Crossover-Time in Quantum Boson and Spin Systems by Gennady P. BermanCrossover-Time in Quantum Boson and Spin Systems by Gennady P. Berman

Crossover-Time in Quantum Boson and Spin Systems

byGennady P. Berman, Evgeny N. Bulgakov, Darryl D. Holm

Paperback | November 10, 2013

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We consider quantum dynamical systems (in general, these could be either Hamiltonian or dissipative, but in this review we shall be interested only in quantum Hamiltonian systems) that have, at least formally, a classical limit. This means, in particular, that each time-dependent quantum-mechanical expectation value X (t) has as i cl Ii -+ 0 a limit Xi(t) -+ x1 )(t) of the corresponding classical sys­ tem. Quantum-mechanical considerations include an additional di­ mensionless parameter f = iiiconst. connected with the Planck constant Ii. Even in the quasiclassical region where f<_20_12c_20_the20_dyc2ad_20_namics20_of20_the20_quantum20_and20_classicalfunctions20_xi28_t29_20_and20_xiccl29_28_t29_20_will20_be20_different2c_20_in20_general2c_20_and20_quantum20_dynamics20_for20_expectation20_valc2ad_20_ues20_may20_coincide20_with20_classical20_dynamics20_only20_for20_some20_finite20_time.20_this20_characteristic20_time-scale2c_20_tii.2c_20_could20_depend20_on20_several20_factors20_which20_will20_be20_discussed20_below2c_20_including3a_20_choice20_of20_expectation20_valc2ad_20_ues2c_20_initial20_state2c_20_physical20_parameters20_and20_so20_on.20_thus2c_20_the20_problem20_arises20_in20_this20_connection3a_20_how20_to20_estimate20_the20_characteristic20_timec2ad_20_scale20_tii.20_of20_the20_validity20_of20_the20_quasiclassical20_approximation20_and20_how20_to20_measure20_it20_in20_an20_experiment3f_20_for20_rather20_simple20_integrable20_quanc2ad_20_tum20_systems20_in20_the20_stable20_regions20_of20_motion20_of20_their20_corresponding20_classical20_phase20_space2c_20_this20_time-scale20_t22_20_usually20_is20_of20_order20_28_see2c_20_for20_example2c_20_5b_25d_29_20_const20_tii.20_3d_20_p2c_li20_2c_20_28_1.129_20_q20_where20_p2c_20_is20_the20_dimensionless20_parameter20_of20_nonlinearity20_28_discussed20_below29_20_and20_a20_is20_a20_constant20_of20_the20_order20_of20_unity. _12c_="" the="" _dyc2ad_="" namics="" of="" quantum="" and="" classicalfunctions="" _xi28_t29_="" _xiccl29_28_t29_="" will="" be="" _different2c_="" in="" _general2c_="" dynamics="" for="" expectation="" _valc2ad_="" ues="" may="" coincide="" with="" classical="" only="" some="" finite="" time.="" this="" characteristic="" _time-scale2c_="" _tii.2c_="" could="" depend="" on="" several="" factors="" which="" discussed="" _below2c_="" _including3a_="" choice="" _ues2c_="" initial="" _state2c_="" physical="" parameters="" so="" on.="" _thus2c_="" problem="" arises="" _connection3a_="" how="" to="" estimate="" _timec2ad_="" scale="" tii.="p%2cli" validity="" quasiclassical="" approximation="" measure="" it="" an="" _experiment3f_="" rather="" simple="" integrable="" _quanc2ad_="" tum="" systems="" stable="" regions="" motion="" their="" corresponding="" phase="" _space2c_="" time-scale="" _t22_="" usually="" is="" order="" _28_see2c_="" _example2c_="" _5b_25d_29_="" const="" _2c_="" _28_1.129_="" q="" where="" _p2c_="" dimensionless="" parameter="" nonlinearity="" _28_discussed="" _below29_="" a="" constant="">
Title:Crossover-Time in Quantum Boson and Spin SystemsFormat:PaperbackDimensions:268 pages, 23.5 × 15.5 × 0.07 inPublished:November 10, 2013Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3662145065

ISBN - 13:9783662145067

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Table of Contents

Method of Coherent States.- The Exact C-Number Equation for Time-Dependent Expectation Values in Coherent States.- Quasiclassical Perturbation Theory for Time-Dependent Expectation Values with Quantum Nonlinear Hamiltonians.- The Characteristic Times of Violation of Quasiclassical Approximation for Integrable Boson and Spin Systems.- Time-Scale ?? for a Kicked Quantum Nonlinear Oscillator.- The Time of Applicability of the Quasiclassical Approach in a Boson System of Two Interacting Quantum Nonlinear Resonances.- Two Interacting Quantum Nonlinear Resonances in a Spin System.- Quantization of a Stochastic Web.- Characteristic Times for Chaotic Dynamics in Wigner Representation.- Quantum Chaos of Atoms in a Resonant Cavity.- Quantum Chaos of Atoms in a Resonant Cavity Driven by an External Resonant Field.- Violation of the Semiclassical Approximation and Quantum Chaos in a Paramagnetic Spin System.- Weak Quantum Chaos in a System of N Atoms in a Resonant Cavity Interacting with an External Resonant Field.- Quantum Dynamics in Stationary Coherent States (SCS).- Discussion.