Showing papers on "Open quantum system published in 1987"
Book•
01 Oct 1987
TL;DR: In this article, the authors developed quantum dynamics of open systems for a wide class of irreversible processes starting from the concept of completely positive semigroups, and presented a wealth of useful examples; in particular, models of unstable and N-level systems are treated systematically and in considerable detail including new types of generated Bloch-equations.
Abstract: In this text the authors develop quantum dynamics of open systems for a wide class of irreversible processes starting from the concept of completely positive semigroups. This unified approach makes the material easily accessible to non-specialists and provides an easy access to practical applications. Written for graduate students, the book presents a wealth of useful examples; in particular, models of unstable and N-level systems are treated systematically and in considerable detail including new types of generated Bloch-equations. The general theory is extensively summarized from abstract dynamical maps to those obtained by a reduction of Hamiltonian dynamics under a Markovian approximation. Various methods of determining semigroup generators and the corresponding master equations are discussed including time-dependent and nonlinear generators. Further topics treated are a generalized H-theorem, quantum detailed balance and return to equilibrium, discrete quantum Boltzmann equation, nonlinear Schrdinger equation, spin relaxation by spin waves, entropy production and its generalization by a measure of irreversibiblity.
1,330 citations
TL;DR: In this article, a master equation which contains a damping term universally violating the quantum mechanics of massive systems was proposed, and it was shown that the quantum mechanical superposition principle breaks down if the states have radically different mass distributions.
457 citations
TL;DR: In this article, a top undergoing constant precession around a magnetic field and suffering a periodic sequence of impulsive nonlinear kicks is discussed, where the quantum dynamics take place in a finite dimensional Hilbert space.
Abstract: We discuss a top undergoing constant precession around a magnetic field and suffering a periodic sequence of impulsive nonlinear kicks. The squared angular momentum being a constant of the motion the quantum dynamics takes place in a finite dimensional Hilbert space. We find a distinction between regular and irregular behavior for times exceeding the quantum mechanical quasiperiod at which classical behavior, whether chaotic or regular, has died out in quantum means. The degree of level repulsion depends on whether or not the top is endowed with a generalized time reversal invariance.
254 citations
TL;DR: In this paper, the authors present analytical and numerical results on the mechanism of excitation and ionization of hydrogen atoms under microwave fields, and they predict the existence of a critical value of the microwave field, the quantum delocalization border, above which the quantum packet delocalizes and strong ionization takes place.
218 citations
01 Apr 1987
TL;DR: Schrodinger as discussed by the authors argued that the wave function itself is the complete picture, and completely determined by the Schrodinger equation, and so evolving smoothly without 'quantum jumps' in the picture.
Abstract: If we have to go on with these damned quantum jumps, then I'm sorry that I ever got involved. E. Schrodinger Introduction I have borrowed the title of a characteristic paper by Schrodinger (Schrodinger, 1952). In it he contrasts the smooth evolution of the Schrodinger wavefunction with the erratic behaviour of the picture by which the wavefunction is usually supplemented, or ‘interpreted’, in the minds of most physicists. He objects in particular to the notion of ‘stationary states’, and above all to ‘quantum jumping’ between those states. He regards these concepts as hangovers from the old Bohr quantum theory, of 1913, and entirely unmotivated by anything in the mathematics of the new theory of 1926. He would like to regard the wavefunction itself as the complete picture, and completely determined by the Schrodinger equation, and so evolving smoothly without ‘quantum jumps’. Nor would he have ‘particles’ in the picture. At an early stage, he had tried to replace ‘particles’ by wavepackets (Schrodinger, 1926). But wavepackets diffuse. And the paper of 1952 ends, rather lamely, with the admission that Schrodinger does not see how, for the present, to account for particle tracks in track chambers… nor, more generally, for the definiteness, the particularity, of the world of experience, as compared with the indefiniteness, the waviness, of the wavefunction. It is the problem that he had had (Schrodinger, 1935 a ) with his cat. He thought that she could not be both dead and alive.
211 citations
TL;DR: In this paper, an adiabatic evolution that approximates the physical dynamics and describes a natural parallel transport in spectral subspaces was studied, and it was shown that the eventual tunneling out of such spectral sub-spaces is smaller than any inverse power of the time scale if the Hamiltonian varies infinitly smoothly over a finite interval.
Abstract: We study an adiabatic evolution that approximates the physical dynamics and describes a natural parallel transport in spectral subspaces. Using this we prove two folk theorems about the adiabatic limit of quantum mechanics: 1. For slow time variation of the Hamiltonian, the time evolution reduces to spectral subspaces bordered by gaps. 2. The eventual tunneling out of such spectral subspaces is smaller than any inverse power of the time scale if the Hamiltonian varies infinitly smoothly over a finite interval. Except for the existence of gaps, no assumptions are made on the nature of the spectrum. We apply these results to charge transport in quantum Hall Hamiltonians and prove that the flux averaged charge transport is an integer in the adiabatic limit.
188 citations
TL;DR: Methods are developed for estimating nonclassical distance and are applied to number states and squeezed states.
Abstract: The nonclassical distance of a state of the electromagnetic field is defined. This distance allows one to say how nonclassical a given state is and places bounds on the extent to which the behavior of that state can deviate from that of classical states. Methods are developed for estimating nonclassical distance and are applied to number states and squeezed states.
170 citations
TL;DR: Quantum effects are shown to be most easily isolated by sending an atom initially prepared in a dressed state for such a state does not evolve further under the influence of a classical field.
Abstract: Solutions of the basic equations of a simplified model of the cavity quantum electrodynamics are presented under the condition that the single-photon Rabi frequency is much larger than the cavity decay rate. Such solutions are used to calculate the quantum-statistical properties of the field and atomic observables under a variety of initial conditions involving the states of the field and atom. Effects of increasing cavity damping and of the addition of thermal photons on collapse and revival phenomena are discussed. Phase-sensitive aspects of the cavity field are also treated. Quantum effects are shown to be most easily isolated by sending an atom initially prepared in a dressed state for such a state does not evolve further under the influence of a classical field. The appearance of squeezing in the cavity field is demonstrated. The squeezing is most prominent for a coherently prepared atom passing through an empty cavity. The quantum features of the complex dipole moment and their detectability are also discussed in detail.
167 citations
Journal Article•
162 citations
TL;DR: In this article, the Bethe-Lamb equations in the context of the two-level model with Weisskopf-Wigner decay included were solved in a two-stage model.
Abstract: Almost forty years ago one of us (W.E.L.) noticed that within the analysis of experiments on the hydrogen fine structure the matter-field interaction was sensitive to the choice of gauge when decaying states were used. In the present paper this problem is resolved for the Bethe-Lamb equations in the context of the two-level model with Weisskopf-Wigner decay included.
TL;DR: It is shown that the effect of the optical instruments may be taken into account by introducing an apparatus function in a way which formally corresponds to that of classical optics, but the calculation of the corresponding convolution integrals is governed by operator ordering rules, which are essential in the case of quantum light fields.
Abstract: A quantum optical formulation of the action of passive, lossless optical instruments on quantum light fields is developed. The quantum Maxwell equations are formally solved and the commutation relations for various combinations of field operators at different times are studied. General relationships between field correlation functions and correlation functions of source-quantity operators and free-field operators are derived. Formulas are presented for the case when the free field is the vacuum field. Furthermore, the mixing of source-field light with coherent free-field light is treated. The theory is applied to the calculation of the photocount distribution. The theory presented renders it possible to take into account the effects of light propagation through the optical system. It is shown that the effect of the optical instruments may be taken into account by introducing an apparatus function in a way which formally corresponds to that of classical optics. However, the calculation of the corresponding convolution integrals is governed by operator ordering rules, which are essential in the case of quantum light fields and which can give rise to substantial differences between classical and quantum optics.
01 Jan 1987
TL;DR: A multi-stage version of the theory of quantum-mechanical measurements and quantum-statistical decisions applied to the non-demolition control problem for quantum objects is developed and it is shown that Gaussian case of quantum one-dimensional linear Markovian dynamical system with a quantum linear transmission line optimal quantum multistage decision rule consists of classical linear optimal control strategy and quantum optimal filtering procedure.
Abstract: A multi-stage version of the theory of quantum-mechanical measurements and quantum-statistical decisions applied to the non-demolition control problem for quantum objects is developed. It is shown that in Gaussian case of quantum one-dimensional linear Markovian dynamical system with a quantum linear transmission line optimal quantum multistage decision rule consists of classical linear optimal control strategy and quantum optimal filtering procedure, the latter contains the optimal quantum coherent measurement on the output of the line and the recursive processing by Kalman-Busy filter. All the results are illustrated by an example of the optimal problem solution for a quantum one-dimensional linear oscillator on the input of a quantum wave transmission line.
TL;DR: In this article, a nonlinear Hamiltonian model is presented for which exact analytic results can be obtained, and it is shown that macroscopically distinguishable quantum states can be generated and detected by means of a homodyne detector.
Abstract: A nonlinear Hamiltonian model is presented for which exact analytic results can be obtained. It is shown that macroscopically distinguishable quantum states can be generated and detected by means of a homodyne detector. The vacuum fluctuations may inhibit their observability; however, this contribution can be subtracted.
TL;DR: In this article, the case of a one-dimensional reaction coordinate coupled to a bath of many harmonic oscillators is treated by quantum mechanical basis set methods, and it is shown how the bath can then be eliminated to obtain an effective Hamiltonian matrix for only the system.
Abstract: The case of a system (e.g., a one‐dimensional reaction coordinate) coupled to a ‘‘bath’’ of many harmonic oscillators is treated by quantum mechanical basis set methods. By choosing the basis set for the bath to incorporate the coupling explicitly, it is shown how the bath can then be eliminated to obtain an effective Hamiltonian matrix for only the system. Numerical calculations are carried out which show that, even in the zeroth version of the approach, the effect on the system (e.g., the tunneling splitting in a double‐well potential) of coupling to the bath is described well, even when the effect is extremely large.
TL;DR: In this paper, the authors derived master equations for a system consisting of two harmonic oscillators for the description of the charge and mass asymmetry degrees of freedom in deep inelastic collisions in nuclear physics.
Abstract: On the basis of the theory of Lindblad (1976) for open quantum systems the author derives master equations for a system consisting of two harmonic oscillators. The time dependence of expectation values, Wigner function and Weyl operator are obtained and discussed. The chosen system can be applied for the description of the charge and mass asymmetry degrees of freedom in deep inelastic collisions in nuclear physics.
TL;DR: In this paper, a rigorous analysis of the vacuum structure of two models of supersymmetric quantum mechanics is presented, which are the quantum mechanics versions of the two-dimensional N = 1 and N = 2 Wess-Zumino quantum field models.
Book•
30 Nov 1987
TL;DR: In this article, the Bohr-Rosenfeld principles of measurement in Quantum Field Theory are discussed. But they do not consider the effect of the Compton Effect on quantum field theory.
Abstract: 1/Quantum Theory and Gravitation.- 2/Quantum Mechanics and Classical Gravitation.- 2.1. Diffraction of Particles by a Grating.- 2.2. Diffraction of Particles by a Gravitational Grating.- 2.3. Gravitational Atomic Model.- 2.4. Equivalence Principle and Heisenberg's Fourth Relation.- 2.5. Quantum Mechanics and the Weak Principle of Equivalence.- 3/Measurement in Quantum Gravity.- 3.1. The Bohr-Rosenfeld Principles of Measurement in Quantum Field Theory.- (a) The Landau-Peierls Arguments.- (b) The Bohr-Rosenfeld Arguments.- 3.2. Measurement in Quantum Gravity.- 3.3. Ehrenfest's Theorems.- 4/Mathematical Descriptions of Quantum Gravity.- 4.1. Heisenberg-Euler-Kockel Approximation.- 4.2. On Gauge Fixing in Quantum Gravity.- 5/Quantum Postulates and the Strong Principle of Equivalence.- 5.1. Gravitons and the Linear Approximation of General Relativity Theory.- 5.2. Gravitons and the Nonlinear High-Frequency Approximation of General Relativity Theory.- 5.3. Compton Effect.- 5.4. Lamb Shift.- 5.5. Black-body Radiation.- 5.6. A Historical Remark: Black-body Radiation and Compton Effect.- 6/Planckions.- 6.1. Heavy Gravitons.- 6.2. Planckions as Biggest Elementary Particles and as Smallest Test Bodies.- 6.3. Foam and Block Spaces.- Appendix A/Massive Shell Models and Shock Waves in Gravitational Theories with Higher Derivatives.- Appendix B/On the Physical Meaning of Planck's 'Natural Units'.- References.
TL;DR: In this paper, the problem of two separated, noninteracting spin − 1/2 particles in a state of zero total spin is analyzed using the consistent history interpretation of quantum mechanics and shown to behave in many respects like a classical system.
Abstract: The familiar problem of two separated, noninteracting spin‐ 1/2 particles in a state of zero total spin is analyzed using the consistent history interpretation of quantum mechanics and shown to behave in many respects like a classical system of two noninteracting objects whose individual properties are unknown but strongly correlated with each other. There is no action at a distance between the particles and a measurement on one has no effect whatsoever on the other. However, the result of a measurement of a spin component of one of the particles can be used to infer (correctly) its value prior to the measurement, and also the corresponding spin component of the other particle at all times prior to when that particle interacts with something else. In these respects the quantum system behaves like its classical counterpart. On the other hand, the paradoxical (nonclassical) aspects of the quantum situation seem to be precisely those already present in the quantum theory of a single particle.
TL;DR: A quantum-mechanical treatment for refraction and reflection is given by applying the formalism of the momentum operator for the radiation field to propagation through a linear dielectric.
Abstract: We have developed a quantum-mechanical formalism which permits the treatment of light propagation within the conceptual framework of quantum optics. The formalism rests on the calculation of the momentum operator for the radiation field, and yields directly a description for the spatial progression of the electromagnetic waves. In this paper we give a quantum-mechanical treatment for refraction and reflection by applying our formalism to propagation through a linear dielectric. The fidelity with which this formalism reproduces all results known from classical optics demonstrates its validity.
TL;DR: It is shown that the path integral automatically picks up a unique combination of the branch Hamiltonians, which is a natural generalization of the Brouwer degree of the Legendre map.
Abstract: When the Lagrangian is not quadratic in the velocities, the situation may arise that the expression for the velocities in terms of the momenta is multivalued. As a consequence, the classical motion is unpredictable since at any time one can jump from one branch of the Hamiltonian to another. Yet, the quantum theory turns out to be perfectly smooth, with wave functions which are regular functions of time. We show that the path integral automatically picks up a unique combination of the branch Hamiltonians, which is a natural generalization of the Brouwer degree of the Legendre map.
TL;DR: In this paper, a covariant Schrodinger formalism is proposed for relativistic quantum field theory, which can be interpreted as a consequence of a space-time metric fluctuation and can be related to mass ensemble theories.
TL;DR: In this article, it is shown that for a system of a fixed number of particles such a model does yield the deterministic de Broglie-Bohm model in an appropriate limit, however, a deterministic limit is unlikely to emerge from a quantum field theory capable of describing particle production and decay.
Abstract: Examines a suggestion by Bell (1984) that a deterministic model might be furnished by the continuum limit of an objective stochastic model which he has proposed for quantum field theory on a lattice. The virtues of models of Bell's type for general quantum systems are discussed, and it is shown that for a system of a fixed number of particles such a model does yield the deterministic de Broglie-Bohm model in an appropriate limit. It is argued, however, that a deterministic limit is unlikely to emerge from a quantum field theory capable of describing particle production and decay. An interpretation of quantum field theory is proposed which has the advantages of Bell's interpretation but is closer to conventional quantum mechanics.
TL;DR: The so-called Feynman-Vernon influence functional theory has been generalized in order to include the possibility of dealing with initial conditions of the system plus environment other than the factorizable one.
Abstract: In this paper the so-called Feynman-Vernon influence functional theory has been generalized in order to include the possibility of dealing with initial conditions of the system plus environment other than the factorizable one. It has been shown that the new influence functional can now be written in terms of paths which represent the coupling of quantum-statistical to quantum-dynamical effects. Once the thermal paths are integrated out of this new influence functional, a generalization of the original Feynman-Vernon expression is obtained.
TL;DR: In this paper, it is shown that the replacement of standard quantum mechanics by QMSL has the only effect of producing an actual reduction of the wave function, which is not the effect of the original quantum mechanics.
Abstract: Quantum mechanics with spontaneous localization (QMSL) is a recently proposed stochastic modification of theN-body Schrodinger equation consistent both with microphysics and macrophysics. QMSL is applied here to the measurement problem. It is shown that the replacement of standard quantum mechanics by QMSL has the only effect of producing an actual reduction of the wave function.
TL;DR: In this article, it has been suggested that (imprecise) measurements of non-commuting observables on correlated quantum systems may lead to observable non-local effects, and the inapplicability of several impossibility proofs to this case is noted; however, a suitable result of Kraus is pointed out, which shows the untenability of such a scheme.
01 Jan 1987
TL;DR: In this paper, a review of the general motivation for the work and the philosophy associated with it is presented, with the assumption that the sorts of effects we are looking for in the superconducting-device area may also occur in other systems, and are most likely to occur in those which show the strongly nonlinear behavior which is the subject of this conference.
Abstract: Since most participants at this conference come from sub-areas of physics different from the one in which most of the technical work associated with the subject of this talk has been done (namely superconducting devices exploiting the Josephson effect), I thought that rather than talking about the technical details it might be more interesting to review the general motivation for the work and the philosophy associated with it. An additional reason for doing so is that I believe that the sorts of effects we are looking for in the superconducting-device area may also occur in other systems, and are most likely to occur in those which show the strongly nonlinear behavior which is the subject of this conference.
01 Jan 1987
TL;DR: In the early universe, however, the classical approximation is unlikely to be valid as discussed by the authors, since quantum fluctuations become important and eventually dominant in the Planck length curvatures of the universe.
Abstract: As far as we know them, the fundamental laws of physics are quantum mechanical in nature. If these laws apply to the universe as a whole, then there must be a description of the universe in quantum mechancial terms. Even our present cosmological observations require such a description in principle, although in practice these observations are so limited and crude that the approximation of classical physics is entirely adequate. In the early universe, however, the classical approximation is unlikely to be valid. There, towards the big bang singularity, at curvatures characterized by the Planck length, (ћG/c 3)1/2 , quantum fluctuations become important and eventually dominant.
TL;DR: In this article, it was shown that the squeezed states of quantum optics are physically and mathematically equivalent to Gaussian wave packets, and the properties of reduced or squeezed fluctuations of the position and momentum operators were investigated in a very simple way.
Abstract: We show that the squeezed states of quantum optics are physically and mathematically equivalent to Gaussian wave packets. In the framework of wave mechanics it is possible to formulate and investigate in a very simple way all the properties of reduced or squeezed fluctuations of the position and momentum operators. We study squeezed quantum fluctuations of a minimum-uncertainty Gaussian wave function under two different dynamical conditions of free evolution and harmonic oscillation.
TL;DR: The intracavity density operator becomes diagonal in the basis which diagonalizes the measured quantity, a quadrature phase amplitude of the field, the ‘‘pointer basis,’’ and this result is the continuous-measurement equivalent of state reduction.
Abstract: An analysis is presented of optical heterodyne detection of an intracavity field within the context of quantum measurement theory. We find the intracavity density operator becomes diagonal in the basis which diagonalizes the measured quantity, a quadrature phase amplitude of the field. This representation is the ‘‘pointer basis,’’ and this result is the continuous-measurement equivalent of state reduction. The model illustrates a general feature of continuous measurement; one parameter given by the product of the system and measuring device coupling bandwidth and the fluctuations in the measuring device completely characterizes the measurement. This constant determines both the rate of diagonalization of the density operator and the rate of growth of fluctuations in the system quantity conjugate to the measured observable.