Reduced quantum dynamics with arbitrary bath spectral densities: Hierarchical equations of motion based on several different bath decomposition schemes

2014 ◽  
Vol 140 (13) ◽  
pp. 134106 ◽  
Author(s):  
Hao Liu ◽  
Lili Zhu ◽  
Shuming Bai ◽  
Qiang Shi
Keyword(s):  
Quantum Dynamics ◽  
Equations Of Motion ◽  
Spectral Densities ◽  
Decomposition Schemes

scholarly journals Dynamics of an orbital polarization of twisted electron beams in electric and magnetic fields

2019 ◽  
Vol 204 ◽  
pp. 10008
Author(s):  
Alexander J. Silenko ◽  
Pengming Zhang ◽  
Liping Zou
Keyword(s):  
Magnetic Field ◽  
Electron Beam ◽  
Magnetic Fields ◽  
Quantum Dynamics ◽  
Electron Beams ◽  
Equations Of Motion ◽  
Vortex Beam ◽  
Dirac Particles ◽  
Electric And Magnetic Fields ◽  
Average Projection

Relativistic classical and quantum dynamics of twisted (vortex) Dirac particles in arbitrary electric and magnetic fields is constructed. The relativistic Hamiltonian and equations of motion in the Foldy-Wouthuysen representation are derived. Methods for the extraction of an electron vortex beam with a given orbital polarization and for the manipulation of such a beam are developed. The new effect of a radiative orbital polarization of a twisted electron beam in a magnetic field resulting in a nonzero average projection of the intrinsic orbital angular momentum on the field direction is predicted.

scholarly journals SYMMETRIES OF THE NEAR HORIZON OF A BLACKHOLE BY GROUP THEORETIC METHODS

2007 ◽  
Vol 22 (08n09) ◽  
pp. 1717-1726
Author(s):  
K. MAHARANA
Keyword(s):  
Black Hole ◽  
Charged Particle ◽  
Magnetic Fields ◽  
Lie Algebras ◽  
Quantum Dynamics ◽  
Equations Of Motion ◽  
Scalar Particle ◽  
Lie Point Symmetries

We use group theoretic methods to obtain the extended Lie point symmetries of the quantum dynamics of a scalar particle probing the near horizon structure of a black hole. Symmetries of the classical equations of motion for a charged particle in the field of an inverse square potential and a monopole, in the presence of certain model magnetic fields and potentials are also studied. Our analysis gives the generators and Lie algebras generating the inherent symmetries.

Quantum mechanics as a statistical theory

1949 ◽  
Vol 45 (1) ◽  
pp. 99-124 ◽  
Author(s):  
J. E. Moyal
Keyword(s):  
Quantum Mechanics ◽  
Statistical Theory ◽  
Phase Space ◽  
Quantum Dynamics ◽  
Transition Probabilities ◽  
Equations Of Motion ◽  
Distribution Functions ◽  
Space Distribution ◽  
Statistical Dynamics ◽  
Space Transformation

An attempt is made to interpret quantum mechanics as a statistical theory, or more exactly as a form of non-deterministic statistical dynamics. The paper falls into three parts. In the first, the distribution functions of the complete set of dynamical variables specifying a mechanical system (phase-space distributions), which are fundamental in any form of statistical dynamics, are expressed in terms of the wave vectors of quantum theory. This is shown to be equivalent to specifying a theory of functions of non-commuting operators, and may hence be considered as an interpretation of quantum kinematics. In the second part, the laws governing the transformation with time of these phase-space distributions are derived from the equations of motion of quantum dynamics and found to be of the required form for a dynamical stochastic process. It is shown that these phase-space transformation equations can be used as an alternative to the Schrödinger equation in the solution of quantum mechanical problems, such as the evolution with time of wave packets, collision problems and the calculation of transition probabilities in perturbed systems; an approximation method is derived for this purpose. The third part, quantum statistics, deals with the phase-space distribution of members of large assemblies, with a view to applications of quantum mechanics to kinetic theories of matter. Finally, the limitations of the theory, its uniqueness and the possibilities of experimental verification are discussed.

scholarly journals Open Quantum Dynamics Theory on the Basis of Periodical System-Bath Model for Discrete Wigner Function

2021 ◽  
Author(s):  
Yuki Iwamoto ◽  
Yoshitaka Tanimura
Keyword(s):  
Distribution Function ◽  
Quantum Dynamics ◽  
Degrees Of Freedom ◽  
Wigner Distribution ◽  
Equations Of Motion ◽  
Heat Bath ◽  
Planck Equation ◽  
Mesh Size ◽  
Dynamics Simulation ◽  
Open Quantum

Abstract Discretizing distribution function in a phase space for an efficient quantum dynamics simulation is non-trivial challenge, in particular for a case that a system is further coupled to environmental degrees of freedom. Such open quantum dynamics is described by a reduced equation of motion (REOM) most notably by a quantum Fokker-Planck equation (QFPE) for a Wigner distribution function (WDF). To develop a discretization scheme that is stable for numerical simulations from the REOM approach, we find that a two-dimensional (2D) periodically invariant system-bath (PISB) model with two heat baths is an ideal platform not only for a periodical system but also for a system confined by a potential. We then derive the numerically ''exact'' hierarchical equations of motion (HEOM) for a discrete WDF in terms of periodically invariant operators in both coordinate and momentum spaces. The obtained equations can treat non-Markovian heat-bath in a non-perturbative manner at finite temperatures regardless of the mesh size. The stability of the present scheme is demonstrated in a high-temperature Markovian case by numerically integrating the discrete QFPE with by a coarse mesh for a 2D free rotor and harmonic potential systems for an initial condition that involves singularity.

scholarly journals Maps for analysis of nonlinear dynamics

1998 ◽  
Vol 2 ◽  
pp. 43-58
Author(s):  
Bronislovas Kaulakys
Keyword(s):  
Nonlinear Dynamics ◽  
Quantum Dynamics ◽  
Microwave Field ◽  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Driven Systems ◽  
Multilevel Systems ◽  
Area Preserving Maps ◽  
Area Preserving ◽  
Field Transition

Area preserving maps provide the simplest and most accurate means to visualize and quantify the behavior of nonlinear systems. Convenience of the mapping equations of motion for investigation of transition to chaotic behavior in dynamics of classical atom in microwave field, transition to nonchaotic behavior in randomly driven systems and induced quantum dynamics of simple and multilevel systems is demonstrated.

scholarly journals Long-time Dynamics of Spontaneous Parametric Down-conversion and Quantum Limitations of Conversion Efficiency

1999 ◽  
Vol 54 (1) ◽  
pp. 57-62 ◽  
Author(s):  
Michael Fleischhauer ◽  
Oliver Veits
Keyword(s):  
Quantum Dynamics ◽  
Equations Of Motion ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Time Dynamics ◽  
Pendulum Equation ◽  
Parametric Down Conversion ◽  
Long Time ◽  
Down Conversion

Abstract We analyze the long-time quantum dynamics of degenerate parametric down-conversion from an initial sub-harmonic vacuum (spontaenous down-conversion). Standard linearization of the Heisenberg equations of motion fails in this case, since it is based on an expansion around an unstable classical solution and neglects pump depletion. Introducing a mean-field approximation we find a periodic exchange of energy between the pump and subharmonic mode goverened by an anharmonic pendulum equation. From this equation the optimum interaction time or crystal length for maximum conversion can be determined. A numerical integration of the 2-mode Schrödinger equation using a dynamically optimized basis of displaced and squeezed number states verifies the characteristic times predicted by the mean-field approximation. In contrast to semiclassical and mean-field predictions it is found that quantum fluctuations of the pump mode lead to a substantial limitation of the efficiency of parametric down-conversion.

Convergence of exponential Lawson-multistep methods for the MCTDHF equations

2019 ◽  
Vol 53 (6) ◽  
pp. 2109-2119 ◽  
Author(s):  
Othmar Koch
Keyword(s):  
Quantum Dynamics ◽  
Multistep Methods ◽  
Equations Of Motion ◽  
Time Integration ◽  
Time Intervals ◽  
Numerical Illustration ◽  
Hartree Fock ◽  
Long Time ◽  
Long Time Integration ◽  
Adaptive Time

We consider exponential Lawson multistep methods for the time integration of the equations of motion associated with the multi-configuration time-dependent Hartree–Fock (MCTDHF) approximation for high-dimensional quantum dynamics. These provide high-order approximations at a minimum of evaluations of the computationally expensive nonlocal potential terms, and have been found to enable stable long-time integration. In this work, we prove convergence of the numerical approximation on finite time intervals under minimal regularity assumptions on the exact solution. A numerical illustration shows adaptive time propagation based on our methods.

scholarly journals Efficient quantum simulation of open quantum dynamics at various Hamiltonians and spectral densities

2021 ◽  
Vol 16 (5) ◽  
Author(s):  
Na-Na Zhang ◽  
Ming-Jie Tao ◽  
Wan-Ting He ◽  
Xin-Yu Chen ◽  
Xiang-Yu Kong ◽  
...  
Keyword(s):  
Quantum Dynamics ◽  
Quantum Simulation ◽  
Spectral Densities ◽  
Open Quantum
Sign in / Sign up

Export Citation Format

Share Document