Jiali; Truhlar, Donald G; Wang, Yingjie; Mazack, Michael J M; Löffler, Patrick; Provorse, Makenzie R; Rehak, Pavel
2014-09-16
Conspectus Molecular mechanical force fields have been successfully used to model condensed-phase and biological systems for a half century. By means of careful parametrization, such classical force fields can be used to provide useful interpretations of experimental findings and predictions of certain properties. Yet, there is a need to further improve computational accuracy for the quantitative prediction of biomolecular interactions and to model properties that depend on the wave functions and not just the energy terms. A new strategy called explicit polarization (X-Pol) has been developed to construct the potential energy surface and wave functions for macromolecular and liquid-phase simulations on the basis of quantummechanics rather than only using quantummechanical results to fit analytic force fields. In this spirit, this approach is called a quantummechanical force field (QMFF). X-Pol is a general fragment method for electronic structure calculations based on the partition of a condensed-phase or macromolecular system into subsystems ("fragments") to achieve computational efficiency. Here, intrafragment energy and the mutual electronic polarization of interfragment interactions are treated explicitly using quantummechanics. X-Pol can be used as a general, multilevel electronic structure model for macromolecular systems, and it can also serve as a new-generation force field. As a quantum chemical model, a variational many-body (VMB) expansion approach is used to systematically improve interfragment interactions, including exchange repulsion, charge delocalization, dispersion, and other correlation energies. As a quantummechanical force field, these energy terms are approximated by empirical functions in the spirit of conventional molecular mechanics. This Account first reviews the formulation of X-Pol, in the full variationally correct version, in the faster embedded version, and with systematic many-body improvements. We discuss illustrative examples
In this paper we apply the last developments of the theory of measurement in quantummechanics to the phenomenon of consciousness and especially to the awareness of unconscious components. Various models of measurement in quantummechanics can be distinguished by the fact that there is, or there is not, a collapse of the wave function. The passive aspect of consciousness seems to agree better with models in which there is no collapse of the wave function, whereas in the active aspect of consciousness—i.e., that which goes together with an act or a choice—there seems to be a collapse of the wave function. As an example of the second possibility we study in detail the photon delayed-choice experiment and its consequences for subjective or psychological time. We apply this as an attempt to explain synchronicity phenomena. As a model of application of the awareness of unconscious components we study the mourning process. We apply also the quantum paradigm to the phenomenon of correlation at a distance between minds, as well as to group correlations that appear during group therapies or group training. Quantum entanglement leads to the formation of group unconscious or collective unconscious. Finally we propose to test the existence of such correlations during sessions of group training.
Geracie, Michael; Haehl, Felix M.; Loganayagam, R.; Narayan, Prithvi; Ramirez, David M.; Rangamani, Mukund
2018-05-01
We examine, in a quantummechanical setting, the Hilbert space representation of the Becchi, Rouet, Stora, and Tyutin (BRST) symmetry associated with Schwinger-Keldysh path integrals. This structure had been postulated to encode important constraints on influence functionals in coarse-grained systems with dissipation, or in open quantumsystems. Operationally, this entails uplifting the standard Schwinger-Keldysh two-copy formalism into superspace by appending BRST ghost degrees of freedom. These statements were previously argued at the level of the correlation functions. We provide herein a complementary perspective by working out the Hilbert space structure explicitly. Our analysis clarifies two crucial issues not evident in earlier works: first, certain background ghost insertions necessary to reproduce the correct Schwinger-Keldysh correlators arise naturally, and, second, the Schwinger-Keldysh difference operators are systematically dressed by the ghost bilinears, which turn out to be necessary to give rise to a consistent operator algebra. We also elaborate on the structure of the final state (which is BRST closed) and the future boundary condition of the ghost fields.
The word 'uncertainty', in the context of quantummechanics, usually evokes an impression of an essential unknowability of what might actually be going on at the quantum level of activity, as is made explicit in Heisenberg's uncertainty principle, and in the fact that the theory normally provides only probabilities for the results of quantum measurement. These issues limit our ultimate understanding of the behaviour of things, if we take quantummechanics to represent an absolute truth. But they do not cause us to put that very 'truth' into question. This article addresses the issue of quantum 'uncertainty' from a different perspective, raising the question of whether this term might be applied to the theory itself, despite its unrefuted huge success over an enormously diverse range of observed phenomena. There are, indeed, seeming internal contradictions in the theory that lead us to infer that a total faith in it at all levels of scale leads us to almost fantastical implications.
Tosi, G.; Christmann, G.; Berloff, N. G.; Tsotsis, P.; Gao, T.; Hatzopoulos, Z.; Savvidis, P. G.; Baumberg, J. J.
2012-03-01
Seeing macroscopic quantum states directly remains an elusive goal. Particles with boson symmetry can condense into quantum fluids, producing rich physical phenomena as well as proven potential for interferometric devices. However, direct imaging of such quantum states is only fleetingly possible in high-vacuum ultracold atomic condensates, and not in superconductors. Recent condensation of solid-state polariton quasiparticles, built from mixing semiconductor excitons with microcavity photons, offers monolithic devices capable of supporting room-temperature quantum states that exhibit superfluid behaviour. Here we use microcavities on a semiconductor chip supporting two-dimensional polariton condensates to directly visualize the formation of a spontaneously oscillating quantum fluid. This system is created on the fly by injecting polaritons at two or more spatially separated pump spots. Although oscillating at tunable THz frequencies, a simple optical microscope can be used to directly image their stable archetypal quantum oscillator wavefunctions in real space. The self-repulsion of polaritons provides a solid-state quasiparticle that is so nonlinear as to modify its own potential. Interference in time and space reveals the condensate wavepackets arise from non-equilibrium solitons. Control of such polariton-condensate wavepackets demonstrates great potential for integrated semiconductor-based condensate devices.
Islam, Rajibul; Ma, Ruichao; Preiss, Philipp M; Tai, M Eric; Lukin, Alexander; Rispoli, Matthew; Greiner, Markus
2015-12-03
Entanglement is one of the most intriguing features of quantummechanics. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. Entanglement is now being studied in diverse fields ranging from condensed matter to quantum gravity. However, measuring entanglement remains a challenge. This is especially so in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here, we measure entanglement in such a system of itinerant particles using quantum interference of many-body twins. Making use of our single-site-resolved control of ultracold bosonic atoms in optical lattices, we prepare two identical copies of a many-body state and interfere them. This enables us to directly measure quantum purity, Rényi entanglement entropy, and mutual information. These experiments pave the way for using entanglement to characterize quantum phases and dynamics of strongly correlated many-body systems.
Using a recent formulation of quantummechanics without a potential function, we present a four-parameter system associated with the Wilson and Racah polynomials. The continuum scattering states are written in terms of the Wilson polynomials whose asymptotics give the scattering amplitude and phase shift. On the other hand, the finite number of discrete bound states are associated with the Racah polynomials.
Barnum, H; Beigi, S; Boixo, S; Elliott, M B; Wehner, S
2010-04-09
We show that, assuming that quantummechanics holds locally, the finite speed of information is the principle that limits all possible correlations between distant parties to be quantummechanical as well. Local quantummechanics means that a Hilbert space is assigned to each party, and then all local positive-operator-valued measurements are (in principle) available; however, the joint system is not necessarily described by a Hilbert space. In particular, we do not assume the tensor product formalism between the joint systems. Our result shows that if any experiment would give nonlocal correlations beyond quantummechanics, quantum theory would be invalidated even locally.
Two distinct types of Quantum Monte Carlo (QMC) calculations are applied to electronic structure problems such as calculating potential energy curves and producing benchmark values for reaction barriers. First, Variational and Diffusion Monte Carlo (VMC and DMC) methods using a trial wavefunction subject to the fixed node approximation were tested using the CASINO code.[1] Next, Full Configuration Interaction Quantum Monte Carlo (FCIQMC), along with its initiator extension (i-FCIQMC) were tested using the NECI code.[2] FCIQMC seeks the FCI energy for a specific basis set. At a reduced cost, the efficient i-FCIQMC method can be applied to systems in which the standard FCIQMC approach proves to be too costly. Since all of these methods are statistical approaches, uncertainties (error-bars) are introduced for each calculated energy. This study tests the performance of the methods relative to traditional quantum chemistry for some benchmark systems. References: [1] R. J. Needs et al., J. Phys.: Condensed Matter 22, 023201 (2010). [2] G. H. Booth et al., J. Chem. Phys. 131, 054106 (2009).
Parametrically modulated optomechanical systems have been recently proposed as a simple and efficient setting for the quantum control of a micromechanical oscillator: relevant possibilities include the generation of squeezing in the oscillator position (or momentum) and the enhancement of entanglement between mechanical and radiation modes. In this paper we further investigate this modulation regime, considering an optomechanical system with one or more parameters being modulated over time. We first apply a sinusoidal modulation of the mechanical frequency and characterize the optimal regime in which the visibility of purely quantum effects is maximal. We then introduce a second modulation on the input laser intensity and analyze the interplay between the two. We find that an interference pattern shows up, so that different choices of the relative phase between the two modulations can either enhance or cancel the desired quantum effects, opening new possibilities for optimal quantum control strategies.
The RIXS technique is best known for significant breakthroughs in the investigation of strongly correlated materials such as cuprates. However, the rapid advancement of RIXS spectrographs has made it increasingly attractive to apply the technique to a broad range of quantum materials outside of this comfort zone. This talk will review lessons learned from our recent measurements on material systems that feature a balance of correlated and itinerant physics, focusing on the hidden order compound URu2Si2, and touching on VO2 and Prussian blue analogue battery electrodes. RIXS spectra are found to reveal essential features defining low energy degrees of freedom in these moderately correlated wavefunctions. In the case of URu2Si2, we show that a principal energy gap defining strong correlations is fragile, and can be melted via modest chemical doping. Work at NYU was supported by the MRSEC Program of the National Science Foundation under Award Number DMR-1420073.
This book covers relativistic quantum theory from the point of view of a particle theory, based on the irreducible representations of the Poincaré group, the group that expresses the symmetry of Einstein relativity. There are several ways of formulating such a theory; this book develops what is called relativistic point form quantummechanics, which, unlike quantum field theory, deals with a fixed number of particles in a relativistically invariant way. A chapter is devoted to applications of point form quantummechanics to nuclear physics.
A scheme for constructing quantummechanics is given that does not have Hilbert space and linear operators as its basic elements. Instead, a version of algebraic approach is considered. Elements of a noncommutative algebra (observables) and functionals on this algebra (elementary states) associated with results of single measurements are used as primary components of the scheme. On the one hand, it is possible to use within the scheme the formalism of the standard (Kolmogorov) probability theory, and, on the other hand, it is possible to reproduce the mathematical formalism of standard quantummechanics, and to study the limits of its applicability. A short outline is given of the necessary material from the theory of algebras and probability theory. It is described how the mathematical scheme of the paper agrees with the theory of quantum measurements, and avoids quantum paradoxes.
The Heisenberg-James-Stapp (quantummechanical) mind model is surveyed and criticized briefly. The criticism points out that the model, while being essentially consistent concerning (human) consciousness, fundamentally lacks the evolutional point of view both onto- and phylogenetically. Ethology and other than Jamesian psychology is quoted and a quantummechanical theoretical scheme is suggested to essentially extend Stapp's frame in an evolutionary context. It is proposed that its central supposition, spontaneous quantum measurement can be better utilized in an investigation of the origin of the "subjective" process, having come about concomitantly with the chemistry of the origin of life. We dwell on its applicability at this latter process, at its heart standing, it is supposed, the endophysical nonlinear "self-measurement" of (quantummechanically describable) matter, and so our investigation is extended to this primeval phenomenon. It is suggested that the life phenomenon is an indirect C* → (W*) → C* quantum algebraic process transition, where the (W*) system would represent the living state. Summarized also are our previous results on an internalized, "reversed", time process, introduced originally by Gunji, which is subordinated to the external "forwards" time evolution, driving towards symmetry by gradual space-mappings, where the original splitting-up must have come about in a spontaneous symmetry breaking nonlinear "self-measurement" of matter in an endophysical World.
A supersymmetric generalization of the Lieb-Liniger-Yang dynamics governing N massive bosons moving on a line with delta interactions among them at coinciding points is developed. The analysis of the delicate balance between integrability and-supersymmetry, starting from the exactly solvable non-supersymmetric LLY system, is one of the paper main concerns. Two extreme regimes of the N parameter are explored: 1) For few bosons we fall in the realm of supersymmetric quantummechanics with a short number of degrees of freedom, e.g., the SUSY Pösch-Teller potentials if N = 1 . 2) For large N we deal with supersymmetric extensions of many-body systems in the thermodynamic limit akin, e.g., to the supersymmetric Calogero-Sutherland systems. Emphasis will be put in the investigation of the ground-state structure of these quantummechanicalsystems enjoying {N}=2 extended supersymmetry without spoiling integrability. The decision about wether or not supersymmetry is spontaneously broken, a central question in SUSY quantummechanics determined from the ground-state structure, is another goal of the paper.
Based on previous studies in a single-particle system in both the integrable [Jarzynski, Quan, and Rahav, Phys. Rev. X 5, 031038 (2015)2160-330810.1103/PhysRevX.5.031038] and the chaotic systems [Zhu, Gong, Wu, and Quan, Phys. Rev. E 93, 062108 (2016)1539-375510.1103/PhysRevE.93.062108], we study the the correspondence principle between quantum and classical work distributions in a quantum many-body system. Even though the interaction and the indistinguishability of identical particles increase the complexity of the system, we find that for a quantum many-body system the quantum work distribution still converges to its classical counterpart in the semiclassical limit. Our results imply that there exists a correspondence principle between quantum and classical work distributions in an interacting quantum many-body system, especially in the large particle number limit, and further justify the definition of quantum work via two-point energy measurements in quantum many-body systems.
Quantummechanics in terms of interactive holography appears as `normal' science [1]. With the holography quantum behavior is determined by the interplay of material formations and their conjugate images. To begin with, this effortlessly elucidates the nonlocality in quantum entanglements. Then, it has been shown that Schr"odinger's dynamics for a single particle arises from Bi-Fragmental random walks of the particle itself and its holographic image. For many particles this picture blurs with fragments merging as bosons or fermions. In biomolecules, swapping of particles and their holographic placeholders leads to self-replication of the living matter. Because of broad interpretations of quantum formalism direct experiments attributing it to holography may not be very compelling. The holographic mechanism better reveals as an absolute frame of reference. A number of physical and biological events exhibit annual variations when Earth orbital position changes with respect to the universal holographic mechanism. The well established calendar variations of heart attacks can be regarded as a positive outcome of a generalization of the Michelson experiment, where holography is interferometry and ailing hearts are detectors of pathologically replicated proteins. Also, there have been already observed calendar changes in radioactive decay rates. The same could be expected for various fine quantum experiences, like, e.g., Josephson tunneling. In other words, QuantumMechanics (February) QuantumMechanics (August). [1] S. Berkovich, ``A comprehensive explanation of quantummechanics,'' www.cs.gwu.edu/research/technical-report/170 .
A generalization of previous treatments of quantum phase is presented. Restrictions on the class of realizable phase statistics are thereby removed; thus, permitting 'phase wavefunction collapse' (and other advantages). This is accomplished by exciting the auxiliary mode of the measurement apparatus in a time-reversed fashion. The mathematical properties of this auxiliary mode are studied in the hope that they will lead to an identification of a physical apparatus which can realize the quantum phase measurement.
We have developed an app for iOS-based smart-phones/tablets that allows a 3-D, complex phase-based colorful visualization of hydrogen atom wave functions. Several important features of the quantum behavior of atomic orbitals can easily be made evident, thus making this app a useful companion in introductory modern physics classes. There are many reasons why quantummechanicalsystems and phenomena are difficult both to teach and deeply understand. They are described by equations that are generally hard to visualize, and they often oppose the so-called "common sense" based on the human perception of the world, which is built on mental images such as locality and causality. Moreover students cannot have direct experience of those systems and solutions, and generally do not even have the possibility to refer to pictures, videos, or experiments to fill this gap. Teachers often encounter quite serious troubles in finding out a sensible way to speak about the wonders of quantum physics at the high school level, where complex formalisms are not accessible at all. One should however consider that this is quite a common issue in physics and, more generally, in science education. There are plenty of natural phenomena whose models (not only at microscopic and atomic levels) are of difficult, if not impossible, visualization. Just think of certain kinds of waves, fields of forces, velocities, energy, angular momentum, and so on. One should also notice that physical reality is not the same as the images we make of it. Pictures (formal, abstract ones, as well as artists' views) are a convenient bridge between these two aspects.
Quantummechanics is usually defined in terms of some loosely connected axioms and rules. Such a foundation is far from the beauty of, e.g., the `principles' underlying classical mechanics. Motivated, in addition, by notorious interpretation problems, there have been numerous attempts to modify or `complete' quantummechanics. A first attempt was based on so-called hidden variables; its proponents essentially tried to expel the non-classical nature of quantummechanics. More recent proposals intend to complete quantummechanics not within mechanics proper but on a `higher (synthetic) level'; by means of a combination with gravitation theory (R Penrose), with quantum information theory (C M Caves, C A Fuchs) or with psychology and brain science (H P Stapp). I think it is fair to say that in each case the combination is with a subject that, per se, suffers from a very limited understanding that is even more severe than that of quantummechanics. This was acceptable, though, if it could convincingly be argued that scientific progress desperately needs to join forces. Quantummechanics of a closed system was a beautiful and well understood theory with its respective state being presented as a point on a deterministic trajectory in Liouville space---not unlike the motion of a classical N-particle system in its 6N-dimensional phase-space. Unfortunately, we need an inside and an outside view, we need an external reference frame, we need an observer. This unavoidable partition is the origin of most of the troubles we have with quantummechanics. A pragmatic solution is introduced in the form of so-called measurement postulates: one of the various incompatible properties of the system under consideration is supposed to be realized (i.e. to become a fact, to be defined without fundamental dispersion) based on `instantaneous' projections within some externally selected measurement basis. As a result, the theory becomes essentially statistical rather than deterministic
Quantum tunneling is a ubiquitous phenomenon in nature and crucial for many technological applications. It allows quantum particles to reach regions in space which are energetically not accessible according to classical mechanics. In this “tunneling region,” the particle density is known to decay exponentially. This behavior is universal across all energy scales from nuclear physics to chemistry and solid state systems. Although typically only a small fraction of a particle wavefunction extends into the tunneling region, we present here an extreme quantumsystem: a gigantic molecule consisting of two helium atoms, with an 80% probability that its two nuclei will be found in this classical forbidden region. This circumstance allows us to directly image the exponentially decaying density of a tunneling particle, which we achieved for over two orders of magnitude. Imaging a tunneling particle shows one of the few features of our world that is truly universal: the probability to find one of the constituents of bound matter far away is never zero but decreases exponentially. The results were obtained by Coulomb explosion imaging using a free electron laser and furthermore yielded He2’s binding energy of 151.9±13.3151.9±13.3 neV, which is in agreement with most recent calculations.
We demonstrate the existence of a novel set of discrete symmetries in the context of the N=2 supersymmetric (SUSY) quantummechanical model with a potential function f(x) that is a generalization of the potential of the 1D SUSY harmonic oscillator. We perform the same exercise for the motion of a charged particle in the X–Y plane under the influence of a magnetic field in the Z-direction. We derive the underlying algebra of the existing continuous symmetry transformations (and corresponding conserved charges) and establish its relevance to the algebraic structures of the de Rham cohomological operators of differential geometry. We showmore » that the discrete symmetry transformations of our present general theories correspond to the Hodge duality operation. Ultimately, we conjecture that any arbitrary N=2 SUSY quantummechanicalsystem can be shown to be a tractable model for the Hodge theory. -- Highlights: •Discrete symmetries of two completely different kinds of N=2 supersymmetric quantummechanical models have been discussed. •The discrete symmetries provide physical realizations of Hodge duality. •The continuous symmetries provide the physical realizations of de Rham cohomological operators. •Our work sheds a new light on the meaning of the above abstract operators.« less
This paper addresses foundational issues related to quantum computing. The need for a universally valid theory such as quantummechanics to describe to some extent its own validation is noted. This includes quantummechanical descriptions of systems that do theoretical calculations (i.e. quantum computers) and systems that perform experiments. Quantum robots interacting with an environment are a small first step in this direction. Quantum robots are described here as mobile quantumsystems with on-board quantum computers that interact with environments. Included are discussions on the carrying out of tasks and the division of tasks into computation and action phases. Specificmore » models based on quantum Turing machines are described. Differences and similarities between quantum robots plus environments and quantum computers are discussed.« less
Kotler, Shlomi; Simmonds, Raymond W.; Leibfried, Dietrich; Wineland, David J.
2017-02-01
Trapped charged particles have been at the forefront of quantum information processing (QIP) for a few decades now, with deterministic two-qubit logic gates reaching record fidelities of 99.9 % and single-qubit operations of much higher fidelity. In a hybrid system involving trapped charges, quantum degrees of freedom of macroscopic objects such as bulk acoustic resonators, superconducting circuits, or nanomechanical membranes, couple to the trapped charges and ideally inherit the coherent properties of the charges. The hybrid system therefore implements a "quantum transducer," where the quantum reality (i.e., superpositions and entanglement) of small objects is extended to include the larger object. Although a hybrid quantumsystem with trapped charges could be valuable both for fundamental research and for QIP applications, no such system exists today. Here we study theoretically the possibilities of coupling the quantum-mechanical motion of a trapped charged particle (e.g., an ion or electron) to the quantum degrees of freedom of superconducting devices, nanomechanical resonators, and quartz bulk acoustic wave resonators. For each case, we estimate the coupling rate between the charged particle and its macroscopic counterpart and compare it to the decoherence rate, i.e., the rate at which quantum superposition decays. A hybrid system can only be considered quantum if the coupling rate significantly exceeds all decoherence rates. Our approach is to examine specific examples by using parameters that are experimentally attainable in the foreseeable future. We conclude that hybrid quantumsystems involving a single atomic ion are unfavorable compared with the use of a single electron because the coupling rates between the ion and its counterpart are slower than the expected decoherence rates. A system based on trapped electrons, on the other hand, might have coupling rates that significantly exceed decoherence rates. Moreover, it might have appealing properties such
First, exact definitions are supplied for the terms: position, velocity, energy, etc. (of the electron, for instance), such that they are valid also in quantummechanics. Canonically conjugated variables are determined simultaneously only with a characteristic uncertainty. This uncertainty is the intrinsic reason for the occurrence of statistical relations in quantummechanics. Mathematical formulation is made possible by the Dirac-Jordan theory. Beginning from the basic principles thus obtained, macroscopic processes are understood from the viewpoint of quantummechanics. Several imaginary experiments are discussed to elucidate the theory.
We perform a theoretical study on quantum correlations in an optomechanical system where the mechanical mirror is perturbatively coupled to an auxiliary qubit. In our study, we consider logarithmic negativity to quantify the degree of stationary entanglement between the cavity field and mechanical mirror, and, Gaussian quantum discord as a witness of the quantumness of the correlation beyond entanglement. Utilizing experimentally feasible parameters, we show that both entanglement and quantum discord enhance significantly with increase in mirror-qubit coupling. Moreover, we find that in presence of the mirror-qubit coupling entanglement could be generated at a considerably lower optomechanical coupling strength, which is also extremely robust against the environmental temperature. Overall, our proposed scheme offers some considerable advantages for realizing the continuous-variable quantum information and communication.
We outline a programme for an axiomatic reconstruction of quantummechanics based on the statistical duality of states and effects that combines the use of a theorem of Solér with the idea of symmetry. We also discuss arguments favouring the choice of the complex field. This article is part of the themed issue `Second quantum revolution: foundational questions'.
Quantum effects in solute-solvent interactions, such as the many-body effect and the dipole-induced dipole, are known to be critical factors influencing the infrared spectra of species in the liquid phase. For accurate spectrum evaluation, the surrounding solvent molecules, in addition to the solute of interest, should be treated using a quantummechanical method. However, conventional quantummechanics/molecular mechanics (QM/MM) methods cannot handle free QM solvent molecules during molecular dynamics (MD) simulation because of the diffusion problem. To deal with this problem, we have previously proposed an adaptive QM/MM "size-consistent multipartitioning (SCMP) method". In the present study, as the first application of the SCMP method, we demonstrate the reproduction of the infrared spectrum of liquid-phase water, and evaluate the quantum effect in comparison with conventional QM/MM simulations.
Superconducting quantum circuit models are widely used to understand superconducting devices. This thesis consists of four studies wherein the superconducting quantum circuit is used to illustrate challenges related to quantum information encoding and processing, quantum simulation, quantum signal detection and amplification. The existence of scalar Aharanov-Bohm phase has been a controversial topic for decades. Scalar AB phase, defined as time integral of electric potential, gives rises to an extra phase factor in wavefunction. We proposed a superconducting quantum Faraday cage to detect temporal interference effect as a consequence of scalar AB phase. Using the superconducting quantum circuit model, the physical system is solved and resulting AB effect is predicted. Further discussion in this chapter shows that treating the experimental apparatus quantummechanically, spatial scalar AB effect, proposed by Aharanov-Bohm, can't be observed. Either a decoherent interference apparatus is used to observe spatial scalar AB effect, or a quantum Faraday cage is used to observe temporal scalar AB effect. The second study involves protecting a quantumsystem from losing coherence, which is crucial to any practical quantum computation scheme. We present a theory to encode any qubit, especially superconducting qubits, into a universal quantum degeneracy point (UQDP) where low frequency noise is suppressed significantly. Numerical simulations for superconducting charge qubit using experimental parameters show that its coherence time is prolong by two orders of magnitude using our universal degeneracy point approach. With this improvement, a set of universal quantum gates can be performed at high fidelity without losing too much quantum coherence. Starting in 2004, the use of circuit QED has enabled the manipulation of superconducting qubits with photons. We applied quantum optical approach to model coupled resonators and obtained a four-wave mixing toolbox to operate photons
Krijtenburg-Lewerissa, K.; Pol, H. J.; Brinkman, A.; van Joolingen, W. R.
2017-06-01
This study presents a review of the current state of research on teaching quantummechanics in secondary and lower undergraduate education. A conceptual approach to quantummechanics is being implemented in more and more introductory physics courses around the world. Because of the differences between the conceptual nature of quantummechanics and classical physics, research on misconceptions, testing, and teaching strategies for introductory quantummechanics is needed. For this review, 74 articles were selected and analyzed for the misconceptions, research tools, teaching strategies, and multimedia applications investigated. Outcomes were categorized according to their contribution to the various subtopics of quantummechanics. Analysis shows that students have difficulty relating quantum physics to physical reality. It also shows that the teaching of complex quantum behavior, such as time dependence, superposition, and the measurement problem, has barely been investigated for the secondary and lower undergraduate level. At the secondary school level, this article shows a need to investigate student difficulties concerning wave functions and potential wells. Investigation of research tools shows the necessity for the development of assessment tools for secondary and lower undergraduate education, which cover all major topics and are suitable for statistical analysis. Furthermore, this article shows the existence of very diverse ideas concerning teaching strategies for quantummechanics and a lack of research into which strategies promote understanding. This article underlines the need for more empirical research into student difficulties, teaching strategies, activities, and research tools intended for a conceptual approach for quantummechanics.
Achuthan, P.; Dept. of Mathematics, Indian Institute of Technology, Madras, 600 036; Narayanankutty, Karuppath
2009-07-02
The world of physical systems at the most fundamental levels is replete with efficient, interesting models possessing sufficient ability to represent the reality to a considerable extent. So far, quantummechanics (QM) forming the basis of almost all natural phenomena, has found beyond doubt its intrinsic ingenuity, capacity and robustness to stand the rigorous tests of validity from and through appropriate calculations and experiments. No serious failures of quantummechanical predictions have been reported, yet. However, Albert Einstein, the greatest theoretical physicist of the twentieth century and some other eminent men of science have stated firmly and categorically that QM,more » though successful by and large, is incomplete. There are classical and quantum reality models including those based on consciousness. Relativistic quantum theoretical approaches to clearly understand the ultimate nature of matter as well as radiation have still much to accomplish in order to qualify for a final theory of everything (TOE). Mathematical models of better, suitable character as also strength are needed to achieve satisfactory explanation of natural processes and phenomena. We, in this paper, discuss some of these matters with certain apt illustrations as well.« less
We are investigating cognitive issues in learning quantummechanics in order to develop effective teaching and learning tools. The analysis of cognitive issues is particularly important for bridging the gap between the quantitative and conceptual aspects of quantummechanics and for ensuring that the learning tools help students build a robust knowledge structure. We discuss the cognitive aspects of quantummechanics that are similar or different from those of introductory physics and their implications for developing strategies to help students develop a good grasp of quantummechanics.
Understanding of the electroluminescence (EL) mechanism in optoelectronic devices is imperative for further optimization of their efficiency and effectiveness. Here, a quantummechanical approach is formulated for modeling the EL processes in nanoscale light emitting diodes (LED). Based on non-equilibrium Green's function quantum transport equations, interactions with the electromagnetic vacuum environment are included to describe electrically driven light emission in the devices. The presented framework is illustrated by numerical simulations of a silicon nanowire LED device. EL spectra of the nanowire device under different bias voltages are obtained and, more importantly, the radiation pattern and polarization of optical emission can be determined using the current approach. This work is an important step forward towards atomistic quantummechanical modeling of the electrically induced optical response in nanoscale systems.
We propose a simple and straightforward method based on Wronskians for the calculation of bound-state energies and wavefunctions of one-dimensional quantum-mechanical problems. We explicitly discuss the asymptotic behaviour of the wavefunction and show that the allowed energies make the divergent part vanish. As illustrative examples we consider…
We investigate the role of quantummechanical effects in the central stability concept of evolutionary game theory, i.e., an evolutionarily stable strategy (ESS). Using two and three-player symmetric quantum games we show how the presence of quantum phenomenon of entanglement can be crucial to decide the course of evolutionary dynamics in a population of interacting individuals.
Conferences and Proceedings: The results were presented at several conferences. These include: 1. M. O. Scully, " Foundations of QuantumMechanics ", in...applications have revealed a strong connection between the fundamental aspects of quantummechanics that governs physical systems and the informational...could be solved in polynomial time using quantum computers. Another set of problems where quantummechanics can carry out computations substantially
The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantummechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantummechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr’s quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions – all advocate for the reliability of assuming PI formalism of quantummechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems. PMID:20087467
The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantummechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantummechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr's quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions - all advocate for the reliability of assuming PI formalism of quantummechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems.
Joshi, Chaitanya; Larson, Jonas; Spiller, Timothy P.
2016-04-01
We investigate a possibility to generate nonclassical states in light-matter coupled noisy quantumsystems, namely, the anisotropic Rabi and Dicke models. In these hybrid quantumsystems, a competing influence of coherent internal dynamics and environment-induced dissipation drives the system into nonequilibrium steady states (NESSs). Explicitly, for the anisotropic Rabi model, the steady state is given by an incoherent mixture of two states of opposite parities, but as each parity state displays light-matter entanglement, we also find that the full state is entangled. Furthermore, as a natural extension of the anisotropic Rabi model to an infinite spin subsystem, we next explored the NESS of the anisotropic Dicke model. The NESS of this linearized Dicke model is also an inseparable state of light and matter. With an aim to enrich the dynamics beyond the sustainable entanglement found for the NESS of these hybrid quantumsystems, we also propose to combine an all-optical feedback strategy for quantum state protection and for establishing quantum control in these systems. Our present work further elucidates the relevance of such hybrid open quantumsystems for potential applications in quantum architectures.
Quantum effects like tunneling, coherence, and zero point energy often play a significant role in phenomena on the scales of atoms and molecules. However, the exact quantum treatment of a system scales exponentially with dimensionality, making it impractical for characterizing reaction rates and mechanisms in complex systems. An ongoing effort in the field of theoretical chemistry and physics is extending scalable, classical trajectory-based simulation methods capable of capturing quantum effects to describe dynamic processes in many-body systems; in the work presented here we explore two such techniques. First, we detail an explicit electron, path integral (PI)-based simulation protocol for predicting the rate of electron transfer in condensed-phase transition metal complex systems. Using a PI representation of the transferring electron and a classical representation of the transition metal complex and solvent atoms, we compute the outer sphere free energy barrier and dynamical recrossing factor of the electron transfer rate while accounting for quantum tunneling and zero point energy effects. We are able to achieve this employing only a single set of force field parameters to describe the system rather than parameterizing along the reaction coordinate. Following our success in describing a simple model system, we discuss our next steps in extending our protocol to technologically relevant materials systems. The latter half focuses on the Mixed Quantum-Classical Initial Value Representation (MQC-IVR) of real-time correlation functions, a semiclassical method which has demonstrated its ability to "tune'' between quantum- and classical-limit correlation functions while maintaining dynamic consistency. Specifically, this is achieved through a parameter that determines the quantumness of individual degrees of freedom. Here, we derive a semiclassical correction term for the MQC-IVR to systematically characterize the error introduced by different choices of simulation
Krijtenburg-Lewerissa, K.; Pol, H. J.; Brinkman, A.; van Joolingen, W. R.
2017-01-01
This study presents a review of the current state of research on teaching quantummechanics in secondary and lower undergraduate education. A conceptual approach to quantummechanics is being implemented in more and more introductory physics courses around the world. Because of the differences between the conceptual nature of quantummechanics and…
In this work, we first solve complex Morse flow equations for the simplest case of a bosonic harmonic oscillator to discuss localization in the context of Picard-Lefschetz theory. We briefly touch on the exact non-BPS solutions of the bosonized supersymmetric quantummechanics on algebraic geometric grounds and report that their complex phases can be accessed through the cohomology of WKB 1-form of the underlying singular spectral curve subject to necessary cohomological corrections for nonzero genus. Motivated by Picard-Lefschetz theory, we write down a general formula for the index of N =4 quantummechanics with background R -symmetry gauge fields. We conjecture that certain symmetries of the refined Witten index and singularities of the moduli space may be used to determine the correct intersection coefficients. A few examples, where this conjecture holds, are shown in both linear and closed quivers with rank-one quiver gauge groups. The R -anomaly removal along the "Morsified" relative homology cycles also called "Lefschetz thimbles" is shown to lead to the appearance of Stokes lines. We show that the Fayet-Iliopoulos parameters appear in the intersection coefficients for the relative homology of the quiver quantummechanics resulting from dimensional reduction of 2 d N =(2 ,2 ) gauge theory on a circle and explicitly calculate integrals along the Lefschetz thimbles in N =4 C Pk -1 model. The Stokes jumping of coefficients and its relation to wall crossing phenomena is briefly discussed. We also find that the notion of "on-the-wall" index is related to the invariant Lefschetz thimbles under Stokes phenomena. An implication of the Lefschetz thimbles in constructing knots from quiver quantummechanics is indicated.
Theoretical explication of a growing body of empirical data on consciousness-related anomalous phenomena is unlikely to be achieved in terms of known physical processes. Rather, it will first be necessary to formulate the basic role of consciousness in the definition of reality before such anomalous experience can adequately be represented. This paper takes the position that reality is constituted only in the interaction of consciousness with its environment, and therefore that any scheme of conceptual organization developed to represent that reality must reflect the processes of consciousness as well as those of its environment. In this spirit, the concepts and formalisms of elementary quantummechanics, as originally proposed to explain anomalous atomic-scale physical phenomena, are appropriated via metaphor to represent the general characteristics of consciousness interacting with any environment. More specifically, if consciousness is represented by a quantummechanical wave function, and its environment by an appropriate potential profile, Schrödinger wave mechanics defines eigenfunctions and eigenvalues that can be associated with the cognitive and emotional experiences of that consciousness in that environment. To articulate this metaphor it is necessary to associate certain aspects of the formalism, such as the coordinate system, the quantum numbers, and even the metric itself, with various impressionistic descriptors of consciousness, such as its intensity, perspective, approach/avoidance attitude, balance between cognitive and emotional activity, and receptive/assertive disposition. With these established, a number of the generic features of quantummechanics, such as the wave/particle duality, and the uncertainty, indistinguishability, and exclusion principles, display metaphoric relevance to familiar individual and collective experiences. Similarly, such traditional quantum theoretic exercises as the central force field and atomic structure, covalent
A century ago quantummechanics created a conceptual revolution whose fruits are now seen in almost any aspect of our day-to-day life. Lasers, transistors and other solid state and optical devices represent the core technology of current computers, memory devices and communication systems. However, all these examples do not exploit fully the quantum revolution as they do not take advantage of the coherent wave-like properties of the quantum wave function. Controlled coherent system and devices at ambient temperatures are challenging to realize. We are developing a novel nano tool box with control coupling between the quantum states and the environment. This tool box that combines nano particles with organic molecules enables the integration of quantum properties with classical existing devices at ambient temperatures. The nano particles generate the quantum states while the organic molecules control the coupling and therefore the energy, charge, spin, or quasi particle transfer between the layers. Coherent effects at ambient temperatures can be measured in the strong coupling regime. In the talk I will present our nano tool box and show studies of charge transfer, spin transfer and energy transfer in the hybrid layers as well as collective transfer phenomena. These enable the realization of room temperature operating quantum electro optical devices. For example I will present in details, our recent development of a new type of chiral molecules based magnetless universal memory exploiting selective spin transfer.
The extended semantic realism ( ESR) model embodies the mathematical formalism of standard (Hilbert space) quantummechanics in a noncontextual framework, reinterpreting quantum probabilities as conditional instead of absolute. We provide here an improved version of this model and show that it predicts that, whenever idealized measurements are performed, a modified Bell-Clauser-Horne-Shimony-Holt ( BCHSH) inequality holds if one takes into account all individual systems that are prepared, standard quantum predictions hold if one considers only the individual systems that are detected, and a standard BCHSH inequality holds at a microscopic (purely theoretical) level. These results admit an intuitive explanation in terms of an unconventional kind of unfair sampling and constitute a first example of the unified perspective that can be attained by adopting the ESR model.
Dreyfus, Benjamin W.; Elby, Andrew; Gupta, Ayush; Sohr, Erin Ronayne
2017-12-01
Mathematical sense-making—looking for coherence between the structure of the mathematical formalism and causal or functional relations in the world—is a core component of physics expertise. Some physics education research studies have explored what mathematical sense-making looks like at the introductory physics level, while some historians and "science studies" have explored how expert physicists engage in it. What is largely missing, with a few exceptions, is theoretical and empirical work at the intermediate level—upper division physics students—especially when they are learning difficult new mathematical formalism. In this paper, we present analysis of a segment of video-recorded discussion between two students grappling with a quantummechanics question to illustrate what mathematical sense-making can look like in quantummechanics. We claim that mathematical sense-making is possible and productive for learning and problem solving in quantummechanics. Mathematical sense-making in quantummechanics is continuous in many ways with mathematical sense-making in introductory physics. However, in the context of quantummechanics, the connections between formalism, intuitive conceptual schema, and the physical world become more compound (nested) and indirect. We illustrate these similarities and differences in part by proposing a new symbolic form, eigenvector eigenvalue, which is composed of multiple primitive symbolic forms.
After showing that the magnetic translation operators are not the symmetries of the quantum Hall effect (QHE) on non-flat surfaces, we show that another set of operators which leads to the quantum group symmetries for some of these surfaces exists. As a first example we show that the su(2) symmetry of the QHE on a sphere leads to 0305-4470/29/3/010/img6(2) algebra in the equator. We explain this result by a contraction of su(2). Second, with the help of the symmetry operators of QHE on the Poincaré upper half plane, we will show that the ground-state wavefunctions form a representation of the 0305-4470/29/3/010/img6(2) algebra.
This article is a revision of two papers submitted to the APS in the past two and a half years. In these papers, arguments and proofs are summarized for the following: (1) The wrong conclusion by EPR that QuantumMechanics is incomplete, perhaps requiring the addition of ``hidden variables'' for completion. Theorems that assume such ``hidden variables,'' such as Bell's theorem, are also wrong. (2) Quantum entanglement is not a realizable physical phenomenon and is based entirely on assuming a probability superposition model for quantum spin. Such a model directly violates conservation of angular momentum. (3) Simultaneous multiple-paths followed by a quantum particle traveling through space also cannot possibly exist. Besides violating Noether's theorem, the multiple-paths theory is based solely on probability calculations. Probability calculations by themselves cannot possibly represent simultaneous physically real events. None of the reviews of the submitted papers actually refuted the arguments and evidence that was presented. These analyses should therefore be carefully evaluated since the conclusions reached have such important impact in quantummechanics and quantum information theory.
The thesis comprises two major themes of quantum statistical dynamics. One is the development of quantum dissipation theory (QDT). It covers the establishment of some basic relations of quantum statistical dynamics, the construction of several nonequivalent complete second-order formulations, and the development of exact QDT. Another is related to the applications of quantum statistical dynamics to a variety of research fields. In particular, unconventional but novel theories of the electron transfer in Debye solvents, quantum transport, and quantum measurement are developed on the basis of QDT formulations. The thesis is organized as follows. In Chapter 1, we present some background knowledge in relation to the aforementioned two themes of this thesis. The key quantity in QDT is the reduced density operator rho(t) ≡ trBrho T(t); i.e., the partial trace of the total system and bath composite rhoT(t) over the bath degrees of freedom. QDT governs the evolution of reduced density operator, where the effects of bath are treated in a quantum statistical manner. In principle, the reduced density operator contains all dynamics information of interest. However, the conventional quantum transport theory is formulated in terms of nonequilibrium Green's function. The newly emerging field of quantum measurement in relation to quantum information and quantum computing does exploit a sort of QDT formalism. Besides the background of the relevant theoretical development, some representative experiments on molecular nanojunctions are also briefly discussed. In chapter 2, we outline some basic (including new) relations that highlight several important issues on QDT. The content includes the background of nonequilibrium quantum statistical mechanics, the general description of the total composite Hamiltonian with stochastic system-bath interaction, a novel parameterization scheme for bath correlation functions, a newly developed exact theory of driven Brownian oscillator (DBO
Benavoli, Alessio; Facchini, Alessandro; Zaffalon, Marco
2017-07-01
Based on a gambling formulation of quantummechanics, we derive a Gleason-type theorem that holds for any dimension n of a quantumsystem, and in particular for n=2. The theorem states that the only logically consistent probability assignments are exactly the ones that are definable as the trace of the product of a projector and a density matrix operator. In addition, we detail the reason why dispersion-free probabilities are actually not valid, or rational, probabilities for quantummechanics, and hence should be excluded from consideration.
Marais, Adriana; Sinayskiy, Ilya; Petruccione, Francesco; van Grondelle, Rienk
2015-03-01
Since the emergence of oxygenic photosynthesis, living systems have developed protective mechanisms against reactive oxygen species. During charge separation in photosynthetic reaction centres, triplet states can react with molecular oxygen generating destructive singlet oxygen. The triplet product yield in bacteria is observed to be reduced by weak magnetic fields. Reaction centres from plants' photosystem II share many features with bacterial reaction centres, including a high-spin iron whose function has remained obscure. To explain observations that the magnetic field effect is reduced by the iron, we propose that its fast-relaxing spin plays a protective role in photosynthesis by generating an effective magnetic field. We consider a simple model of the system, derive an analytical expression for the effective magnetic field and analyse the resulting triplet yield reduction. The protective mechanism is robust for realistic parameter ranges, constituting a clear example of a quantum effect playing a macroscopic role vital for life.
Marais, Adriana; Sinayskiy, Ilya; Petruccione, Francesco; van Grondelle, Rienk
2015-03-03
Since the emergence of oxygenic photosynthesis, living systems have developed protective mechanisms against reactive oxygen species. During charge separation in photosynthetic reaction centres, triplet states can react with molecular oxygen generating destructive singlet oxygen. The triplet product yield in bacteria is observed to be reduced by weak magnetic fields. Reaction centres from plants' photosystem II share many features with bacterial reaction centres, including a high-spin iron whose function has remained obscure. To explain observations that the magnetic field effect is reduced by the iron, we propose that its fast-relaxing spin plays a protective role in photosynthesis by generating an effective magnetic field. We consider a simple model of the system, derive an analytical expression for the effective magnetic field and analyse the resulting triplet yield reduction. The protective mechanism is robust for realistic parameter ranges, constituting a clear example of a quantum effect playing a macroscopic role vital for life.
Castrigiano, Domenico P. L., E-mail: castrig@ma.tum.de; Leiseifer, Andreas D., E-mail: andreas.leiseifer@tum.de
2015-07-15
Causal localizations describe the position of quantumsystems moving not faster than light. They are constructed for the systems with finite spinor dimension. At the center of interest are the massive relativistic systems. For every positive mass, there is the sequence of Dirac tensor-localizations, which provides a complete set of inequivalent irreducible causal localizations. They obey the principle of special relativity and are fully Poincaré covariant. The boosters are determined by the causal position operator and the other Poincaré generators. The localization with minimal spinor dimension is the Dirac localization. Thus, the Dirac equation is derived here as a meremore » consequence of the principle of causality. Moreover, the higher tensor-localizations, not known so far, follow from Dirac’s localization by a simple construction. The probability of localization for positive energy states results to be described by causal positive operator valued (PO-) localizations, which are the traces of the causal localizations on the subspaces of positive energy. These causal Poincaré covariant PO-localizations for every irreducible massive relativistic system were, all the more, not known before. They are shown to be separated. Hence, the positive energy systems can be localized within every open region by a suitable preparation as accurately as desired. Finally, the attempt is made to provide an interpretation of the PO-localization operators within the frame of conventional quantummechanics attributing an important role to the negative energy states.« less
Castrigiano, Domenico P. L.; Leiseifer, Andreas D.
2015-07-01
Causal localizations describe the position of quantumsystems moving not faster than light. They are constructed for the systems with finite spinor dimension. At the center of interest are the massive relativistic systems. For every positive mass, there is the sequence of Dirac tensor-localizations, which provides a complete set of inequivalent irreducible causal localizations. They obey the principle of special relativity and are fully Poincaré covariant. The boosters are determined by the causal position operator and the other Poincaré generators. The localization with minimal spinor dimension is the Dirac localization. Thus, the Dirac equation is derived here as a mere consequence of the principle of causality. Moreover, the higher tensor-localizations, not known so far, follow from Dirac's localization by a simple construction. The probability of localization for positive energy states results to be described by causal positive operator valued (PO-) localizations, which are the traces of the causal localizations on the subspaces of positive energy. These causal Poincaré covariant PO-localizations for every irreducible massive relativistic system were, all the more, not known before. They are shown to be separated. Hence, the positive energy systems can be localized within every open region by a suitable preparation as accurately as desired. Finally, the attempt is made to provide an interpretation of the PO-localization operators within the frame of conventional quantummechanics attributing an important role to the negative energy states.
The concept and subsequent experimental verification of the proportionality between pulse amplitude and detector transit time for microchannel-plate detectors is presented. This discovery has led to considerable improvement in the overall timing resolution for detection of high-energy ggr-photons. Utilizing a 22Na positron source, a full width half maximum (FWHM) timing resolution of 138 ps has been achieved. This FWHM includes detector transit-time spread for both chevron-stack-type detectors, timing spread due to uncertainties in annihilation location, all electronic uncertainty and any remaining quantummechanical uncertainty. The first measurement of the minimum quantum uncertainty in the time interval between detection of the two annihilation photons is reported. The experimental results give strong evidence against instantaneous spatial localization of ggr-photons due to measurement-induced nonlocal quantumwavefunction collapse. The experimental results are also the first that imply momentum is conserved only after the quantum uncertainty in time has elapsed (Yukawa H 1935 Proc. Phys. Math. Soc. Japan 17 48).
SUSY quantummechanics can be applied to solve Schrodinger equation for high dimensional system that can be reduced into one dimensional system and represented in lowering and raising operators. Lowering and raising operators can be obtained using relationship between original Hamiltonian equation and the (super) potential equation. In this paper SUSY quantummechanics is used as a method to obtain the wave function and the energy level of the Modified Poschl Teller potential. The graph of wave function equation and probability density is simulated by using Delphi 7.0 programming language. Finally, the expectation value of quantummechanics operator could be calculated analytically using integral form or probability density graph resulted by the programming.
Although the presentation of quantummechanics found in traditional textbooks is intellectually well founded, it suffers from a number of deficiencies. Specifically introducing quantummechanics as a solution to the arcane dilemma, the ultraviolet catastrophe, does little to impress a nonscientific audience of the tremendous paradigmatic shift…
Einstein's equivalence principle (EP) states the complete physical equivalence of a gravitational field and corresponding inertial field in an accelerated reference frame. However, to what extent the EP remains valid in non-relativistic quantummechanics is a controversial issue. To avoid violation of the EP, Bargmann's superselection rule forbids a coherent superposition of states with different masses. Here we suggest a quantum simulation of non-relativistic Schrödinger particle dynamics in non-inertial reference frames, which is based on the propagation of polarization-entangled photon pairs in curved and birefringent optical waveguides and Hong-Ou-Mandel quantum interference measurement. The photonic simulator can emulate superposition of mass states, which would lead to violation of the EP.
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.
In this work, we present an optimized perturbative quantummechanics/molecular mechanics (QM/MM) method for use in Metropolis Monte Carlo simulations. The model adopted is particularly tailored for the simulation of molecular systems in solution but can be readily extended to other applications, such as catalysis in enzymatic environments. The electrostatic coupling between the QM and MM systems is simplified by applying perturbation theory to estimate the energy changes caused by a movement in the MM system. This approximation, together with the effective use of GPU acceleration, leads to a negligible added computational cost for the sampling of the environment. Benchmark calculations are carried out to evaluate the impact of the approximations applied and the overall computational performance.
In this work, we present an optimized perturbative quantummechanics/molecular mechanics (QM/MM) method for use in Metropolis Monte Carlo simulations. The model adopted is particularly tailored for the simulation of molecular systems in solution but can be readily extended to other applications, such as catalysis in enzymatic environments. The electrostatic coupling between the QM and MM systems is simplified by applying perturbation theory to estimate the energy changes caused by a movement in the MM system. This approximation, together with the effective use of GPU acceleration, leads to a negligible added computational cost for the sampling of the environment. Benchmark calculations are carried out to evaluate the impact of the approximations applied and the overall computational performance.
Asano, M.; Bliokh, K. Y.; Bliokh, Y. P.; Kofman, A. G.; Ikuta, R.; Yamamoto, T.; Kivshar, Y. S.; Yang, L.; Imoto, N.; Özdemir, Ş.K.; Nori, F.
2016-01-01
Quantum weak measurements, wavepacket shifts and optical vortices are universal wave phenomena, which originate from fine interference of multiple plane waves. These effects have attracted considerable attention in both classical and quantum wave systems. Here we report on a phenomenon that brings together all the above topics in a simple one-dimensional scalar wave system. We consider inelastic scattering of Gaussian wave packets with parameters close to a zero of the complex scattering coefficient. We demonstrate that the scattered wave packets experience anomalously large time and frequency shifts in such near-zero scattering. These shifts reveal close analogies with the Goos–Hänchen beam shifts and quantum weak measurements of the momentum in a vortex wavefunction. We verify our general theory by an optical experiment using the near-zero transmission (near-critical coupling) of Gaussian pulses propagating through a nano-fibre with a side-coupled toroidal micro-resonator. Measurements demonstrate the amplification of the time delays from the typical inverse-resonator-linewidth scale to the pulse-duration scale. PMID:27841269
Halbertal, D.; Cuppens, J.; Shalom, M. Ben; Embon, L.; Shadmi, N.; Anahory, Y.; Naren, H. R.; Sarkar, J.; Uri, A.; Ronen, Y.; Myasoedov, Y.; Levitov, L. S.; Joselevich, E.; Geim, A. K.; Zeldov, E.
2016-11-01
Energy dissipation is a fundamental process governing the dynamics of physical, chemical and biological systems. It is also one of the main characteristics that distinguish quantum from classical phenomena. In particular, in condensed matter physics, scattering mechanisms, loss of quantum information or breakdown of topological protection are deeply rooted in the intricate details of how and where the dissipation occurs. Yet the microscopic behaviour of a system is usually not formulated in terms of dissipation because energy dissipation is not a readily measurable quantity on the micrometre scale. Although nanoscale thermometry has gained much recent interest, existing thermal imaging methods are not sensitive enough for the study of quantumsystems and are also unsuitable for the low-temperature operation that is required. Here we report a nano-thermometer based on a superconducting quantum interference device with a diameter of less than 50 nanometres that resides at the apex of a sharp pipette: it provides scanning cryogenic thermal sensing that is four orders of magnitude more sensitive than previous devices—below 1 μK Hz-1/2. This non-contact, non-invasive thermometry allows thermal imaging of very low intensity, nanoscale energy dissipation down to the fundamental Landauer limit of 40 femtowatts for continuous readout of a single qubit at one gigahertz at 4.2 kelvin. These advances enable the observation of changes in dissipation due to single-electron charging of individual quantum dots in carbon nanotubes. They also reveal a dissipation mechanism attributable to resonant localized states in graphene encapsulated within hexagonal boron nitride, opening the door to direct thermal imaging of nanoscale dissipation processes in quantum matter.
We discuss the categorization of 20 quantummechanics problems by physics professors and undergraduate students from two honours-level quantummechanics courses. Professors and students were asked to categorize the problems based upon similarity of solution. We also had individual discussions with professors who categorized the problems. Faculty…
Kohnle, Antje; Douglass, Margaret; Edwards, Tom J.; Gillies, Alastair D.; Hooley, Christopher A.; Sinclair, Bruce D.
2010-01-01
In this paper, we describe animations and animated visualizations for introductory and intermediate-level quantummechanics instruction developed at the University of St Andrews. The animations aim to help students build mental representations of quantummechanics concepts. They focus on known areas of student difficulty and misconceptions by…
Benavoli, Alessio; Facchini, Alessandro; Zaffalon, Marco
2016-10-01
We consider the problem of gambling on a quantum experiment and enforce rational behavior by a few rules. These rules yield, in the classical case, the Bayesian theory of probability via duality theorems. In our quantum setting, they yield the Bayesian theory generalized to the space of Hermitian matrices. This very theory is quantummechanics: in fact, we derive all its four postulates from the generalized Bayesian theory. This implies that quantummechanics is self-consistent. It also leads us to reinterpret the main operations in quantummechanics as probability rules: Bayes' rule (measurement), marginalization (partial tracing), independence (tensor product). To say it with a slogan, we obtain that quantummechanics is the Bayesian theory in the complex numbers.
Lodola, Alessio; Mor, Marco; Sirirak, Jitnapa; Mulholland, Adrian J
2009-04-01
FAAH (fatty acid amide hydrolase) is a promising target for the treatment of several central nervous system and peripheral disorders. Combined QM/MM (quantummechanics/molecular mechanics) calculations have elucidated the role of its unusual catalytic triad in the hydrolysis of oleamide and oleoylmethyl ester substrates, and have identified the productive inhibitor-binding orientation for the carbamoylating compound URB524. These are potentially crucial insights for designing new covalent inhibitors of this drug target.
[This paper is part of the Focused Collection on Upper Division Physics Courses.] Compared with introductory physics, relatively little is known about the development of expertise in advanced physics courses, especially in the case of quantummechanics. Here, we describe a framework for understanding the patterns of student reasoning difficulties and how students develop expertise in quantummechanics. The framework posits that the challenges many students face in developing expertise in quantummechanics are analogous to the challenges introductory students face in developing expertise in introductory classical mechanics. This framework incorporates both the effects of diversity in upper-level students' prior preparation, goals, and motivation in general (i.e., the facts that even in upper-level courses, students may be inadequately prepared, have unclear goals, and have insufficient motivation to excel) as well as the "paradigm shift" from classical mechanics to quantummechanics. The framework is based on empirical investigations demonstrating that the patterns of reasoning, problem-solving, and self-monitoring difficulties in quantummechanics bear a striking resemblance to those found in introductory classical mechanics. Examples from research in quantummechanics and introductory classical mechanics are discussed to illustrate how the patterns of difficulties are analogous as students learn to unpack the respective principles and grasp the formalism in each knowledge domain during the development of expertise. Embracing such a framework and contemplating the parallels between the difficulties in these two knowledge domains can enable researchers to leverage the extensive literature for introductory physics education research to guide the design of teaching and learning tools for helping students develop expertise in quantummechanics.
where an optical cavity mode is coupled to the square of the position of a mechanical oscillator. The optomechanical system can then be regarded as a quantum optical spring, i.e., a spring whose spring constant depends on the quantum state of another system. In particular, we consider the situation where the field inside the cavity is in a coherent state and the oscillator is prepared in its ground state. The quantized nature of the field produces new features in the optomechanical system.
A scheme to achieve strong quantum squeezing of a mechanical resonator in a membrane-in-the-middle optomechanical system is developed. To this end, simultaneous linear and nonlinear coupling between the mechanical resonator and the cavity modes is applied. A two-tone driving light field, comprising unequal red-detuned and blue-detuned sidebands, helps in generating a coherent feedback force through the linear coupling with the membrane resonator. Another driving light field with its amplitude modulated at twice the mechanical frequency drives the mechanical parametric amplification through a second-order coupling with the resonator. The combined effect produces strong quantum squeezing of the mechanical state. The proposed scheme is quite robust to excess second-order coupling observed in coherent feedback operations and can suppress the fluctuations in the mechanical quadrature to far below the zero point and achieve strong squeezing (greater than 10 dB) for realistic parameters.
Last year, in 2008, I gave a talk titled Quantum Calisthenics. This year I am going to tell you about how the work I described then has spun off into a most unlikely direction. What I am going to talk about is how one maps the problem of finding clusters in a given data set into a problem in quantummechanics. I will then use the tricks I described to let quantum evolution lets the clusters come together on their own.
In this study, students' conceptual difficulties about some basic concepts in quantummechanics like one-dimensional potential well problems and probability density of tunneling particles were identified. For this aim, a multiple choice instrument named QuantumMechanics Conceptual Test has been developed by one of the researchers of this study…
Modir, Bahar; Thompson, John D.; Sayre, Eleanor C.
2017-01-01
Students' difficulties in quantummechanics may be the result of unproductive framing and not a fundamental inability to solve the problems or misconceptions about physics content. We observed groups of students solving quantummechanics problems in an upper-division physics course. Using the lens of epistemological framing, we investigated four…
There are no phase-space trajectories for anharmonic quantumsystems, but Wigner's phase-space representation of quantummechanics features Wigner current J . This current reveals fine details of quantum dynamics —finer than is ordinarily thought accessible according to quantum folklore invoking Heisenberg's uncertainty principle. Here, we focus on the simplest, most intuitive, and analytically accessible aspects of J. We investigate features of J for bound states of time-reversible, weakly-anharmonic one-dimensional quantum-mechanicalsystems which are weakly-excited. We establish that weakly-anharmonic potentials can be grouped into three distinct classes: hard, soft, and odd potentials. We stress connections between each other and the harmonic case. We show that their Wigner current fieldline patterns can be characterised by J's discrete stagnation points, how these arise and how a quantumsystem's dynamics is constrained by the stagnation points' topological charge conservation. We additionally show that quantum dynamics in phase space, in the case of vanishing Planck constant ℏ or vanishing anharmonicity, does not pointwise converge to classical dynamics.
It is argued that, although in the Many-Worlds Interpretation of quantummechanics there is no "probability" for an outcome of a quantum experiment in the usual sense, we can understand why we have an illusion of probability. The explanation involves: (a) A "sleeping pill" gedanken experiment which makes correspondence between an illegitimate question: "What is the probability of an outcome of a quantum measurement?" with a legitimate question: "What is the probability that `I' am in the world corresponding to that outcome?"; (b) A gedanken experiment which splits the world into several worlds which are identical according to some symmetry condition; and (c) Relativistic causality, which together with (b) explain the Born rule of standard quantummechanics. The Quantum Sleeping Beauty controversy and "caring measure" replacing probability measure are discussed.
Quantum Entanglement Molecular Absorption Spectrum Simulator (QE-MASS) is a computer program for simulating two photon molecular-absorption spectroscopy using quantum-entangled photons. More specifically, QE-MASS simulates the molecular absorption of two quantum-entangled photons generated by the spontaneous parametric down-conversion (SPDC) of a fixed-frequency photon from a laser. The two-photon absorption process is modeled via a combination of rovibrational and electronic single-photon transitions, using a wave-function formalism. A two-photon absorption cross section as a function of the entanglement delay time between the two photons is computed, then subjected to a fast Fourier transform to produce an energy spectrum. The program then detects peaks in the Fourier spectrum and displays the energy levels of very short-lived intermediate quantum states (or virtual states) of the molecule. Such virtual states were only previously accessible using ultra-fast (femtosecond) laser systems. However, with the use of a single-frequency continuous wave laser to produce SPDC photons, and QEMASS program, these short-lived molecular states can now be studied using much simpler laser systems. QE-MASS can also show the dependence of the Fourier spectrum on the tuning range of the entanglement time of any externally introduced optical-path delay time. QE-MASS can be extended to any molecule for which an appropriate spectroscopic database is available. It is a means of performing an a priori parametric analysis of entangled photon spectroscopy for development and implementation of emerging quantum-spectroscopic sensing techniques. QE-MASS is currently implemented using the Mathcad software package.
Spekkens’ toy model is a non-contextual hidden variable model with an epistemic restriction, a constraint on what an observer can know about reality. The aim of the model, developed for continuous and discrete prime degrees of freedom, is to advocate the epistemic view of quantum theory, where quantum states are states of incomplete knowledge about a deeper underlying reality. Many aspects of quantummechanics and protocols from quantum information can be reproduced in the model. In spite of its significance, a number of aspects of Spekkens’ model remained incomplete. Formal rules for the update of states after measurement had not been written down, and the theory had only been constructed for prime-dimensional and infinite dimensional systems. In this work, we remedy this, by deriving measurement update rules and extending the framework to derive models in all dimensions, both prime and non-prime. Stabiliser quantummechanics (SQM) is a sub-theory of quantummechanics with restricted states, transformations and measurements. First derived for the purpose of constructing error correcting codes, it now plays a role in many areas of quantum information theory. Previously, it had been shown that Spekkens’ model was operationally equivalent to SQM in the case of odd prime dimensions. Here, exploiting known results on Wigner functions, we extend this to show that Spekkens’ model is equivalent to SQM in all odd dimensions, prime and non-prime. This equivalence provides new technical tools for the study of technically difficult compound-dimensional SQM.
Kotler, Shlomi; Leibfried, Dietrich; Simmonds, Raymond; Wineland, Dave
We will review a joint effort by the Ion Storage Group and the Advanced Microwave Photonics Group at NIST (Boulder, CO) to design a hybrid system that interfaces charged particles with macroscopic high-Q resonators. We specifically consider coupling trapped charges to superconducting LC resonators, the mechanical modes of Silicon-Nitride membranes, and piezo-electric materials. We aim to achieve the strong coupling regime, where a single quantum of motion of the trapped charge can be coherently exchanged with harmonic motion of the macroscopic entity (electrical and/or mechanical). These kind of devices could potentially take advantage of both macroscopic control techniques and the long quantum coherence of its trapped charged particles.
The QuantumMechanics Conceptual Survey (QMCS) is a 12-question survey of students' conceptual understanding of quantummechanics. It is intended to be used to measure the relative effectiveness of different instructional methods in modern physics courses. In this paper, we describe the design and validation of the survey, a process that included…
We review the first successes and failures of a "new wave" of quantum chemistry-based approaches to the treatment of protein/ligand interactions. These approaches share the use of "enhanced", dispersion (D), and/or hydrogen-bond (H) corrected density functional theory (DFT) or semi-empirical quantummechanical (SQM) methods, in combination with ensemble weighting techniques of some form to capture entropic effects. Benchmark and model system calculations in comparison to high-level theoretical as well as experimental references have shown that both DFT-D (dispersion-corrected density functional theory) and SQM-DH (dispersion and hydrogen bond-corrected semi-empirical quantummechanical) perform much more accurately than older DFT and SQM approaches and also standard docking methods. In addition, DFT-D might soon become and SQM-DH already is fast enough to compute a large number of binding modes of comparably large protein/ligand complexes, thus allowing for a more accurate assessment of entropic effects.
We provide a unified method for obtaining upper bounds for certain functional integrals appearing in quantummechanics and non-relativistic 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 Feynman-Kac 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 quantummechanical 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 non-relativistic quantum field theories for particles moving in a quantized Bose field, including the optical polaron and Nelson models.
Many textbooks on QuantumMechanics are not very precise as to the meaning of making a measurement: as a consequence, they frequently make assertions which are not based on a dynamical description of the measurement process. A model proposed by von Neumann allows a dynamical description of measurement in QuantumMechanics, including the measuring instrument in the formalism. In this article we apply von Neumann's model to illustrate the measurement of an observable by means of a measuring instrument and show how various results, which are sometimens postulated without a dynamical basis, actually emerge. We also investigate the more complex, intriguing and fundamental problem of two successive measurements in QuantumMechanics, extending von Neumann's model to two measuring instruments. We present a description which allows obtaining, in a unified way, various results that have been given in the literature.
Biological macromolecules, such as proteins or nucleic acids, are (still) molecules and thus they follow the same chemical rules that any simple molecule follows, even if their size generally renders accurate studies unhelpful. However, in the context of drug discovery, a detailed analysis of ligand association is required for understanding or predicting their interactions and hybrid quantummechanics/molecular mechanics (QM/MM) computations are relevant tools to help elucidate this process. In this review, the authors explore the use of QM/MM for drug discovery. After a brief description of the molecular mechanics (MM) technique, the authors describe the subtractive and additive techniques for QM/MM computations. The authors then present several application cases in topics involved in drug discovery. QM/MM have been widely employed during the last decades to study chemical processes such as enzyme-inhibitor interactions. However, despite the enthusiasm around this area, plain MM simulations may be more meaningful than QM/MM. To obtain reliable results, the authors suggest fixing several keystone parameters according to the underlying chemistry of each studied system.
Biological macromolecules, such as proteins or nucleic acids, are (still) molecules and thus they follow the same chemical rules that any simple molecule follows, even if their size generally renders accurate studies unhelpful. However, in the context of drug discovery, a detailed analysis of ligand association is required for understanding or predicting their interactions and hybrid quantummechanics/molecular mechanics (QM/MM) computations are relevant tools to help elucidate this process. Areas covered: In this review, the authors explore the use of QM/MM for drug discovery. After a brief description of the molecular mechanics (MM) technique, the authors describe the subtractive and additive techniques for QM/MM computations. The authors then present several application cases in topics involved in drug discovery. Expert opinion: QM/MM have been widely employed during the last decades to study chemical processes such as enzyme-inhibitor interactions. However, despite the enthusiasm around this area, plain MM simulations may be more meaningful than QM/MM. To obtain reliable results, the authors suggest fixing several keystone parameters according to the underlying chemistry of each studied system.
A mechanism to generate fermion-mass hierarchy in SO(10) grand unified theories is considered. We find that the lopsided family structure, which is suitable to the large angle Mikheyev-Smirnov-Wolfenstein solution to solar neutrino oscillation, is realized without introducing extra matter fields if the hierarchy originates from the wave-function profile in an extra dimension. Unlike the Froggatt-Nielsen mechanism, the SO(10) breaking effect may directly contribute to the source of the hierarchy, i.e., the bulk mass terms. It naturally explains the difference of the hierarchical patterns between the quark and the lepton sectors. We also find the possibility of horizontal unification, in which three generations of matter fields are unified to a 3-dimensional representation of an SU(2) gauge group.
Compared with introductory physics, relatively little is known about the development of expertise in advanced physics courses, especially in the case of quantummechanics. We describe a theoretical framework for understanding the patterns of student reasoning difficulties and how students develop expertise in quantummechanics. The framework posits that the challenges many students face in developing expertise in quantummechanics are analogous to the challenges introductory students face in developing expertise in introductory classical mechanics. This framework incorporates the effects of diversity in students' prior preparation, goals and motivation for taking upper-level physics courses in general as well as the ``paradigm shift'' from classical mechanics to quantummechanics. The framework is based on empirical investigations demonstrating that the patterns of reasoning, problem-solving, and self-monitoring difficulties in quantummechanics bear a striking resemblance to those found in introductory classical mechanics. Examples from research in quantummechanics and introductory classical mechanics will be discussed to illustrate how the patterns of difficulties are analogous as students learn to unpack the respective principles and grasp the formalism in each knowledge domain during the development of expertise. Embracing such a theoretical framework and contemplating the parallels between the difficulties in these two knowledge domains can enable researchers to leverage the extensive literature for introductory physics education research to guide the design of teaching and learning tools for helping students develop expertise in quantummechanics. Support from the National Science Foundation is gratefully acknowledged.
SU(2|1) supersymmetric multi-particle quantummechanics with additional semi-dynamical spin degrees of freedom is considered. In particular, we provide an N=4 supersymmetrization of the quantum U(2) spin Calogero-Moser model, with an intrinsic mass parameter coming from the centrally-extended superalgebra \\widehat{su}(2\\Big|1) . The full system admits an SU(2|1) covariant separation into the center-of-mass sector and the quotient. We derive explicit expressions for the classical and quantum SU(2|1) generators in both sectors as well as for the total system, and we determine the relevant energy spectra, degeneracies, and the sets of physical states.
After a quarter century of discoveries that rattled the foundations of classical mechanics and electrodynamics, the year 1926 saw the publication of two works intended to provide a theoretical structure to support new quantum explanations of the subatomic world. Heisenberg's matrix mechanics and Schrödinger's wave mechanics provided compatible but mathematically disparate ways of unifying the discoveries of Planck, Einstein, Bohr and many others. Efforts began immediately to prove the equivalence of these two structures, culminated successfully by John von Neumann's 1932 volume Mathematical Foundations of QuantumMechanics. This forms the springboard for the current effort. We begin with a presentation of a minimal set of von Neumann postulates while introducing language and notation to facilitate subsequent discussion of quantum calculations based in finite dimensional Hilbert spaces. Chapters that follow address two-state quantumsystems (with spin one-half as the primary example), entanglement of multiple two-state systems, quantum angular momentum theory and quantum approaches to statistical mechanics. A concluding chapter gives an overview of issues associated with quantummechanics in continuous infinite-dimensional Hilbert spaces. [Planck1900] PlanckM1900Zur Teorie des Gesetzes der Energieverteilung in NormalspektrumVerhandlung der Deutscher Physikalischen Gesellschaft 2 237[Heisenberg1925] HeisenbergW1925
The symmetry of self-duality (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…
Alvaro, M; Bonilla, L L; Carretero, M; Melnik, R V N; Prabhakar, S
2013-08-21
In this paper we develop a kinetic model for the analysis of semiconductor superlattices, accounting for quantum effects. The model consists of a Boltzmann-Poisson type system of equations with simplified Bhatnagar-Gross-Krook collisions, obtained from the general time-dependent Schrödinger-Poisson model using Wigner functions. This system for superlattice transport is supplemented by the quantummechanical part of the model based on the Ben-Daniel-Duke form of the Schrödinger equation for a cylindrical superlattice of finite radius. The resulting energy spectrum is used to characterize the Fermi-Dirac distribution that appears in the Bhatnagar-Gross-Krook collision, thereby coupling the quantummechanical and kinetic parts of the model. The kinetic model uses the dispersion relation obtained by the generalized Kronig-Penney method, and allows us to estimate radii of quantum wire superlattices that have the same miniband widths as in experiments. It also allows us to determine more accurately the time-dependent characteristics of superlattices, in particular their current density. Results, for several experimentally grown superlattices, are discussed in the context of self-sustained coherent oscillations of the current density which are important in an increasing range of current and potential applications.
Learning quantummechanics is challenging, even for upper-level undergraduate and graduate students. Research-validated interactive tutorials that build on students' prior knowledge can be useful tools to enhance student learning. We have been investigating student difficulties with quantummechanics pertaining to the double-slit experiment in…
We ask whether the basic Everett assumption, that there are no changes of the wavefunction other than those given by the Schrödinger equation, is compatible with experience. We conclude that it is, provided we allow the world of observation to be partially a creation of consciousness. The model suggests the possible existence of quantum paranormal effects.
The limits of optical measurement and control of mechanical motion are set by the quantum nature of light. The familiar shot noise limit can be avoided by increasing the optical power, but at high enough powers, the backaction of the randomly-arriving photons' radiation pressure can grow to become the dominant force on the system. This thesis will describe an experiment showing how backaction limits the laser cooling of macroscopic drumhead membranes, as well as work on how these membranes can be used to upconvert microwave signals to optical frequencies, potentially preserving the fragile quantum state of the upconverted signal.
We discuss the theory of knots, and describe how knot invariants arise naturally in gravitational physics. The focus of this review is to delineate the relationship between knot theory and the loop representation of non-perturbative canonical quantum general relativity (loop quantum gravity). This leads naturally to a discussion of the Kodama wavefunction, a state which is conjectured to be the ground state of the gravitational field with positive cosmological constant. This review can serve as a self-contained introduction to loop quantum gravity and related areas. Our intent is to make the paper accessible to a wider audience that may include topologists, knot theorists, and other persons innocent of the physical background to this approach to quantum gravity.
Explore the relationship between quantummechanics and information-age applications This volume takes an altogether unique approach to quantummechanics. Providing an in-depth exposition of quantummechanics fundamentals, it shows how these concepts are applied to most of today's information technologies, whether they are electronic devices or materials. No other text makes this critical, essential leap from theory to real-world applications. The book's lively discussion of the mathematics involved fits right in with contemporary multidisciplinary trends in education: Once the basic formulation has been derived in a given chapter, the connection to important technological problems is summarily described. The many helpful features include * Twenty-eight application-oriented sections that focus on lasers, transistors, magnetic memories, superconductors, nuclear magnetic resonance (NMR), and other important technology-driving materials and devices * One hundred solved examples, with an emphasis on numerical results and the connection between the physics and its applications * End-of-chapter problems that ground the student in both fundamental and applied concepts * Numerous figures and tables to clarify the various topics and provide a global view of the problems under discussion * Over two hundred illustrations to highlight problems and text A book for the information age, QuantumMechanics: Fundamentals and Applications to Technology promises to become a standard in departments of electrical engineering, applied physics, and materials science, as well as physics. It is an excellent text for senior undergraduate and graduate students, and a helpful reference for practicing scientists, engineers, and chemists in the semiconductor and electronic industries.
States that the existence of an essential underdetermination in the interpretation of the formalism of quantummechanics, in spite of the widespread belief that logic and empirical considerations alone demand an indeterministic world view in physics, legitimizes the analysis of hermeneutics in science education. (LZ)
The rampant success of quantum theory is the result of applications of the 'new' quantummechanics of Schrodinger and Heisenberg (1926-7), the Feynman-Schwinger-Tomonaga Quantum Electro-dynamics (1946-51), the electro-weak theory of Salaam, Weinberg, and Glashow (1967-9), and Quantum Chromodynamics (1973-); in fact, this success of 'the' quantum theory has depended on a continuous stream of brilliant and quite disparate mathematical formulations. In this carefully concealed ferment there lie plenty of unresolved difficulties, simply because in churning out fabulously accurate calculational tools there has been no sensible explanation of all that is going on. It is even argued that such an understanding is nothing to do with physics. A long-standing and famous illustration of this is the paradoxical thought-experiment of Einstein, Podolsky and Rosen (1935). Fundamental to all quantum theories, and also their paradoxes, is the location of sub-microscopic objects; or, rather, that the specification of such a location is fraught with mathematical inconsistency. This project encompasses a detailed, critical survey of the tangled history of Position within quantum theories. The first step is to show that, contrary to appearances, canonical quantummechanics has only a vague notion of locality. After analysing a number of previous attempts at a 'relativistic quantummechanics', two lines of thought are considered in detail. The first is the work of Wan and students, which is shown to be no real improvement on the iisu.al 'nonrelativistic' theory. The second is based on an idea of Dirac's - using backwards-in-time light-cones as the hypersurface in space-time. There remain considerable difficulties in the way of producing a consistent scheme here. To keep things nicely stirred up, the author then proposes his own approach - an adaptation of Feynman's QED propagators. This new approach is distinguished from Feynman's since the propagator or Green's function is not obtained
Scale relativity is a new approach to the problem of the origin of fundamental scales and of scaling laws in physics, which consists in generalizing Einstein's principle of relativity to the case of scale transformations of resolutions. We recall here how it leads one to the concept of fractal space-time, and to introduce a new complex time derivative operator which allows to recover the Schrödinger equation, then to generalize it. In high energy quantum physics, it leads to the introduction of a Lorentzian renormalization group, in which the Planck length is reinterpreted as a lowest, unpassable scale, invariant under dilatations. These methods are successively applied to two problems: in quantummechanics, that of the mass spectrum of elementary particles; in chaotic dynamics, that of the distribution of planets in the Solar System.
WavePacket is an open-source program package for the numerical simulation of quantum-mechanical dynamics. It can be used to solve time-independent or time-dependent linear Schrödinger and Liouville-von Neumann-equations in one or more dimensions. Also coupled equations can be treated, which allows to simulate molecular quantum dynamics beyond the Born-Oppenheimer approximation. Optionally accounting for the interaction with external electric fields within the semiclassical dipole approximation, WavePacket can be used to simulate experiments involving tailored light pulses in photo-induced physics or chemistry. The graphical capabilities allow visualization of quantum dynamics 'on the fly', including Wigner phase space representations. Being easy to use and highly versatile, WavePacket is well suited for the teaching of quantummechanics as well as for research projects in atomic, molecular and optical physics or in physical or theoretical chemistry. The present Part I deals with the description of closed quantumsystems in terms of Schrödinger equations. The emphasis is on discrete variable representations for spatial discretization as well as various techniques for temporal discretization. The upcoming Part II will focus on open quantumsystems and dimension reduction; it also describes the codes for optimal control of quantum dynamics. The present work introduces the MATLAB version of WavePacket 5.2.1 which is hosted at the Sourceforge platform, where extensive Wiki-documentation as well as worked-out demonstration examples can be found.
In a thought-provoking paper, Couder and Fort [Phys. Rev. Lett. 97, 154101 (2006)] describe a version of the famous double-slit experiment performed with droplets bouncing on a vertically vibrated fluid surface. In the experiment, an interference pattern in the single-particle statistics is found even though it is possible to determine unambiguously which slit the walking droplet passes. Here we argue, however, that the single-particle statistics in such an experiment will be fundamentally different from the single-particle statistics of quantummechanics. Quantummechanical interference takes place between different classical paths with precise amplitude and phase relations. In the double-slit experiment with walking droplets, these relations are lost since one of the paths is singled out by the droplet. To support our conclusions, we have carried out our own double-slit experiment, and our results, in particular the long and variable slit passage times of the droplets, cast strong doubt on the feasibility of the interference claimed by Couder and Fort. To understand theoretically the limitations of wave-driven particle systems as analogs to quantummechanics, we introduce a Schrödinger equation with a source term originating from a localized particle that generates a wave while being simultaneously guided by it. We show that the ensuing particle-wave dynamics can capture some characteristics of quantummechanics such as orbital quantization. However, the particle-wave dynamics can not reproduce quantummechanics in general, and we show that the single-particle statistics for our model in a double-slit experiment with an additional splitter plate differs qualitatively from that of quantummechanics.
The fractional uncertainty relation is a mathematical formulation of Heisenberg's uncertainty principle in the framework of fractional quantummechanics. Two mistaken statements presented in the Comment have been revealed. The origin of each mistaken statement has been clarified and corrected statements have been made. A map between standard quantummechanics and fractional quantummechanics has been presented to emphasize the features of fractional quantummechanics and to avoid misinterpretations of the fractional uncertainty relation. It has been shown that the fractional probability current equation is correct in the area of its applicability. Further studies have to be done to find meaningful quantum physics problems with involvement of the fractional probability current density vector and the extra term emerging in the framework of fractional quantummechanics.
Seveso, Luigi, E-mail: luigi.seveso@unimi.it; Paris, Matteo G.A.; INFN, Sezione di Milano, I-20133 Milano
We address the question whether quantum probes in a gravitational field can be considered as test particles obeying the weak equivalence principle (WEP). A formulation of the WEP is proposed which applies also in the quantum regime, while maintaining the physical content of its classical counterpart. Such formulation requires the introduction of a gravitational field not to modify the Fisher information about the mass of a freely-falling probe, extractable through measurements of its position. We discover that, while in a uniform field quantum probes satisfy our formulation of the WEP exactly, gravity gradients can encode nontrivial information about the particle’smore » mass in its wavefunction, leading to violations of the WEP. - Highlights: • Can quantum probes under gravity be approximated as test-bodies? • A formulation of the weak equivalence principle for quantum probes is proposed. • Quantum probes are found to violate it as a matter of principle.« less
Recent studies on quantum evolutionary problems in Demiralp’s group have arrived at a stage where the construction of an expectation value formula for a given algebraic function operator depending on only position operator becomes possible. It has also been shown that this formula turns into an algebraic recursion amongst some finite number of consecutive elements in a set of expectation values of an appropriately chosen basis set over the natural number powers of the position operator as long as the function under consideration and the system Hamiltonian are both autonomous. This recursion corresponds to a denumerable infinite number of algebraicmore » equations whose solutions can or can not be obtained analytically. This idea is not completely original. There are many recursive relations amongst the expectation values of the natural number powers of position operator. However, those recursions may not be always efficient to get the system energy values and especially the eigenstate wavefunctions. The present approach is somehow improved and generalized form of those expansions. We focus on this issue for a specific system where the Hamiltonian is defined on the coordinate of a curved space instead of the Cartesian one.« less
This paper describes the effects of a complex scalar scaling field on quantummechanics. 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 quantummechanics 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 quantummechanics. 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
Since the quantummechanics was born, quantummechanics was argued among scientists because the differences between quantummechanics and the classical physics. Because of this, some people give hidden variable theory. One of the hidden variable theory is non-contextual hidden variable theory, and KS inequalities are famous in non-contextual hidden variable theory. But the original KS inequalities have 117 directions to measure, so it is almost impossible to test the KS inequalities in experiment. However bout two years ago, Sixia Yu and C.H. Oh point out that for a single qutrit, we only need to measure 13 directions, then we can test the KS inequalities. This makes it possible to test the KS inequalities in experiment. We use the polarization and the path of single photon to construct a qutrit, and we use the half-wave plates, the beam displacers and polar beam splitters to prepare the quantum state and finish the measurement. And the result prove that quantummechanics is right and non-contextual hidden variable theory is wrong.
Yamaguchi, Yukio; Schaefer, Henry F., III; Frenking, Gernot
A study of first and second derivatives of the orbital, electronic, nuclear and total energies for the self-consistent field (SCF) wavefunction has been applied to general open-shell SCF systems. The diagonal elements of the Lagrangian matrix for the general open-shell SCF wavefunction are adapted as the 'oŕbital' energies. The first and second derivatives of the orbital energies in terms of the normal coordinates are determined via the finite difference method, while those of the electronic, nuclear and total energies are obtained by analytical techniques. Using three low lying states of the CH2 and H2CO molecules as examples, it is demonstrated that the derivatives of the SCF energetic quantities with respect to the normal coordinates provide useful chemical information concerning the respective molecular structures and reactivities. The conventional concept of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) has been extended to the molecular vibrational motion, and the terminology of vibrationally active MOs (va-MOs), va-HOMO and va-LUMO has been introduced for each normal coordinate. The energy derivative analysis method may be used as a powerful semi-quantitative modelin understanding and interpreting various chemical phenomena.
Bennie, Simon J.; Stella, Martina; Miller, Thomas F.; Manby, Frederick R.
2015-07-01
Methods where an accurate wavefunction is embedded in a density-functional description of the surrounding environment have recently been simplified through the use of a projection operator to ensure orthogonality of orbital subspaces. Projector embedding already offers significant performance gains over conventional post-Hartree-Fock methods by reducing the number of correlated occupied orbitals. However, in our first applications of the method, we used the atomic-orbital basis for the full system, even for the correlated wavefunction calculation in a small, active subsystem. Here, we further develop our method for truncating the atomic-orbital basis to include only functions within or close to the active subsystem. The number of atomic orbitals in a calculation on a fixed active subsystem becomes asymptotically independent of the size of the environment, producing the required O ( N 0 ) scaling of cost of the calculation in the active subsystem, and accuracy is controlled by a single parameter. The applicability of this approach is demonstrated for the embedded many-body expansion of binding energies of water hexamers and calculation of reaction barriers of SN2 substitution of fluorine by chlorine in α-fluoroalkanes.
Results obtained in the past for free boson systems at zero and nonzero temperatures are revisited to clarify the physical meaning of current algebra reducible functionals which are associated to systems with density fluctuations, leading to observable effects on phase transitions. To use current algebra as a tool for the formulation of quantum statistical mechanics amounts to the construction of unitary representations of diffeomorphism groups. Two mathematical equivalent procedures exist for this purpose. One searches for quasi-invariant measures on configuration spaces, the other for a cyclic vector in Hilbert space. Here, one argues that the second approach is closer to the physical intuition when modelling complex systems. An example of application of the current algebra methodology to the pairing phenomenon in two-dimensional fermion systems is discussed.
Zollman, Dean A.; Rebello, N. Sanjay; Hogg, Kirsten
2002-01-01
Explains a hands-on approach to teaching quantummechanics that challenges the belief shared by many physics instructors that quantummechanics is a very abstract subject that cannot be understood until students have learned much of the classical physics. (Contains 23 references.) (Author/YDS)
Vanner, M. R.; Pikovski, I.; Cole, G. D.; Kim, M. S.; Brukner, Č.; Hammerer, K.; Milburn, G. J.; Aspelmeyer, M.
2011-01-01
Studying mechanical resonators via radiation pressure offers a rich avenue for the exploration of quantummechanical behavior in a macroscopic regime. However, quantum state preparation and especially quantum state reconstruction of mechanical oscillators remains a significant challenge. Here we propose a scheme to realize quantum state tomography, squeezing, and state purification of a mechanical resonator using short optical pulses. The scheme presented allows observation of mechanicalquantum features despite preparation from a thermal state and is shown to be experimentally feasible using optical microcavities. Our framework thus provides a promising means to explore the quantum nature of massive mechanical oscillators and can be applied to other systems such as trapped ions. PMID:21900608
The transactional interpretation of quantummechanics (TI) is summarized and various points concerning the TI and its relation to the Copenhagen interpretation (CI) are considered. Questions concerning mapping the TI onto the CI, of advanced waves as solutions to proper wave equations, of collapse and the QM formalism, and of the relation of quantummechanical interpretations to experimental tests and results are discussed.
We summarize the transactional interpretation (TI) of quantummechanics (QM) and consider various points concerning the TI and its relation to the Copenhagen interpretation (CI). Questions concerning mapping the TI onto the CI, of advanced waves as solutions to proper wave equations, of collapse and the QM formalism, and of the relation of quantummechanical interpretations to experimental tests and results are discussed.
Quantum dissipation arises when a large system can be split in a quantumsystem and an environment to which the energy of the former flows. Understanding the effect of dissipation on quantum many-body systems is of particular importance due to its potential relationship with quantum information. We propose a conceptually simple approach to introduce dissipation into interacting quantumsystems in a thermodynamical context, in which every site of a one-dimensional (1D) lattice is coupled off-diagonally to its own bath. The interplay between quantum dissipation and interactions gives rise to counterintuitive interpretations such as a compressible zero-temperature state with spontaneous discrete symmetry breaking and a thermal phase transition in a 1D dissipative quantum many-body system as revealed by quantum Monte Carlo path-integral simulations.
Fatollahi, Amir H.; Shariati, Ahmad; Khorrami, Mohammad
2009-04-01
Quantummechanics of models is considered which are constructed in spaces with Lie algebra type commutation relations between spatial coordinates. The case is specialized to that of the group SU(2), for which the formulation of the problem via the Euler parameterization is also presented. SU(2)-invariant systems are discussed, and the corresponding eigenvalue problem for the Hamiltonian is reduced to an ordinary differential equation, as is the case with such models on commutative spaces.
A long-standing debate over the interpretation of quantummechanics has centered on the meaning of Schroedinger's wave function {psi} for an electron. Broadly speaking, there are two major opposing schools. On the one side, the Copenhagen school(led by Bohr, Heisenberg and Pauli) holds that {psi} provides a complete description of a single electron state; hence the probability interpretation of {psi}{psi}* expresses an irreducible uncertainty in electron behavior that is intrinsic in nature. On the other side, the realist school(led by Einstein, de Broglie, Bohm and Jaynes) holds that {psi} represents a statistical ensemble of possible electron states; hence it ismore » an incomplete description of a single electron state. I contend that the debaters have overlooked crucial facts about the electron revealed by Dirac theory. In particular, analysis of electron zitterbewegung(first noticed by Schroedinger) opens a window to particle substructure in quantummechanics that explains the physical significance of the complex phase factor in {psi}. This led to a testable model for particle substructure with surprising support by recent experimental evidence. If the explanation is upheld by further research, it will resolve the debate in favor of the realist school. I give details. The perils of research on the foundations of quantummechanics have been foreseen by Lewis Carroll in The Hunting of the Snark{exclamation_point}.« less
The author has previously pointed out some similarities between selforganizing neural networks and quantummechanics. These types of neural networks were originally conceived of as away of emulating the cognitive capabilities of the human brain. Recently extensions of these networks, collectively referred to as deep learning networks, have strengthened the connection between self-organizing neural networks and human cognitive capabilities. In this note we consider whether hardware quantum devices might be useful for emulating neural networks with human-like cognitive capabilities, or alternatively whether implementations of deep learning neural networks using conventional computers might lead to better algorithms for solving the many body Schrodinger equation.
This article furnishes an introduction to the properties of time-dependent electronic wavefunctions in atoms and to physics at the interface between the quantum and classical worlds. We describe how, almost 100 years after the introduction of the Bohr model of the atom, it is now possible using pulsed electric fields to create in the laboratory localized wavepackets in high-n (n ~ 300) Rydberg atoms that travel in near-circular Bohr-like orbits mimicking the behavior of a classical electron. The control protocols employed are explained with the aid of quantum and classical dynamics. Remarkably, while many aspects of the underlying behavior canmore » be described using classical arguments, even at n ~ 300 purely quantum effects such as revivals can be seen.« less
Pedersen, Mads Kock; Skyum, Birk; Heck, Robert; Müller, Romain; Bason, Mark; Lieberoth, Andreas; Sherson, Jacob F.
2016-06-01
A virtual learning environment can engage university students in the learning process in ways that the traditional lectures and lab formats cannot. We present our virtual learning environment StudentResearcher, which incorporates simulations, multiple-choice quizzes, video lectures, and gamification into a learning path for quantummechanics at the advanced university level. StudentResearcher is built upon the experiences gathered from workshops with the citizen science game Quantum Moves at the high-school and university level, where the games were used extensively to illustrate the basic concepts of quantummechanics. The first test of this new virtual learning environment was a 2014 course in advanced quantummechanics at Aarhus University with 47 enrolled students. We found increased learning for the students who were more active on the platform independent of their previous performances.
Zhang, Xu; Xiang, Hongping; Zhang, Mingliang; Lu, Gang
2017-09-01
Plasmonic resonance of metallic nanoparticles results from coherent motion of its conduction electrons, driven by incident light. For the nanoparticles less than 10 nm in diameter, localized surface plasmonic resonances become sensitive to the quantum nature of the conduction electrons. Unfortunately, quantummechanical simulations based on time-dependent Kohn-Sham density functional theory are computationally too expensive to tackle metal particles larger than 2 nm. Herein, we introduce the recently developed time-dependent orbital-free density functional theory (TD-OFDFT) approach which enables large-scale quantummechanical simulations of plasmonic responses of metallic nanostructures. Using TD-OFDFT, we have performed quantummechanical simulations to understand size-dependent plasmonic response of Na nanoparticles and plasmonic responses in Na nanoparticle dimers and trimers. An outlook of future development of the TD-OFDFT method is also presented.
It has been suggested that an appeal to holographic and quantum properties will be ultimately required for the understanding of higher brain functions. On the other hand, successful quantum-like approaches to cognitive and behavioral processes bear witness to the usefulness of quantum prescriptions as applied to the analysis of complex non-quantumsystems. Here, we show that the signal-tuned Gabor approach for modeling cortical neurons, although not based on quantum assumptions, also admits a quantum-like interpretation. Recently, the equation of motion for the signal-tuned complex cell response has been derived and proven equivalent to the Schrödinger equation for a dissipative quantumsystem whose solutions come under two guises: as plane-wave and Airy-packet responses. By interpreting the squared magnitude of the plane-wave solution as a probability density, in accordance with the quantummechanics prescription, we arrive at a Poisson spiking probability — a common model of neuronal response — while spike propagation can be described by the Airy-packet solution. The signal-tuned approach is also proven consistent with holonomic brain theories, as it is based on Gabor functions which provide a holographic representation of the cell’s input, in the sense that any restricted subset of these functions still allows stimulus reconstruction.
This dissertation describes research on student understanding of quantummechanics across multiple levels of instruction. The primary focus has been to identify patterns in student reasoning related to key concepts in quantummechanics. The specific topics include quantum measurements, time dependence, vector spaces, and angular momentum. The research has spanned a variety of different quantum courses intended for introductory physics students, upper-division physics majors, and graduate students in physics. The results of this research have been used to develop a set of curriculum, Tutorials in Physics: QuantumMechanics, for addressing the most persistent student difficulties. We document both the development of this curriculum and how it has impacted and improved student understanding of quantummechanics.
In the early 1960s, a PhD student in physics, Costas Papaliolios, designed a simple—and playful—system of Polaroid polarizer filters with a specific goal in mind: explaining the core principles behind Julian Schwinger's quantummechanical measurement algebra, developed at Harvard in the late 1940s and based on the Stern-Gerlach experiment confirming the quantization of electron spin. Papaliolios dubbed his invention "quantum toys." This article looks at the origins and function of this amusing pedagogical device, which landed half a century later in the Collection of Historical Scientific Instruments at Harvard University. Rendering the abstract tangible was one of Papaliolios's demonstration tactics in reforming basic teaching of quantummechanics. This article contends that Papaliolios's motivation in creating the quantum toys came from a renowned endeavor aimed, inter alia, at reforming high-school physics training in the United States: Harvard Project Physics. The pedagogical study of these quantum toys, finally, compels us to revisit the central role playful discovery performs in pedagogy, at all levels of training and in all fields of knowledge.
Rokob, Tibor András; Srnec, Martin; Rulíšek, Lubomír
2012-05-21
In the last decade, we have witnessed substantial progress in the development of quantum chemical methodologies. Simultaneously, robust solvation models and various combined quantum and molecular mechanical (QM/MM) approaches have become an integral part of quantum chemical programs. Along with the steady growth of computer power and, more importantly, the dramatic increase of the computer performance to price ratio, this has led to a situation where computational chemistry, when exercised with the proper amount of diligence and expertise, reproduces, predicts, and complements the experimental data. In this perspective, we review some of the latest achievements in the field of theoretical (quantum) bioinorganic chemistry, concentrating mostly on accurate calculations of the spectroscopic and physico-chemical properties of open-shell bioinorganic systems by wave-function (ab initio) and DFT methods. In our opinion, the one-to-one mapping between the calculated properties and individual molecular structures represents a major advantage of quantum chemical modelling since this type of information is very difficult to obtain experimentally. Once (and only once) the physico-chemical, thermodynamic and spectroscopic properties of complex bioinorganic systems are quantitatively reproduced by theoretical calculations may we consider the outcome of theoretical modelling, such as reaction profiles and the various decompositions of the calculated parameters into individual spatial or physical contributions, to be reliable. In an ideal situation, agreement between theory and experiment may imply that the practical problem at hand, such as the reaction mechanism of the studied metalloprotein, can be considered as essentially solved.
Rationality is the universal invariant among human behavior, universe physical laws and ordered and complex biological systems. Econophysics isboth the use of physical concepts in Finance and Economics, and the use of Information Economics in Physics. In special, we will show that it is possible to obtain the QuantumMechanics principles using Information and Game Theory.
We present a hybrid quantummechanics/molecular mechanics/coarse-grained (QM/MM/CG) multiresolution approach for solvated biomolecular systems. The chemically important active-site region is treated at the QM level. The biomolecular environment is described by an atomistic MM force field, and the solvent is modeled with the CG Martini force field using standard or polarizable (pol-CG) water. Interactions within the QM, MM, and CG regions, and between the QM and MM regions, are treated in the usual manner, whereas the CG-MM and CG-QM interactions are evaluated using the virtual sites approach. The accuracy and efficiency of our implementation is tested for two enzymes, chorismate mutase (CM) and p-hydroxybenzoate hydroxylase (PHBH). In CM, the QM/MM/CG potential energy scans along the reaction coordinate yield reaction energies that are too large, both for the standard and polarizable Martini CG water models, which can be attributed to adverse effects of using large CG water beads. The inclusion of an atomistic MM water layer (10 Å for uncharged CG water and 5 Å for polarizable CG water) around the QM region improves the energy profiles compared to the reference QM/MM calculations. In analogous QM/MM/CG calculations on PHBH, the use of the pol-CG description for the outer water does not affect the stabilization of the highly charged FADHOOH-pOHB transition state compared to the fully atomistic QM/MM calculations. Detailed performance analysis in a glycine-water model system indicates that computation times for QM energy and gradient evaluations at the density functional level are typically reduced by 40-70% for QM/MM/CG relative to fully atomistic QM/MM calculations.
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 quantummechanics (the latter is treated as an epistemic model), namely, prequantum classical statistical field theory (PCSFT), we propose the natural physical interpretation for the basic quantummechanical entity-the 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 principle-by using the formalism of classical field correlations. In classical mechanics the phase space description can be considered as the ontic description, here states are given by points λ =(x , p) of phase space. The dynamics of the ontic state is given by the system of Hamiltonian equations.We can also consider probability distributions on the phase space (or equivalently random variables valued in it). We call them probabilistic ontic states. Dynamics of probabilistic ontic states is given by the Liouville equation.In classical physics we can (at least in principle) measure both the coordinate and momentum and hence ontic states can be treated as epistemic states as well (or it is better to say that here epistemic states can be treated as ontic states). Probabilistic ontic states represent probabilities for outcomes of joint measurement of position and momentum.However, this was
Quantum optomechanics provides a universal tool to achieve the quantum control of mechanical motion. It does that in devices spanning a vast range of parameters, with mechanical frequencies from a few Hertz to GHz, and with masses from 10-20 g to several kilos. Its underlying ideas can be traced back to the study of gravitational wave antennas, quantum optics, cavity QED and laser cooling which, when combined with the recent availability of advanced micromechanical and nanomechanical devices, opens a path to the realization of macroscopic mechanicalsystems that operate deep in the quantum regime. At the fundamental level this development paves the way to experiments that will lead to a more profound understanding of quantummechanics; and from the point of view of applications, quantum optomechanical techniques will provide motion and force sensing near the fundamental limit imposed by quantummechanics (quantum metrology) and significantly expand the toolbox of quantum information science. After a brief summary of key historical developments, the talk will give a broad overview of the current state of the art of quantum optomechanics, and comment on future prospects both in applied and in fundamental science. Work supported by NSF, ARO and the DARPA QuASAR and ORCHID programs.
mode operation is important to prevent standby power dissipation in circuits. The relevant struc- ture consists of a quantum well one half of which...is intentionally doped while the other half is left undoped. In the absence of any external electric field, electrons mostly reside in the doped half ...electron wavefunction to the undoped half in which the mobility is much higher because of the absence of in-situ impurity scatterir". Consequently the
Laser cooling is a fundamental technique used in primary atomic frequency standards, quantum computers, quantum condensed matter physics and tests of fundamental physics, among other areas. It has been known since the early 1990s that laser cooling can, in principle, be improved by using squeezed light as an electromagnetic reservoir; while quantum feedback control using a squeezed light probe is also predicted to allow improved cooling. Here we show the implementation of quantum feedback control of a micro-mechanical oscillator using squeezed probe light. This allows quantum-enhanced feedback cooling with a measurement rate greater than it is possible with classical light, and a consequent reduction in the final oscillator temperature. Our results have significance for future applications in areas ranging from quantum information networks, to quantum-enhanced force and displacement measurements and fundamental tests of macroscopic quantummechanics.
This roadmap bundles fast developing topics in experimental optical quantum sciences, addressing current challenges as well as potential advances in future research. We have focused on three main areas: quantum assisted high precision measurements, quantum information/simulation, and quantum gases. Quantum assisted high precision measurements are discussed in the first three sections, which review optical clocks, atom interferometry, and optical magnetometry. These fields are already successfully utilized in various applied areas. We will discuss approaches to extend this impact even further. In the quantum information/simulation section, we start with the traditionally successful employed systems based on neutral atoms and ions. In addition the marvelous demonstrations of systems suitable for quantum information is not progressing, unsolved challenges remain and will be discussed. We will also review, as an alternative approach, the utilization of hybrid quantumsystems based on superconducting quantum devices and ultracold atoms. Novel developments in atomtronics promise unique access in exploring solid-state systems with ultracold gases and are investigated in depth. The sections discussing the continuously fast-developing quantum gases include a review on dipolar heteronuclear diatomic gases, Rydberg gases, and ultracold plasma. Overall, we have accomplished a roadmap of selected areas undergoing rapid progress in quantum optics, highlighting current advances and future challenges. These exciting developments and vast advances will shape the field of quantum optics in the future.
A systematic approach to the non-Markovian quantum dynamics of open systems is given by the projection operator techniques of nonequilibrium statistical mechanics. Combining these methods with concepts from quantum information theory and from the theory of positive maps, we derive a class of correlated projection superoperators that take into account in an efficient way statistical correlations between the open system and its environment. The result is used to develop a generalization of the Lindblad theory to the regime of highly non-Markovian quantum processes in structured environments.
Why is quantummechanics considered a hard and inaccessible subject? Part of the difficulty is due to the nature of the subject itself. However, no small part of the difficulty is its pedagogy, which often relies on out-of-date historical motivation and experimental evidence that is disconnected from day-to-day experiences. In this first talk, we explore ways in which video games are well-suited to teaching quantummechanics, in particular with regards to building intuition, as well as some of their limitations. We then illustrate these considerations through qCraft, an extension for Minecraft that incorporates aspects of quantummechanics into the game.
The Schrodinger Equation has been available for about 83 years, but today, we still strain to apply it accurately to molecules of interest. The difficulty is not theoretical in nature, but practical, since we're held back by lack of sufficient computing power. Consequently, effort is applied to find acceptable approximations to facilitate real time solutions. In the meantime, computer technology has begun rapidly advancing and changing the way we think about efficient algorithms. For those who can reorganize their formulas to take advantage of these changes and thereby lift some approximations, incredible new opportunities await. Over the last decade, we've seen the emergence of a new kind of computer processor, the graphics card. Designed to accelerate computer games by optimizing quantity instead of quality in processor, they have become of sufficient quality to be useful to some scientists. In this thesis, we explore the first known use of a graphics card to computational chemistry by rewriting our Quantum Monte Carlo software into the requisite "data parallel" formalism. We find that notwithstanding precision considerations, we are able to speed up our software by about a factor of 6. The success of a Quantum Monte Carlo calculation depends on more than just processing power. It also requires the scientist to carefully design the trial wavefunction used to guide simulated electrons. We have studied the use of Generalized Valence Bond wavefunctions to simply, and yet effectively, captured the essential static correlation in atoms and molecules. Furthermore, we have developed significantly improved two particle correlation functions, designed with both flexibility and simplicity considerations, representing an effective and reliable way to add the necessary dynamic correlation. Lastly, we present our method for stabilizing the statistical nature of the calculation, by manipulating configuration weights, thus facilitating efficient and robust calculations. Our
Bob hides a ball in one of four drawers. Alice is to locate it. Classically she has to open up to three drawers, quantally just one. The fundamental reason for this quantum speedup is not known. The usual representation of the quantum algorithm is limited to the process of solving the problem. We extend it to the process of setting the problem. The number of the drawer with the ball becomes a unitary transformation of the random outcome of the preparation measurement. This extended, time-symmetric, representation brings in relational quantummechanics. It is with respect to Bob and any external observer and cannot be with respect to Alice. It would tell her the number of the drawer with the ball before she opens any drawer. To Alice, the projection of the quantum state due to the preparation measurement should be retarded at the end of her search; in the input state of the search, the drawer number is determined to Bob and undetermined to Alice. We show that, mathematically, one can ascribe any part of the selection of the random outcome of the preparation measurement to the final Alice's measurement. Ascribing half of it explains the speedup of the present algorithm. This leaves the input state to Bob unaltered and projects that to Alice on a state of lower entropy where she knows half of the number of the drawer with the ball in advance. The quantum algorithm turns out to be a sum over histories in each of which Alice knows in advance that the ball is in a pair of drawers and locates it by opening one of the two. In the sample of quantum algorithms examined, the part of the random outcome of the initial measurement selected by the final measurement is one half or slightly above it. Conversely, given an oracle problem, the assumption it is one half always corresponds to an existing quantum algorithm and gives the order of magnitude of the number of oracle queries required by the optimal one.
Kohnle, Antje; Benfield, Cory; Hahner, Georg; Paetkau, Mark
2017-01-01
The QuVis QuantumMechanics Visualization Project provides freely available research-based interactive simulations with accompanying activities for the teaching and learning of quantummechanics across a wide range of topics and levels. This article gives an overview of some of the simulations and describes their use in an introductory physical…
The MCSCF method provides a correct zero-order wavefunction for all regions of molecular potential energy surfaces. To obtain quantitative accuracy a proper treatment of the dynamic correlation problem must be implemented. Traditionally this has been achieved through multireference variants of perturbation theory, configuration interaction and coupled cluster theory. The computational cost of such techniques makes them prohibitive for all but the smallest molecular problems. Reported here is an investigation into the efficacy of two-body density functionals in providing the dynamic correlation energy for MCSCF reference states. Tests were made on the two-body density functionals of Colle and Salvetti (CS), Moscardó and San-Fabián (MSF), and Moscardó and Pérez-Jiménez (MPJ5) in predicting the equilibrium bond lengths, harmonic frequencies and dissociation energies of fifteen diatomic molecules (3B2, 3BN, 2BS, 1C2, 2CN, 1CO, 1F2, 1FCl, 1N2, 3NCl, 3O2, 1PN, 3Si2, 3SiO, 3SO) using full valence-shell CASSCF reference wavefunctions. Also studied were modifications of these functionals recently suggested by Miehlich, Stoll and Savin (MSS) and Gräfenstein and Cremer (GC). The results obtained show accuracy comparable with and typically superior to the popular Kohn-Sham BLYP and B3LYP methods. However, the latter methods are not applicable in all regions of a potential energy surface, and even predict incorrect ground states for some systems. The use of two-body density functionals with MCSCF reference states does not share this shortcoming.
We suggest to excite dipole-forbidden transitions in quantummechanicalsystems by using appropriately designed optical nanoantennas. The antennas are tailored such that their near field contains sufficiently strong contributions of higher-order multipole moments. The strengths of these moments exceed their free-space analogs by several orders of magnitude. The impact of such excitation enhancement is exemplarily investigated by studying the dynamics of a three-level system. It decays upon excitation by an electric quadrupole transition via two electric dipole transitions. Since one dipole transition is assumed to be radiative, the enhancement of this emission serves as a figure of merit. Such self-consistent treatment of excitation, emission, and internal dynamics as developed in this contribution is the key to predict any observable quantity. The suggested scheme may represent a blueprint for future experiments and will find many obvious spectroscopic and sensing applications.
Enzymes have evolved to increase the rate of biological reactions using fundamental physical processes. Until recently, the nature of catalysis has been based upon a classical model but it has since been considered that certain aspects of catalysis, particularly those concerning the transfer of a hydrogen species, may be accounted for using the theory of quantummechanics. This thesis reports the use of reaction paths obtained using QMMM (combined quantummechanics-molecular mechanics), combined with canonical variational transition state theory and multidimensional tunnelling corrections, to study two dehydrogenase enzymes, Liver Alcohol Dehydrogenase (LADH) and Methylamine Dehydrogenase (MADH). These methods are used to investigate the nature of these models in explaining reported experimental data indicative of quantummechanical tunnelling within these enzymes. The results obtained are in good agreement with experimental data indicating the presence of tunnelling in LADH and, to a greater degree, in MADH, reflected in the magnitude of the calculated kinetic isotope effects (KIEs). For LADH, a primary tritium KIE of 5.6 is reported, calculated using transition state theory (TST) with a Wigner tunnelling correction, and compares favourably with an experimental value of 7.1. For MADH, a KIE of 11.1 was determined using canonical variational theory (CVT) with a small curvature tunnelling (SCT) correction, and compared favourably with an experimental value of 16.8. In addition, a relationship is observed between the contribution due to tunnelling in each system and the geometric positioning of the donating and accepting atoms of the transferring species, and is in qualitative agreement with current opinion concerning tunnelling and the dynamic nature of catalysis. Potential energy barriers have been obtained for both systems using QMMM. For LADH, barriers of 8.2 kcal mol-1 and 22.0 kcal mol-1, and reaction energies of -25.7 kcal mol-1 and +3.4 kcal mol-1, are
Reiser, Andreas; Schubert, Klaus R.; Stiewe, Jürgen
2012-08-01
Weak interactions break time-reversal (T) symmetry in the two-state system of neutral K-mesons. We present and discuss a two-state mechanicalsystem, i.e. a Foucault-type pendulum on a rotating table, for a full representation of {K^0}{{\\overlineK}{}^0} transitions by the pendulum motions including T violation. The pendulum moves with two different oscillation frequencies and two different magnetic dampings. Its equation of motion is identical to the differential equation for the real part of the CPT-symmetric K-meson wavefunction. The pendulum is able to represent microscopic CP and T violation with CPT symmetry owing to the macroscopic Coriolis force, which breaks the symmetry under reversal-of-motion. Video clips of the pendulum motions are given as supplementary material.
Quantum tunneling of the magnetic moment in a nanomagnet must conserve the total angular momentum. For a nanomagnet embedded in a rigid body, reversal of the magnetic moment will cause the body to rotate as a whole. When embedded in an elastic environment, tunneling of the magnetic moment will cause local elastic twists of the crystal structure. In this thesis, I will present a theoretical study of the interplay between magnetization and rotations in a variety of nanomagnetic systems which have some degree of rotational freedom. We investigate the effect of rotational freedom on the tunnel splitting of a nanomagnet which is free to rotate about its easy axis. Calculating the exact instanton of the coupled equations of motion shows that mechanical freedom of the particle renormalizes the easy axis anisotropy, increasing the tunnel splitting. To understand magnetization dynamics in free particles, we study a quantummechanical model of a tunneling spin embedded in a rigid rotor. The exact energy levels for a symmetric rotor exhibit first and second order quantum phase transitions between states with different values the magnetic moment. A quantum phase diagram is obtained in which the magnetic moment depends strongly on the moments of inertia. An intrinsic contribution to decoherence of current oscillations of a flux qubit must come from the angular momentum it transfers to the surrounding body. Within exactly solvable models of a qubit embedded in a rigid body and an elastic medium, we show that slow decoherence is permitted if the solid is macroscopically large. The spin-boson model is one of the simplest representations of a two-level system interacting with a quantum harmonic oscillator, yet has eluded a closed-form solution. I investigate some possible approaches to understanding its spectrum. The Landau-Zener dynamics of a tunneling spin coupled to a torsional resonator show that for certain parameter ranges the system exhibits multiple Landau-Zener transitions
Eagle, Forrest W.; Seaney, Kyser D.; Grubb, Michael P.
2017-01-01
Quantummechanics is a notoriously difficult subject to learn, due to a lack of real-world analogies that might help provide an intuitive grasp of the underlying ideas. Discrete energy levels and absorption and emission wavelengths in atoms are sometimes described as uniquely quantum phenomena, but are actually general to spatially confined waves…
Quantummechanics has provided philosophers of science with many counterintuitive insights and interpretive puzzles, but little has been written about the role that time plays in the theory. One reason for this is the celebrated argument of Wolfgang Pauli against the inclusion of time as an observable of the theory, which has been seen as a demonstration that time may only enter the theory as a classical parameter. Against this orthodoxy I argue that there are good reasons to expect certain kinds of `time observables' to find a representation within quantum theory, including clock operators (which provide the means to measure the passage of time) and event time operators, which provide predictions for the time at which a particular event occurs, such as the appearance of a dot on a luminescent screen. I contend that these time operators deserve full status as observables of the theory, and on re ection provide a uniquely compelling reason to expand the set of observables allowed by the standard formalism of quantummechanics. In addition, I provide a novel association of event time operators with conditional probabilities, and propose a temporally extended form of quantum theory to better accommodate the time of an event as an observable quantity. This leads to a proposal to interpret quantum theory within an event ontology, inspired by Bertrand Russell's Analysis of Matter. On this basis I mount a defense of Russell's relational theory of time against a recent attack.
According to the “no-node" theorem, the many-body ground state wavefunctions of conventional Bose—Einstein condensations (BEC) are positive-definite, thus time-reversal symmetry cannot be spontaneously broken. We find that multi-component bosons with spin-orbit coupling provide an unconventional type of BECs beyond this paradigm. We focus on a subtle case of isotropic Rashba spin-orbit coupling and the spin-independent interaction. In the limit of the weak confining potential, the condensate wavefunctions are frustrated at the Hartree—Fock level due to the degeneracy of the Rashba ring. Quantum zero-point energy selects the spin-spiral type condensate through the “order-from-disorder" mechanism. In a strong harmonic confining trap, the condensate spontaneously generates a half-quantum vortex combined with the skyrmion type of spin texture. In both cases, time-reversal symmetry is spontaneously broken. These phenomena can be realized in both cold atom systems with artificial spin-orbit couplings generated from atom-laser interactions and exciton condensates in semi-conductor systems.
Quantum information theory has considerably helped in the understanding of quantum many-body systems. The role of quantum correlations and in particular, bipartite entanglement, has become crucial to characterise, classify and simulate quantum many body systems. Furthermore, the scaling of entanglement has inspired modifications to numerical techniques for the simulation of many-body systems leading to the, now established, area of tensor networks. However, the notions and methods brought by quantum information do not end with bipartite entanglement. There are other forms of correlations embedded in the ground, excited and thermal states of quantum many-body systems that also need to be explored and might be utilised as potential resources for quantum technologies. The aim of this work is to review the most recent developments regarding correlations in quantum many-body systems focussing on multipartite entanglement, quantum nonlocality, quantum discord, mutual information but also other non classical measures of correlations based on quantum coherence. Moreover, we also discuss applications of quantum metrology in quantum many-body systems.
It is widely held that quantummechanics is the first scientific theory to present scientifically internal, fundamental difficulties for a realistic interpretation (in the philosophical sense). The standard (Copenhagen) interpretation of the quantum theory is often described as the inevitable instrumentalistic response. It is the purpose of the present article to argue that quantum theory does not present fundamental new problems to a realistic interpretation. The formalism of quantum theory has the same states—it will be argued—as the formalisms of older physical theories and is capable of the same kinds of philosophical interpretation. This result is reached via an analysis of what it means to give a realistic interpretation to a theory. The main point of difference between quantummechanics and other theories—as far as the possibilities of interpretation are concerned—is the special treatment given to measurement by the “projection postulate.” But it is possible to do without this postulate. Moreover, rejection of the projection postulate does not, in spite of what is often maintained in the literature, automatically lead to the many-worlds interpretation of quantummechanics. A realistic interpretation is possible in which only the reality of one (our) world is recognized. It is argued that the Copenhagen interpretation as expounded by Bohr is not in conflict with the here proposed realistic interpretation of quantum theory.
Describes a presentation of basic quantummechanics for nonscience majors that relies on a computer-generated graphic display to circumvent the usual mathematical difficulties. It allows a detailed treatment of free-particle motion in a wave picture. (MLH)
The constraints imposed on observables by the requirement that transmission not occur in the Einstein-Podolsky-Rosen (EPR) experiment are determined, leading to a different treatment of separated systems from that originally proposed by Weinberg (1989). It is found that forbidding EPR communication in nonlinear quantummechanics necessarily leads to another sort of unusual communication: that between different branches of the wave function.
Yuan, Gangcheng; Gómez, Daniel E; Kirkwood, Nicholas; Boldt, Klaus; Mulvaney, Paul
2018-04-24
Many potential applications of quantum dots (QDs) can only be realized once the luminescence from single nanocrystals (NCs) is understood. These applications include the development of quantum logic devices, single-photon sources, long-life LEDs, and single-molecule biolabels. At the single-nanocrystal level, random fluctuations in the QD photoluminescence occur, a phenomenon termed blinking. There are two competing models to explain this blinking: Auger recombination and surface trap induced recombination. Here we use lifetime scaling on core-shell chalcogenide NCs to demonstrate that both types of blinking occur in the same QDs. We prove that Auger-blinking can yield single-exponential on/off times in contrast to earlier work. The surface passivation strategy determines which blinking mechanism dominates. This study summarizes earlier studies on blinking mechanisms and provides some clues that stable single QDs can be engineered for optoelectronic applications.
Y. Aharonov and A. Shimony both conjectured that two axioms - relativistic causality (``no superluminal signalling'') and nonlocality - so nearly contradict each other that only quantummechanics reconciles them. Can we indeed derive quantummechanics, at least in part, from these two axioms? No: ``PR-box'' correlations show that quantum correlations are not the most nonlocal correlations consistent with relativistic causality. Here we replace ``nonlocality'' with ``retrocausality'' and supplement the axioms of relativistic causality and retrocausality with a natural and minimal third axiom: the existence of a classical limit, in which macroscopic observables commute. That is, just as quantummechanics has a classical limit, so must any generalization of quantummechanics. In this limit, PR-box correlations violaterelativistic causality. Generalized to all stronger-than-quantum bipartite correlations, this result is a derivation of Tsirelson's bound (a theorem of quantummechanics) from the three axioms of relativistic causality, retrocausality and the existence of a classical limit. Although the derivation does not assume quantummechanics, it points to the Hilbert space structure that underlies quantum correlations. I thank the John Templeton Foundation (Project ID 43297) and the Israel Science Foundation (Grant No. 1190/13) for support.
Latta, C; Haupt, F; Hanl, M; Weichselbaum, A; Claassen, M; Wuester, W; Fallahi, P; Faelt, S; Glazman, L; von Delft, J; Türeci, H E; Imamoglu, A
2011-06-29
The interaction between a single confined spin and the spins of an electron reservoir leads to one of the most remarkable phenomena of many-body physics--the Kondo effect. Electronic transport measurements on single artificial atoms, or quantum dots, have made it possible to study the effect in great detail. Here we report optical measurements on a single semiconductor quantum dot tunnel-coupled to a degenerate electron gas which show that absorption of a single photon leads to an abrupt change in the system Hamiltonian and a quantum quench of Kondo correlations. By inferring the characteristic power-law exponents from the experimental absorption line shapes, we find a unique signature of the quench in the form of an Anderson orthogonality catastrophe, induced by a vanishing overlap between the initial and final many-body wavefunctions. We show that the power-law exponent that determines the degree of orthogonality can be tuned using an external magnetic field, which unequivocally demonstrates that the observed absorption line shape originates from Kondo correlations. Our experiments demonstrate that optical measurements on single artificial atoms offer new perspectives on many-body phenomena previously studied using transport spectroscopy only.
The Berry phase, which was discovered more than two decades ago, provides very deep insight into the geometric structure of quantummechanics. Its classical counterpart, Hannay's angle, is defined if closed curves of action variables return to the same curves in phase space after a time evolution. In this paper we study the Berry phase and Hannay's angle in a quantum-classical hybrid system under the Born-Oppenheimer approximation. By the term quantum-classical hybrid system, we mean a composite system consists of a quantum subsystem and a classical subsystem. The effects of subsystem-subsystem couplings on the Berry phase and Hannay's angle aremore » explored. The results show that the Berry phase has been changed sharply by the couplings, whereas the couplings have a small effect on the Hannay's angle.« less
Deng, Dong-Ling; Li, Xiaopeng; Pixley, J. H.; Wu, Yang-Le; Das Sarma, S.
2017-01-01
We theoretically study the response of a many-body localized system to a local quench from a quantum information perspective. We find that the local quench triggers entanglement growth throughout the whole system, giving rise to a logarithmic lightcone. This saturates the modified Lieb-Robinson bound for quantum information propagation in many-body localized systems previously conjectured based on the existence of local integrals of motion. In addition, near the localization-delocalization transition, we find that the final states after the local quench exhibit volume-law entanglement. We also show that the local quench induces a deterministic orthogonality catastrophe for highly excited eigenstates, where the typical wave-function overlap between the pre- and postquench eigenstates decays exponentially with the system size.
Macroscopic quantumsystems (MQS) are macroscopic systems driven by quantum rather than classical mechanics, a long studied area with minimal success till recently. Harnessing the benefits of quantummechanics on a macroscopic level would revolutionize fields ranging from telecommunication to biology, the latter focused on here for reasons discussed. Contrary to misconceptions, there are no known physical laws that prevent the development of MQS. Instead, they are generally believed universally lost in complex systems from environmental entanglements (decoherence). But we argue success is achievable MQS with decoherence compensation developed, naturally or artificially, from top-down rather current reductionist approaches. This paper advances the MQS field by a complex systems approach to decoherence. First, why complex system decoherence approaches (top-down) are needed is discussed. Specifically, complex adaptive systems (CAS) are not amenable to reductionist models (and their master equations) because of emergent behaviour, approximation failures, not accounting for quantum compensatory mechanisms, ignoring path integrals, and the subentity problem. In addition, since MQS must exist within the context of the classical world, where rapid decoherence and prolonged coherence are both needed. Nature has already demonstrated this for quantum subsystems such as photosynthesis and magnetoreception. Second, we perform a preliminary study that illustrates a top-down approach to potential MQS. In summary, reductionist arguments against MQS are not justifiable. It is more likely they are not easily detectable in large intact classical systems or have been destroyed by reductionist experimental set-ups. This complex systems decoherence approach, using top down investigations, is critical to paradigm shifts in MQS research both in biological and non-biological systems. PMID:29200743
Macroscopic quantumsystems (MQS) are macroscopic systems driven by quantum rather than classical mechanics, a long studied area with minimal success till recently. Harnessing the benefits of quantummechanics on a macroscopic level would revolutionize fields ranging from telecommunication to biology, the latter focused on here for reasons discussed. Contrary to misconceptions, there are no known physical laws that prevent the development of MQS. Instead, they are generally believed universally lost in complex systems from environmental entanglements (decoherence). But we argue success is achievable MQS with decoherence compensation developed, naturally or artificially, from top-down rather current reductionist approaches. This paper advances the MQS field by a complex systems approach to decoherence. First, why complex system decoherence approaches (top-down) are needed is discussed. Specifically, complex adaptive systems (CAS) are not amenable to reductionist models (and their master equations) because of emergent behaviour, approximation failures, not accounting for quantum compensatory mechanisms, ignoring path integrals, and the subentity problem. In addition, since MQS must exist within the context of the classical world, where rapid decoherence and prolonged coherence are both needed. Nature has already demonstrated this for quantum subsystems such as photosynthesis and magnetoreception. Second, we perform a preliminary study that illustrates a top-down approach to potential MQS. In summary, reductionist arguments against MQS are not justifiable. It is more likely they are not easily detectable in large intact classical systems or have been destroyed by reductionist experimental set-ups. This complex systems decoherence approach, using top down investigations, is critical to paradigm shifts in MQS research both in biological and non-biological systems.
During the last decade, several quantum information protocols, such as quantum key distribution, teleportation or quantum computation, have attracted a lot of interest. Despite the recent success and research efforts in quantum information processing, however, we are just at the beginning of understanding the role of entanglement and the behavior of quantumsystems in noisy environments, i.e. for nonideal implementations. Therefore, in order to facilitate the investigation of entanglement and decoherence in n-qubit quantum registers, here we present a revised version of the FEYNMAN program for working with quantum operations and their associated (Jamiołkowski) dual states. Based on the implementation of several popular decoherence models, we provide tools especially for the quantitative analysis of quantum operations. Apart from the implementation of different noise models, the current program extension may help investigate the fragility of many quantum states, one of the main obstacles in realizing quantum information protocols today. Program summaryTitle of program: Feynman Catalogue identifier: ADWE_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWE_v3_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: None Operating systems: Any system that supports MAPLE; tested under Microsoft Windows XP, SuSe Linux 10 Program language used:MAPLE 10 Typical time and memory requirements: Most commands that act upon quantum registers with five or less qubits take ⩽10 seconds of processor time (on a Pentium 4 processor with ⩾2 GHz or equivalent) and 5-20 MB of memory. Especially when working with symbolic expressions, however, the memory and time requirements critically depend on the number of qubits in the quantum registers, owing to the exponential dimension growth of the associated Hilbert space. For example, complex (symbolic) noise models (with several Kraus operators) for multi-qubit systems
We study the quantum dynamics of a spinless charged-particle propagating through a magnetic lattice in a transport line or storage ring. Starting from the Klein-Gordon equation and by applying the paraxial approximation, we derive a Schroedinger-like equation for the betatron motion. A suitable unitary transformation reduces the problem to that of a simple harmonic oscillator. As a result we are able to find an explicit expression for the particle wavefunction.
Quantum spin Hall system can exhibit exotic spin transport phenomena, mediated by its topological edge states. The concept of bending strain engineering to tune the spin transport properties of a quantum spin Hall system is demonstrated. Here, we show that bending strain can be used to control the spin orientation of counter-propagating edge states of a quantum spin system to generate a non-zero spin current. This physics mechanism can be applied to effectively tune the spin current and pure spin current decoupled from charge current in a quantum spin Hall system by control of its bending curvature. Moreover, the curvedmore » quantum spin Hall system can be achieved by the concept of topological nanomechanical architecture in a controllable way, as demonstrated by the material example of Bi/Cl/Si(111) nanofilm. This concept of bending strain engineering of spins via topological nanomechanical architecture affords a promising route towards the realization of topological nano-mechanospintronics.« less
Quantum spin Hall system can exhibit exotic spin transport phenomena, mediated by its topological edge states. The concept of bending strain engineering to tune the spin transport properties of a quantum spin Hall system is demonstrated. Here, we show that bending strain can be used to control the spin orientation of counter-propagating edge states of a quantum spin system to generate a non-zero spin current. This physics mechanism can be applied to effectively tune the spin current and pure spin current decoupled from charge current in a quantum spin Hall system by control of its bending curvature. Moreover, the curvedmore » quantum spin Hall system can be achieved by the concept of topological nanomechanical architecture in a controllable way, as demonstrated by the material example of Bi/Cl/Si(111) nanofilm. This concept of bending strain engineering of spins via topological nanomechanical architecture affords a promising route towards the realization of topological nano-mechanospintronics.« less
. 179 (2008) 647 Does the new version supersede the previous version?: Yes Nature of problem: During the last decade, the field of quantum information science has largely contributed to our understanding of quantummechanics, and has provided also new and efficient protocols that are used on quantum entanglement. To further analyze the amount and transfer of entanglement in n-qubit quantum protocols, symbolic and numerical simulations need to be handled efficiently. Solution method: Using the computer algebra system Maple, we developed a set of procedures in order to support the definition, manipulation and analysis of n-qubit quantum registers. These procedures also help to deal with (unitary) logic gates and (nonunitary) quantum operations and measurements that act upon the quantum registers. All commands are organized in a hierarchical order and can be used interactively in order to simulate and analyze the evolution of n-qubit quantumsystems, both in ideal and noisy quantum circuits. Reasons for new version: Until the present, the FEYNMAN program supported the basic data structures and operations of n-qubit quantum registers [1], a good number of separability and entanglement measures [2], quantum operations (noisy channels) [3] as well as the parametrizations of various frequently applied objects, such as (pure and mixed) quantum states, hermitian and unitary matrices or classical probability distributions [4]. With the current extension, we here add all necessary features to simulate quantum measurements, including the projective measurements in various single-qubit and the two-qubit Bell basis, and POVM measurements. Together with the previously implemented functionality, this greatly enhances the possibilities of analyzing quantum information protocols in which measurements play a central role, e.g., one-way computation. Running time: Most commands require ⩽10 seconds of processor time on a Pentium 4 processor with ⩾2 GHz RAM or newer, if they work with
Coherent manipulation of quantumsystems with light is expected to be a cornerstone of future information and communication technology, including quantum computation and cryptography. The transfer of an optical phase onto a quantumwavefunction is a defining aspect of coherent interactions and forms the basis of quantum state preparation, synchronization and metrology. Light-phase-modulated electron states near atoms and molecules are essential for the techniques of attosecond science, including the generation of extreme-ultraviolet pulses and orbital tomography. In contrast, the quantum-coherent phase-modulation of energetic free-electron beams has not been demonstrated, although it promises direct access to ultrafast imaging and spectroscopy with tailored electron pulses on the attosecond scale. Here we demonstrate the coherent quantum state manipulation of free-electron populations in an electron microscope beam. We employ the interaction of ultrashort electron pulses with optical near-fields to induce Rabi oscillations in the populations of electron momentum states, observed as a function of the optical driving field. Excellent agreement with the scaling of an equal-Rabi multilevel quantum ladder is obtained, representing the observation of a light-driven 'quantum walk' coherently reshaping electron density in momentum space. We note that, after the interaction, the optically generated superposition of momentum states evolves into a train of attosecond electron pulses. Our results reveal the potential of quantum control for the precision structuring of electron densities, with possible applications ranging from ultrafast electron spectroscopy and microscopy to accelerator science and free-electron lasers.
Coherent manipulation of quantumsystems with light is expected to be a cornerstone of future information and communication technology, including quantum computation and cryptography. The transfer of an optical phase onto a quantumwavefunction is a defining aspect of coherent interactions and forms the basis of quantum state preparation, synchronization and metrology. Light-phase-modulated electron states near atoms and molecules are essential for the techniques of attosecond science, including the generation of extreme-ultraviolet pulses and orbital tomography. In contrast, the quantum-coherent phase-modulation of energetic free-electron beams has not been demonstrated, although it promises direct access to ultrafast imaging and spectroscopy with tailored electron pulses on the attosecond scale. Here we demonstrate the coherent quantum state manipulation of free-electron populations in an electron microscope beam. We employ the interaction of ultrashort electron pulses with optical near-fields to induce Rabi oscillations in the populations of electron momentum states, observed as a function of the optical driving field. Excellent agreement with the scaling of an equal-Rabi multilevel quantum ladder is obtained, representing the observation of a light-driven `quantum walk' coherently reshaping electron density in momentum space. We note that, after the interaction, the optically generated superposition of momentum states evolves into a train of attosecond electron pulses. Our results reveal the potential of quantum control for the precision structuring of electron densities, with possible applications ranging from ultrafast electron spectroscopy and microscopy to accelerator science and free-electron lasers.
These proceedings comprise the invited lectures of the second international symposium on Emergent QuantumMechanics (EmQM13), which was held at the premises of the Austrian Academy of Sciences in Vienna, Austria, 3-6 October 2013. The symposium was held at the ''Theatersaal'' of the Academy of Sciences, and was devoted to the open exploration of emergent quantummechanics, a possible ''deeper level theory'' that interconnects three fields of knowledge: emergence, the quantum, and information. Could there appear a revised image of physical reality from recognizing new links between emergence, the quantum, and information? Could a novel synthesis pave the way towards a 21st century, ''superclassical'' physics? The symposium provided a forum for discussing (i) important obstacles which need to be overcome as well as (ii) promising developments and research opportunities on the way towards emergent quantummechanics. Contributions were invited that presented current advances in both standard as well as unconventional approaches to quantummechanics. The EmQM13 symposium was co-organized by Gerhard Grössing (Austrian Institute for Nonlinear Studies (AINS), Vienna), and by Jan Walleczek (Fetzer Franklin Fund, USA, and Phenoscience Laboratories, Berlin). After a very successful first conference on the same topic in 2011, the new partnership between AINS and the Fetzer Franklin Fund in producing the EmQM13 symposium was able to further expand interest in the promise of emergent quantummechanics. The symposium consisted of two parts, an opening evening addressing the general public, and the scientific program of the conference proper. The opening evening took place at the Great Ceremonial Hall (Grosser Festsaal) of the Austrian Academy of Sciences, and it presented talks and a panel discussion on ''The Future of QuantumMechanics'' with three distinguished speakers: Stephen Adler (Princeton), Gerard 't Hooft (Utrecht) and Masanao Ozawa (Nagoya). The articles contained in
We give a review of the basic themes of my recent book: Adler S L 2004 Quantum Theory as an Emergent Phenomenon (Cambridge: Cambridge University Press). We first give motivations for considering the possibility that quantummechanics is not exact, but is instead an accurate asymptotic approximation to a deeper level theory. For this deeper level, we propose a non-commutative generalization of classical mechanics, that we call "trace dynamics", and we give a brief survey of how it works, considering for simplicity only the bosonic case. We then discuss the statistical mechanics of trace dynamics and give our argument that with suitable approximations, the Ward identities for trace dynamics imply that ensemble averages in the canonical ensemble correspond to Wightman functions in quantum field theory. Thus, quantum theory emerges as the statistical thermodynamics of trace dynamics. Finally, we argue that Brownian motion corrections to this thermodynamics lead to stochastic corrections to the Schrödinger equation, of the type that have been much studied in the "continuous spontaneous localization" model of objective state vector reduction. In appendices to the talk, we give details of the existence of a conserved operator in trace dynamics that encodes the structure of the canonical algebra, of the derivation of the Ward identities, and of the proof that the stochastically-modified Schrödinger equation leads to state vector reduction with Born rule probabilities.
Research-based tools to educate college students in physics courses from introductory level to graduate level are essential for helping students with a diverse set of goals and backgrounds learn physics. This thesis explores issues related to student common difficulties with some topics in undergraduate quantummechanics and thermodynamics courses. Student difficulties in learning quantummechanics and thermodynamics are investigated by administering written tests and surveys to many classes and conducting individual interviews with a subset of students outside the class to unpack the cognitive mechanisms of the difficulties. The quantummechanics research also focuses on using the research on student difficulties for the development and evaluation of a Quantum Interactive Learning Tutorial (QuILT) to help students learn about the time-dependence of expectation values using the context of Larmor precession of spin and evaluating the role of asking students to self-diagnose their mistakes on midterm examination on their performance on subsequent problem solving. The QuILT on Larmor precession of spin has both paper-pencil activities and a simulation component to help students learn these foundational issues in quantummechanics. Preliminary evaluations suggest that the QuILT, which strives to help students build a robust knowledge structure of time-dependence of expectation values in quantummechanics using a guided approach, is successful in helping students learn these topics in the junior-senior level quantummechanics courses. The technique to help upper-level students in quantummechanics courses effectively engage in the process of learning from their mistakes is also found to be effective. In particular, research shows that the self-diagnosis activity in upper-level quantummechanics significantly helps students who are struggling and this activity can reduce the gap between the high and low achieving students on subsequent problem solving. Finally, a survey
The interpretation of quantummechanics (QM) is discussed in terms of the principles and logic of empiricism. First, we list a set of issues that should be settled before any consistent interpretation is attempted. This includes questions such as whether we can use an exophysical perspective or an endophysical perspective, and whether a completely reductionist approach makes sense or are we forced to incorporate emergent laws of physics. We then list the scientific pr nciples that should be strictly adhered to in any debate on QM. We follow this with a list of cautions and warnings about misleading concepts that should be avoided, such as ignoring contextuality and the meaning of scientific truth values. These principles and warning are then used to decide on the issues we first identified, giving us a basis for an interpretation of QM from the perspective of observers and quantum signal states of apparatus, rather than in terms of qu ntum states of systems under observation. Finally, we review a proposed mathematical formalism that encodes this interpretation in terms of quantum registers.
While ultimately they are described by quantummechanics, macroscopic mechanicalsystems are nevertheless observed to follow the trajectories predicted by classical mechanics. Hence, in the regime defining macroscopic physics, the trajectories of the correct classical motion must emerge from quantummechanics, a process referred to as the quantum to classical transition. Extending previous work [Bhattacharya, Habib, and Jacobs, Phys. Rev. Lett. 85, 4852 (2000)], here we elucidate this transition in some detail, showing that once the measurement processes that affect all macroscopic systems are taken into account, quantummechanics indeed predicts the emergence of classical motion. We derive inequalities thatmore » describe the parameter regime in which classical motion is obtained, and provide numerical examples. We also demonstrate two further important properties of the classical limit: first, that multiple observers all agree on the motion of an object, and second, that classical statistical inference may be used to correctly track the classical motion.« less
Topological properties lie at the heart of many fascinating phenomena in solid-state systems such as quantum Hall systems or Chern insulators. The topology of the bands can be captured by the distribution of Berry curvature, which describes the geometry of the eigenstates across the Brillouin zone. Using fermionic ultracold atoms in a hexagonal optical lattice, we engineered the Berry curvature of the Bloch bands using resonant driving and show a full momentum-resolved state tomography from which we obtain the Berry curvature and Chern number. Furthermore, we study the time-evolution of the many-body wavefunction after a sudden quench of the lattce parameters and observe the appearance, movement, and annihilation of vortices in reciprocal space. We identify their number as a dynamical topological order parameter, which suddenly changes its value at critical times. Our measurements constitute the first observation of a so called dynamical topological phase transition`, which we show to be a fruitful concept for the understanding of quantum dynamics far from equilibrium
The ability to engineer and manipulate different types of quantummechanical objects allows us to take advantage of their unique properties and create useful hybrid technologies. Thus far, complex quantum states and exquisite quantum control have been demonstrated in systems ranging from trapped ions to superconducting resonators. Recently, there have been many efforts to extend these demonstrations to the motion of complex, macroscopic objects. These mechanical objects have important applications as quantum memories or transducers for measuring and connecting different types of quantumsystems. In particular, there have been a few experiments that couple motion to nonlinear quantum objects such as superconducting qubits. This opens up the possibility of creating, storing, and manipulating non-Gaussian quantum states in mechanical degrees of freedom. However, before sophisticated quantum control of mechanical motion can be achieved, we must realize systems with long coherence times while maintaining a sufficient interaction strength. These systems should be implemented in a simple and robust manner that allows for increasing complexity and scalability in the future. In this talk, I will describe our recent experiments demonstrating a high frequency bulk acoustic wave resonator that is strongly coupled to a superconducting qubit using piezoelectric transduction. In contrast to previous experiments with qubit-mechanicalsystems, our device requires only simple fabrication methods, extends coherence times to many microseconds, and provides controllable access to a multitude of phonon modes. We use this system to demonstrate basic quantum operations on the coupled qubit-phonon system. Straightforward improvements to the current device will allow for advanced protocols analogous to what has been shown in optical and microwave resonators, resulting in a novel resource for implementing hybrid quantum technologies.
Non-Gaussian quantum states are key resources for quantum optics with continuous-variable oscillators. The non-Gaussian states can be deterministically prepared by a continuous evolution of the mechanical oscillator isolated in a nonlinear potential. We propose feasible and deterministic transfer of non-Gaussian quantum states of mechanical oscillators to a traveling light beam, using purely all-optical methods. The method relies on only basic feasible and high-quality elements of quantum optics: squeezed states of light, linear optics, homodyne detection, and electro-optical feedforward control of light. By this method, a wide range of novel non-Gaussian states of light can be produced in the future from the mechanical states of levitating particles in optical tweezers, including states necessary for the implementation of an important cubic phase gate.
We propose an experimental method for a quantum protocol termed quantum energy teleportation (QET), which allows energy transportation to a remote location without physical carriers. Using a quantum Hall system as a realistic model, we discuss the physical significance of QET and estimate the order of energy gain using reasonable experimental parameters.
Greenberger-Horne-Zeilinger (GHZ) and cluster states are two typical kinds of multipartite entangled states and can respectively be used for realizing quantum networks and one-way computation. We propose a feasible scheme for generating Gaussian GHZ and cluster states of multiple mechanical oscillators by pulsed cavity optomechanics. In our scheme, each optomechanical cavity is driven by a blue-detuned pulse to establish quantum steerable correlations between the cavity output field and the mechanical oscillator, and the cavity outputs are combined at a beam-splitter array with given transmissivity and reflectivity for each beam splitter. We show that by harnessing the light-mechanical steerable correlations, the mechanical GHZ and cluster states can be realized via homodyne detection on the amplitude and phase quadratures of the output fields from the beam-splitter array. These achieved mechanical entangled states can be viewed as the output states of an effective mechanical beam-splitter array with the mechanical inputs prepared in squeezed states with the light-mechanical steering. The effects of detection efficiency and thermal noise on the achieved mechanical states are investigated. The present scheme does not require externally injected squeezing and it can also be applicable to other systems such as light-atomic-ensemble interface, apart from optomechanical systems.
The cosmological particle horizon is the maximum measurable length in the Universe. The existence of such a maximum observable length scale implies a modification of the quantum uncertainty principle. Thus due to nonlocality of quantummechanics, the global properties of the Universe could produce a signature on the behavior of local quantumsystems. A generalized uncertainty principle (GUP) that is consistent with the existence of such a maximum observable length scale lmax is Δ x Δ p ≥ℏ2/1/1 -α Δ x2 where α =lmax-2≃(H0/c )2 (H0 is the Hubble parameter and c is the speed of light). In addition to the existence of a maximum measurable length lmax=1/√{α }, this form of GUP implies also the existence of a minimum measurable momentum pmin=3/√{3 } 4 ℏ√{α }. Using appropriate representation of the position and momentum quantum operators we show that the spectrum of the one-dimensional harmonic oscillator becomes E¯n=2 n +1 +λnα ¯ where E¯n≡2 En/ℏω is the dimensionless properly normalized n th energy level, α ¯ is a dimensionless parameter with α ¯≡α ℏ/m ω and λn˜n2 for n ≫1 (we show the full form of λn in the text). For a typical vibrating diatomic molecule and lmax=c /H0 we find α ¯˜10-77 and therefore for such a system, this effect is beyond the reach of current experiments. However, this effect could be more important in the early Universe and could produce signatures in the primordial perturbation spectrum induced by quantum fluctuations of the inflaton field.
The peculiar properties of quantummechanics allow two remote parties to communicate a private, secret key, which is protected from eavesdropping by the laws of physics. So-called quantum key distribution (QKD) implementations always rely on detectors to measure the relevant quantum property of single photons. Here we demonstrate experimentally that the detectors in two commercially available QKD systems can be fully remote-controlled using specially tailored bright illumination. This makes it possible to tracelessly acquire the full secret key; we propose an eavesdropping apparatus built from off-the-shelf components. The loophole is likely to be present in most QKD systems using avalanche photodiodes to detect single photons. We believe that our findings are crucial for strengthening the security of practical QKD, by identifying and patching technological deficiencies.
