QUANTUM PROPERTIES OF LIGHT IN LINEAR MEDIA WITH TIME-DEPENDENT PARAMETERS BY LEWIS–RIESENFELD INVARIANT OPERATOR METHOD

2005 ◽  
Vol 19 (14) ◽  
pp. 2213-2224 ◽  
Author(s):  
JEONG RYEOL CHOI ◽  
KYU HWANG YEON
Keyword(s):  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Scalar Potential ◽  
Operator Method ◽  
Invariant Operator ◽  
Quantum States ◽  
Time Dependent ◽  
Continuous Mode ◽  
Quantum Properties ◽  
Electric And Magnetic Fields

We investigated exact quantum states of the light confined in cubes filled with conductive media whose parameters are explicitly dependent on time and the light propagating under periodic boundary condition by making use of the LR (Lewis–Riesenfeld) invariant operator method. The choice of Coulomb gauge in the charge free space allowed us to evaluate quantized electric and magnetic fields by expanding only the vector potential, since the scalar potential is zero. We also described the fields with a spectrum of continuous mode, which can be obtained by setting the side L to infinity.

GEOMETRIC PHASES, SQUEEZED QUANTUM STATES AND GAUSSIAN WAVE PACKET STATES OF RELIC GRAVITONS

2012 ◽  
Vol 18 ◽  
pp. 13-17
Author(s):  
K. BAKKE ◽  
I. A. PEDROSA ◽  
C. FURTADO
Keyword(s):  
Wave Packet ◽  
Linear Time ◽  
Invariant Operator ◽  
Quantum States ◽  
Time Dependent ◽  
Gaussian Wave Packet ◽  
Geometric Phases ◽  
Uncertainty Product ◽  
Quantized Field ◽  
Generalized Time

In this contribution, we discuss quantum effects on relic gravitons described by the Friedmann-Robertson-Walker (FRW) spacetime background by reducing the problem to that of a generalized time-dependent harmonic oscillator, and find the corresponding Schrödinger states with the help of the dynamical invariant method. Then, by considering a quadratic time-dependent invariant operator, we show that we can obtain the geometric phases and squeezed quantum states for this system. Furthermore, we also show that we can construct Gaussian wave packet states by considering a linear time-dependent invariant operator. In both cases, we also discuss the uncertainty product for each mode of the quantized field.

On the dynamics of a time-dependent mesoscopic LC circuit with a negative inductance

2016 ◽  
Vol 30 (12) ◽  
pp. 1650122 ◽  
Author(s):  
I. A. Pedrosa ◽  
E. Nogueira ◽  
I. Guedes
Keyword(s):  
Magnetic Flux ◽  
Wave Packet ◽  
Operator Method ◽  
Invariant Operator ◽  
Time Dependent ◽  
Expectation Values ◽  
Gaussian States ◽  
Faraday’S Law ◽  
Uncertainty Product ◽  
Lc Circuit

We discuss the problem of a mesoscopic LC circuit with a negative inductance ruled by a time-dependent Hermitian Hamiltonian. Classically, we find unusual expressions for the Faraday’s law and for the inductance of a solenoid. Quantum mechanically, we solve exactly the time-dependent Schrödinger equation through the Lewis and Riesenfeld invariant operator method and construct Gaussian wave packet solutions for this time-dependent LC circuit. We also evaluate the expectation values of the charge and the magnetic flux in these Gaussian states, their quantum fluctuations and the corresponding uncertainty product.

COMPLETE EXACT QUANTUM STATES OF THE GENERALIZED TIME-DEPENDENT HARMONIC OSCILLATOR

2004 ◽  
Vol 18 (24) ◽  
pp. 1267-1274 ◽  
Author(s):  
I. A. PEDROSA
Keyword(s):  
General Solution ◽  
Harmonic Oscillator ◽  
Exact Solutions ◽  
Continuous Spectrum ◽  
Invariant Operator ◽  
Quantum States ◽  
Time Dependent ◽  
Quadratic Invariants ◽  
Generalized Time ◽  
Discrete And Continuous Spectrum

By making use of linear and quadratic invariants and the invariant operator formulation of Lewis and Riesenfeld, the complete exact solutions of the Schrödinger equation for the generalized time-dependent harmonic oscillator are obtained. It is shown that the general solution of the system under consideration contains both the discrete and continuous spectrum. The connection between linear and quadratic invariants and their corresponding eigenstates via time-dependent auxiliary equations is also established.

scholarly journals Analyzing Density Operator in Thermal State for Complicated Time-Dependent Optical Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Jeong Ryeol Choi ◽  
Ji Nny Song ◽  
Yeontaek Choi
Keyword(s):  
Optical System ◽  
Operator Theory ◽  
Density Operator ◽  
Thermal State ◽  
Invariant Operator ◽  
Quantum States ◽  
Time Dependent ◽  
Optical Systems ◽  
Time Varying ◽  
The One

Density operator of oscillatory optical systems with time-dependent parameters is analyzed. In this case, a system is described by a time-dependent Hamiltonian. Invariant operator theory is introduced in order to describe time-varying behavior of the system. Due to the time dependence of parameters, the frequency of oscillation, so-called a modified frequency of the system, is somewhat different from the natural frequency. In general, density operator of a time-dependent optical system is represented in terms of the modified frequency. We showed how to determine density operator of complicated time-dependent optical systems in thermal state. Usually, density operator description of quantum states is more general than the one described in terms of the state vector.

scholarly journals Time-dependent particle production and particle number in cosmological de Sitter space

2015 ◽  
Vol 24 (05) ◽  
pp. 1550031 ◽  
Author(s):  
Eric Greenwood
Keyword(s):  
Particle Production ◽  
Occupation Number ◽  
Operator Method ◽  
Large Mass ◽  
Invariant Operator ◽  
Time Dependent ◽  
De Sitter ◽  
Power Law Distribution ◽  
Bogolyubov Transformation ◽  
Thermal Distribution

In this paper, we consider the occupation number of induced quasi-particles which are produced during a time-dependent process using three different methods: Instantaneous diagonalization, the usual Bogolyubov transformation between two different vacua (more precisely the instantaneous vacuum and the so-called adiabatic vacuum), and the Unruh–DeWitt detector methods. Here we consider the Hamiltonian for a time-dependent Harmonic oscillator, where both the mass and frequency are taken to be time-dependent. From the Hamiltonian we derive the occupation number of the induced quasi-particles using the invariant operator method. In deriving the occupation number we also point out and make the connection between the Functional Schrödinger formalism, quantum kinetic equation, and Bogolyubov transformation between two different Fock space basis at equal times and explain the role in which the invariant operator method plays. As a concrete example, we consider particle production in the flat FRW chart of de Sitter spacetime. Here we show that the different methods lead to different results: The instantaneous diagonalization method leads to a power law distribution, while the usual Bogolyubov transformation and Unruh–DeWitt detector methods both lead to thermal distributions (however the dimensionality of the results are not consistent with the dimensionality of the problem; the usual Bogolyubov transformation method implies that the dimensionality is 3D while the Unruh–DeWitt detector method implies that the dimensionality is 7D/2). It is shown that the source of the descrepency between the instantaneous diagonalization and usual Bogolyubov methods is the fact that there is no notion of well-defined particles in the out vacuum due to a divergent term. In the usual Bogolyubov method, this divergent term cancels leading to the thermal distribution, while in the instantaneous diagonalization method there is no such cancelation leading to the power law distribution. However, to obtain the thermal distribution in the usual Bogolyubov method, one must use the large mass limit. On physical grounds, one should expect that only the modes which have been allowed to sample the horizon would be thermal, thus in the large mass limit these modes are well within the horizon and, even though they do grow, they remain well within the horizon due to the mass. Thus, one should not expect a thermal distribution since the modes will not have a chance to thermalize.

OPERATOR METHOD FOR A NONCONSERVATIVE HARMONIC OSCILLATOR WITH AND WITHOUT SINGULAR PERTURBATION

2002 ◽  
Vol 16 (31) ◽  
pp. 4733-4742 ◽  
Author(s):  
JEONG RYEOL CHOI ◽  
BO HA KWEON
Keyword(s):  
Singular Perturbation ◽  
Harmonic Oscillator ◽  
Operator Method ◽  
Invariant Operator ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
Expectation Values ◽  
Ladder Operators ◽  
Raising Operators ◽  
Quantum Mechanical Solution

We used dynamical invariant operator method to find the quantum mechanical solution of a harmonic plus inverse harmonic oscillator with time-dependent coefficients. The eigenvalue of invariant operator is obtained and is constant with time. We constructed lowering and raising operators from the invariant operator. The solution of Schrödinger equation is obtained using operator method. We have also used ladder operators to obtain various expectation values of the time-dependent system. The results in this manuscript are not only more general than the existing results in the literatures but also well match with others.

COMMUTATION RELATIONS AND SELF-CONSISTENCY IN ELECTRODYNAMICS FOR THE FIELDS IN TIME-VARYING MEDIA

2008 ◽  
Vol 22 (03) ◽  
pp. 267-280 ◽  
Author(s):  
JEONG RYEOL CHOI ◽  
JUN-YOUNG OH
Keyword(s):  
Commutation Relation ◽  
Operator Method ◽  
Equation Of Motion ◽  
Invariant Operator ◽  
Time Dependent ◽  
Heisenberg Equation ◽  
Time Varying ◽  
Commutation Relations ◽  
Self Consistent ◽  
Self Consistency

In linear media with time-dependent parameters, various commutation relations for the field operators obtained from the Lewis–Riesenfeld invariant operator method are calculated. We investigated whether our development is self-consistent or not by evaluating the Heisenberg equation of motion for field operators using the associated commutation relation.

A Temperature Fourier Series Solution for a Hollow Sphere

2006 ◽  
Vol 128 (9) ◽  
pp. 963-968 ◽  
Author(s):  
Gholamali Atefi ◽  
Mahdi Moghimi
Keyword(s):  
Boundary Condition ◽  
Fourier Series ◽  
Hollow Sphere ◽  
Periodic Boundary Condition ◽  
Series Solution ◽  
Periodic Boundary ◽  
Solid Sphere ◽  
Time Dependent ◽  
Two Dimensional ◽  
Theoretical Results

In this paper, we derive an analytical solution of a two-dimensional temperature field in a hollow sphere subjected to periodic boundary condition. The material is assumed to be homogeneous and isotropic with time-independent thermal properties. Because of the time-dependent term in the boundary condition, Duhamel’s theorem is used to solve the problem for a periodic boundary condition. The boundary condition is decomposed by Fourier series. In order to check the validity of the results, the technique was also applied to a solid sphere under harmonic boundary condition for which theoretical results were available in the literature. The agreement between the results of the proposed method and those reported by others for this particular geometry under harmonic boundary condition was realized to be very good, confirming the applicability of the technique utilized in the present work.

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