Justification of the “symmetric damping” model of the dynamical Casimir effect in a cavity with a semiconductor mirror*

A “microscopic” justification of the “symmetric damping” model of a quantum oscillator with time-dependent frequency and time-dependent damping is given. This model is used to predict the results of experiments on simulating the dynamical Casimir effect in a cavity with a photo-excited semiconductor mirror. It is shown that the most general bilinear time-dependent coupling of a selected oscillator (field mode) to a bath of harmonic oscillators results in two equal friction coefficients for the both quadratures, provided all the coupling coefficients are proportional to a single arbitrary function of time whose duration is much shorter than the periods of all oscillators. The choice of coupling in the rotating wave approximation form leads to the “minimum noise” model of the quantum damped oscillator, introduced earlier in a pure phenomenological way.     

Dynamics of a quantum oscillator strongly and off-resonantly coupled with a two-level system

Beyond the rotating-wave approximation, the dynamics of a quantum oscillator interacting strongly and off-resonantly with a two-level system exhibit beatings, whose period equals the revival time of the two-level system. On a longer time scale, the quantum oscillator shows collapses, revivals and fractional revivals, which are encountered in oscillator observables like the mean number of oscillator quanta and in the two-level inversion population. Also the scattered oscillator field shows doublets with symmetrically displaced peaks.     

Time Dependence of Joint Entropy of Oscillating Quantum Systems

The time dependent entropy (or Leipnik’s entropy) of harmonic and damped harmonic oscillator systems is studied by using time dependent wave function obtained by the Feynman path integral method. The Leipnik entropy and its envelope change as a function of time, angular frequency and damping factor. Our results for simple harmonic oscillator are in agreement with the literature. However, the joint entropy of damped harmonic oscillator shows remarkable discontinuity with time for certain values of damping factor. The envelope of the joint entropy curve increases with time monotonically. These results show the general properties of the envelope of the joint entropy curve for quantum systems.     

Gravitational induced uncertainty and dynamics of harmonic oscillator

As a consequence of gravitational induced uncertainty, equation of motion for harmonic oscillator differs considerably from usual quantum mechanical situation. This paper considers the dynamics of a simple harmonic oscillator in the context of Generalized (Gravitational) Uncertainty Principle (GUP). Using Heisenberg Picture of quantum mechanics, we find time evolution of position and momentum operators and we will show that expectation values have an unusual complicated mass dependence. Also we will show that since the notion of locality breaks down, Ehrenfest theorem is not satisfied for harmonic oscillator in GUP.     

Effect of free electron-hole pairs on the saturation of excitonic absorption in GaAs/AlGaAs quantum wells

The pump-probe experimental method is used to investigate the effect of photoexcited carriers on the dynamics of the exciton absorption spectra of GaAs / Al_xGa_1–x As-multilayer quantum wells. Use of the method of moment analysis for processing the results makes it possible to identify the simultaneous contribution of changes in oscillator strength and width of the exciton lines in the saturation of exciton absorption. It was found that the oscillator strength recovers its initial value in the course of the first 100–130 ps, whereas broadening and energy-shift of the exciton lines is observed for 700–800 ps. These are the first experimental measurements of the excitation densities at which the oscillator strength of the excitonic state saturates when the latter is perturbed only by free-electron-hole pairs, and when it is perturbed only by other excitons. Fiz. Tverd. Tela (St. Petersburg) 40, 1130–1133 (June 1998)     

Problem of the choice of time in cosmology

A class of gauge conditions is obtained from an isotropic cosmological model with a conformally invariant scalar field, leading to a Hamiltonian dynamics with a time independent Hamiltonian which coincides with that of a harmonic oscillator. The quantum dynamics of the model is considered, and the inevitability of a singularity in its quantum version is shown.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 29–32, January, 1990.In conclusion, the authors thank L. D. Faddeev and V. V. Nesterenko for useful discussions.     

Wigner's pseudo-particle relativistic dynamics in external potential field

The Wigner's pseudo-particle formalism has been generalized to describe quantum dynamics of relativistic particle in external potential field. As a simplest application of the developed formalism the time evolution of the 1D relativistic quantum harmonic oscillator been considered. Due to the complex structure of the evolution equation for Wigner function, the only numerical treatment is possible by combining Monte Carlo and molecular dynamics methods. Relativistic dynamics results in appearance of the new physical effects as opposed to non-relativistic case. Interesting is the complete changing of the shape of the momentum and coordinate distribution functions as well as formation of ‘unexpected’ protuberances. To analyze the influence of relativistic effects on average values of quantum operators, the dependencies on time of average momentum, position, their dispersions and energy have been compared for the non-relativistic and relativistic dynamics.     

Molecular motion under the influence of a coherent infrared-laser field

The quantum dynamics of molecular vibrations under the influence of coherent infrared-laser multiphoton excitation is irregular, in most cases, on the time scale of experimental interest. This irregularity arises from the anharmonic nature of the molecular force fields and is already present in one dimensional anharmonic oscillators. We analyse the onset of the irregularity in the model of a Morse oscillator and discuss the role of statistical or “chaotic” behaviour of the time dependent probability density. We further discuss the role of direct multiphoton excitation in these multilevel systems and compare the results with exact solutions for the harmonic oscillator.     

A density matrix approach to the dynamical properties of a two-site Holstein model

The two-site Holstein model represents a first non-trivial paradigm for the interaction between an itinerant charge with a quantum oscillator, a very common topic in different ambits. Exact results can be achieved both analytically and numerically, nevertheless it can be useful to compare them with approximate, semi-classical techniques in order to highlight the role of quantum effects. In this paper we consider the adiabatic limit in which the oscillator is slower than the electron. A density matrix approach is introduced for studying the charge dynamics and the exact results are compared with two different approximations: a Born-Oppenheimer-based Static Approximation for the oscillator (SA) and a Quantum-classical (QC) dynamics.     

Quantum Dynamics in Noisy Backgrounds: from Sampling to Dissipation and Fluctuations

We investigate the dynamics of a quantum system coupled linearly to Gaussian white noise using functional methods. By performing the integration over the noisy field in the evolution operator, we get an equivalent non-Hermitian Hamiltonian, which evolves the quantum state with a dissipative dynamics. We also show that if the integration over the noisy field is done for the time evolution of the density matrix, a gain contribution from the fluctuations can be accessed in addition to the loss one from the non-hermitian Hamiltonian dynamics. We illustrate our study by computing analytically the effective non-Hermitian Hamiltonian, which we found to be the complex frequency harmonic oscillator, with a known evolution operator. It leads to space and time localisation, a common feature of noisy quantum systems in general applications.     

The crossover from classical to quantum behavior in Duffing oscillator based on quantum state diffusion

The classical Duffing oscillator is a dissipative chaotic system, and so there is not a definite Hamiltonian. We quantize the Duffing oscillator on the basis of quantum state diffusion (QSD) which is a formulation for open quantum systems and a useful tool for analyzing nonlinear problems and classical limits. We can define a ‘Lyapunov exponent’, which corresponds to the classical one in the proper limit, and investigate the behavior of the system by varying the Planck constant effectively. We show that there exists a critical stage, where the behavior of the system crosses over from classical to quantum one.     

Dynamics of excitonic states in GaAs/AlGaAs quantum wells

The influence of photoexcited carriers on the dynamics of the absorption spectra of GaAs/Al_xGa_1−2x As multilayer quantum wells is investigated experimentally. It is found that at quasiparticle densities all the way up to 10¹¹ cm⁻² the saturation of the excitonic absorption is due to both a decrease of oscillator strength and broadening of the excitonic lines. It is shown that in the case of femtosecond resonance laser exci-tation the decrease of oscillator strength is due to free electron-hole pairs, while the broadening and energy shift of the excitonic lines are due to the exciton-exciton interaction. The lifetimes of free electron-hole pairs and excitons (≈65 ps and ≈410 ps, respectively) are determined from the exponential decrease of the change in the oscillator strength and in the width and energy position of the excitonic lines. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 3, 139–144 (10 August 1997)     

Wigner dynamics of quantum semi-relativistic oscillator

The integral Wigner–Liouville equation describing time evolution of the semi-relativistic quantum 1D harmonic oscillator have been exactly solved by combination of the Monte Carlo procedure and molecular dynamics methods. The strong influence of the relativistic effects on the time evolution of the momentum, velocity and coordinate Wigner distribution functions and the average values of quantum operators have been studied. Unexpected ‘protuberances’ in time evolution of the distribution functions were observed. Relativistic proper time dilation for oscillator have been calculated.     

Quantum chaos production in anharmonic oscillator under train of Gaussian pulses

The regimes of quantum chaos for anharmonic oscillator under train of Gaussian pulses are studied depending on the pulse parameters. The presented results are derived in the semiclassical limit within the framework of Poincaré section and Lyapunov exponent. In the quantum limit the regimes of chaos are considered on the basis of the Wigner function. Relations between system parameters are found when chaotic dynamics appears at mesoscopic level of oscillator excitation numbers.     

Gauge covariant construction of the coherent states for a time-dependent harmonic oscillator by algebraic dynamical method

Time-dependent coherent states for a time-dependent harmonic oscillator are constructed in the framework of algebraic dynamics. These coherent states are gauge-covariant, and its time evolution is governed only by the solutions of a linear differential equation which describes the motion of the corresponding classical timedependent harmonic oscillator. Its non-classical and quantum statistical properties can thus be controlled by a proper choice of the frequency of the harmonic oscillator. Our coherent states reduce to Glauber coherent states in the case as the frequency is independent of time.     

Dynamics of Time Evolution of Quantum Oscillator Excitation by Electromagnetic Pulses

Journal of Experimental and Theoretical Physics - The dynamics of time evolution of quantum oscillator excitation by electromagnetic pulses is investigated theoretically for an arbitrary field...