Asymmetrical quantum sextic anharmonic oscillator: Eigenstates and thermal properties

Lee, J. Y.; Liu, K. L.; Lo, Chi‐Fai

doi:10.1103/physreva.58.3433

Cited by 11 publications

(5 citation statements)

References 21 publications

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“…In this paper, we use unitary transformation method in order to derive quantum mechanical solution of non-dissipative mesoscopic inductance coupled circuit with a power source. Although many actual dynamical systems have been solved approximately using perturbation theory [37][38][39][40][41], we confine our concern to the investigation of the exact solution of the Schrödinger equation of the system. This paper is organized in the following order.…”

Section: Introductionmentioning

confidence: 99%

Type II Superconducting Cylindrical Filament in a Non-Uniform Parallel Magnetic Field

Masale¹

2003

Phys. Scr.

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By means of a two-step unitary transformation, the exact quantum mechanical solution of two-dimensional mesoscopic circuit coupled via inductance is derived. The wavefunction, propagator and expectation value of Hamiltonian are evaluated. The fluctuations of charges and currents are calculated and uncertainty products between charges and their conjugate currents are obtained. We apply our results to the system with special cases of the power source such as the sinusoidal and the sawtooth power source and show that the probability densities oscillate with time due to the power source.

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Section: Introductionmentioning

confidence: 99%

Type II Superconducting Cylindrical Filament in a Non-Uniform Parallel Magnetic Field

Masale¹

2003

Phys. Scr.

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“…To illustrate the aforementioned features, we show in figure 1 the response of a system with the symmetric double-well potential U 4 (x) = (−0.5x 2 + 0.25x 4 ) and D = 0.3, for different degrees of subdiffusiveness. Our eigenfunctions and eigenvalues are obtained by the state-dependent diagonalization method [34]. The series shown in equations ( 24) and ( 26) are found to converge rapidly.…”

Section: Response To a Rectangular Pulsementioning

confidence: 99%

“…] osc , where the second term, associated with the coefficients given in equation (34), can be written as a Fourier series…”

Section: Response To a Telegraph Signalmentioning

confidence: 99%

“…When a similar long-period approximation is applied to equation (34), we obtain [a n (t; γ )] res λ −1 n H (t) which, by equation ( 19), leads to P 1 (x, t) D −1 H (t)(X 00 −x)P 0 (x) for large t. It can be verified that this P 1 indeed yields the asymptotic secular linear response mentioned above. The corresponding PDF is given by P (x, t) = P 0 (x)…”

Section: Response To a Telegraph Signalmentioning

confidence: 99%

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The response of subdiffusive bistable fractional Fokker–Planck systems to rectangular signals

Yim¹,

Liu

2007

J. Phys. A: Math. Theor.

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We study the response of one-dimensional subdiffusive fractional Fokker–Planck systems with a general confining potential, when it is perturbed from its stationary state by a time-dependent non-sinusoidal driving force. Three types of rectangular driving signals have been investigated: a rectangular pulse, a periodic telegraph signal and a generalized telegraph signal with a fractional duty cycle. We derive analytic expressions for the linear response and the input energy in one period of the driving signal. In particular, for signals with a long period, we obtain several asymptotic results concerning the wave form of the response and the stochastic energetics. Numerical results for representative symmetric, as well as asymmetric, subdiffusive bistable systems are presented and discussed.

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“…We will do the same for the system that replaced the ordinary effective mass with a time-dependent effective mass. Although many actual dynamical systems have been solved approximately using perturbation theory [24][25][26],we will confine our concern with the investigation of the exact quantum theory of the system. In most of the cases, the evolution of the time-dependent systems are periodic.…”

Section: Introductionmentioning

confidence: 99%

Exact quantum theory of noninteracting electrons with time-dependent effective mass in a time-dependent magnetic field

Choi

2003

J. Phys.: Condens. Matter

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We investigated the quantum states of a free electron with time-dependent effective mass subjected to a time-dependent magnetic field by solving the Schrödinger equation under the choice of Landau and symmetric gauges. Using the invariant operator and unitary transformation methods together, we derived exact wavefunctions of the system. The wavefunctions rely on the solution of associated classical dynamical systems. We confirmed that the quantum analysis of the system under the two gauges coincides mutually.

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Asymmetrical quantum sextic anharmonic oscillator: Eigenstates and thermal properties

Cited by 11 publications

References 21 publications

Type II Superconducting Cylindrical Filament in a Non-Uniform Parallel Magnetic Field

Type II Superconducting Cylindrical Filament in a Non-Uniform Parallel Magnetic Field

The response of subdiffusive bistable fractional Fokker–Planck systems to rectangular signals

Exact quantum theory of noninteracting electrons with time-dependent effective mass in a time-dependent magnetic field

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