scholarly journals Evolution of coherent states as quantum counterpart of classical dynamics

2021 ◽  
Vol 104 (8) ◽  
Author(s):  
Lasha Berezhiani ◽  
Michael Zantedeschi
Keyword(s):  
Coherent States ◽  
Classical Dynamics ◽  
Quantum Counterpart

scholarly journals QUANTUM DYNAMICS OF THE CUBIT SYSTEM IN EXTERNAL FIELDS

2021 ◽  
Vol 26 (4) ◽  
pp. 68-75
Author(s):  
A. V. Gorokhov ◽  
G. I. Eremenko
Keyword(s):  
Symmetry Group ◽  
Time Evolution ◽  
Coherent States ◽  
Quantum Dynamics ◽  
Dynamic Symmetry ◽  
Classical Dynamics ◽  
External Fields

A system of two dipole-dipole interacting two-level elements (qubits) in external fields is considered. It is shown that using the coherent states (CS) of the dynamic symmetry group of the SU(2)SU(2) system, the time evolution can be reduced to the "classical" dynamics of the complex parameters of the CS. The trajectories of the CS are constructed and the time dependences of the probability of finding qubits at the upper levels are calculated.

scholarly journals Paths of canonical transformations and their quantization

2015 ◽  
Vol 27 (06) ◽  
pp. 1530003 ◽  
Author(s):  
Maurice A. de Gosson
Keyword(s):  
Quantum Mechanics ◽  
Classical Mechanics ◽  
Hamiltonian Function ◽  
Hamiltonian Mechanics ◽  
Classical Dynamics ◽  
Classical Concept ◽  
Metaplectic Representation ◽  
Hamiltonian Flows ◽  
Close Relationship ◽  
Quantum Counterpart

In their simplest formulations, classical dynamics is the study of Hamiltonian flows and quantum mechanics of propagators. Both are linked, and emerge from the datum of a single classical concept, the Hamiltonian function. We study and emphasize the analogies between Hamiltonian flows and quantum propagators; this allows us to verify G. Mackey's observation that quantum mechanics (in its Weyl formulation) is a refinement of Hamiltonian mechanics. We discuss in detail the metaplectic representation, which very explicitly shows the close relationship between classical mechanics and quantum mechanics; the latter emerging from the first by lifting Hamiltonian flows to the double covering of the symplectic group. We also give explicit formulas for the factorization of Hamiltonian flows into simpler flows, and prove a quantum counterpart of these results.

scholarly journals CONTINUOUS VARIABLE QUANTUM KEY DISTRIBUTION USING POLARIZED COHERENT STATES

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1287-1296 ◽  
Author(s):  
A. VIDIELLA-BARRANCO ◽  
L. F. M. BORELLI
Keyword(s):  
Quantum Key Distribution ◽  
Coherent States ◽  
Key Distribution ◽  
Continuous Variable ◽  
Stokes Parameters ◽  
Continuous Variables ◽  
Commuting Operators ◽  
Incoming Beam ◽  
Ideal Situation ◽  
Quantum Counterpart

We discuss a continuous variables method of quantum key distribution employing strongly polarized coherent states of light. The key encoding is performed using the variables known as Stokes parameters, rather than the field quadratures. Their quantum counterpart, the Stokes operators Ŝi ( i =1,2,3), constitute a set of non-commuting operators, being the precision of simultaneous measurements of a pair of them limited by an uncertainty-like relation. Alice transmits a conveniently modulated two-mode coherent state, and Bob randomly measures one of the Stokes parameters of the incoming beam. After performing reconciliation and privacy amplification procedures, it is possible to distill a secret common key. We also consider a non-ideal situation, in which coherent states with thermal noise, instead of pure coherent states, are used for encoding.

scholarly journals Static Coherent States Method: One- and Two-Electron Laser-Induced Systems with Classical Nuclear Dynamics

2018 ◽  
Vol 8 (8) ◽  
pp. 1252 ◽  
Author(s):  
Mohammadreza Eidi ◽  
Mohsen Vafaee ◽  
Alexandra Landsman
Keyword(s):  
Coherent States ◽  
Equations Of Motion ◽  
Intense Laser ◽  
Classical Dynamics ◽  
Electron Dynamics ◽  
Charge Migration ◽  
Nuclear Dynamics ◽  
Charge Localization ◽  
Quantum Electron ◽  
State Potential

In this report, we introduce the static coherent states (SCS) method for investigating quantum electron dynamics in a one- or two-electron laser-induced system. The SCS method solves the time-dependent Schrödinger equation (TDSE) both in imaginary and real times on the basis of a static grid of coherent states (CSs). Moreover, we consider classical dynamics for the nuclei by solving their Newtonian equations of motion. By implementing classical nuclear dynamics, we compute the electronic-state potential energy curves of H2+ in the absence and presence of an ultra-short intense laser field. We used this method to investigate charge migration in H2+. In particular, we found that the charge migration time increased exponentially with inter-nuclear distance. We also observed substantial charge localization for sufficiently long molecular bonds.

Coherent states and localization in a quantized discrete NLS lattice

2016 ◽  
Vol 25 (04) ◽  
pp. 1650047 ◽  
Author(s):  
R. Martinez-Galicia ◽  
Panayotis Panayotaros
Keyword(s):  
Coherent States ◽  
Initial Conditions ◽  
Classical System ◽  
Classical Dynamics ◽  
Nonlinear Schrödinger

We study the evolution of a quantum discrete nonlinear Schrödinger (DNLS) system using as initial conditions coherent states corresponding to points in the vicinity of breather solutions of the classical system. We consider various examples of stable and unstable breathers and examine the distance between exactly evolved states and coherent states with parameters that evolve according to classical dynamics. Initial conditions near stable breathers and their vicinity are seen to lead to recurrences to small distances between the two evolving states. Similar recurrences are not observed for initial conditions near unstable breathers.

Gazeau- Klouder Coherent states on a sphere

2019 ◽  
Vol 19 (2) ◽  
pp. 379-390
Author(s):  
Z Heibati ◽  
A Mahdifar ◽  
E Amooghorban ◽  
◽  
◽  
...  
Keyword(s):  
Coherent States

Quantum simulations

2017 ◽  
Author(s):  
Michael P. Allen ◽  
Dominic J. Tildesley
Keyword(s):  
Ab Initio ◽  
Quantum Monte Carlo ◽  
Degrees Of Freedom ◽  
Small Region ◽  
Time Correlation ◽  
Ab Initio Molecular Dynamics ◽  
Classical Dynamics ◽  
Integral Methods ◽  
Quantum Time ◽  
Low Mass

This chapter covers the introduction of quantum mechanics into computer simulation methods. The chapter begins by explaining how electronic degrees of freedom may be handled in an ab initio fashion and how the resulting forces are included in the classical dynamics of the nuclei. The technique for combining the ab initio molecular dynamics of a small region, with classical dynamics or molecular mechanics applied to the surrounding environment, is explained. There is a section on handling quantum degrees of freedom, such as low-mass nuclei, by discretized path integral methods, complete with practical code examples. The problem of calculating quantum time correlation functions is addressed. Ground-state quantum Monte Carlo methods are explained, and the chapter concludes with a forward look to the future development of such techniques particularly to systems that include excited electronic states.

scholarly journals Semi-Classical Localisation Properties of Quantum Oscillators on a Noncommutative Configuration Space

2015 ◽  
Vol 22 (04) ◽  
pp. 1550021 ◽  
Author(s):  
Fabio Benatti ◽  
Laure Gouba
Keyword(s):  
Phase Space ◽  
Configuration Space ◽  
Classical Limit ◽  
Coherent States ◽  
Point Of View ◽  
Quantum Mechanical ◽  
Wigner Functions ◽  
Quantum Mechanical Oscillators ◽  
Mechanical Oscillators ◽  
Space Noncommutativity

When dealing with the classical limit of two quantum mechanical oscillators on a noncommutative configuration space, the limits corresponding to the removal of configuration-space noncommutativity and position-momentum noncommutativity do not commute. We address this behaviour from the point of view of the phase-space localisation properties of the Wigner functions of coherent states under the two limits.

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