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.

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.

scholarly journals Climate change, in the framework of the constructal law

2011 ◽  
Vol 2 (1) ◽  
pp. 241-270 ◽  
Author(s):  
M. Clausse ◽  
F. Meunier ◽  
A. H. Reis ◽  
A. Bejan
Keyword(s):  
Time Scales ◽  
Thermal State ◽  
Thermal Inertia ◽  
Thermal Response ◽  
Continuous Model ◽  
Time Dependent ◽  
Heat Current ◽  
Constructal Law ◽  
Complex Models ◽  
The One

Abstract. Here we present a simple and transparent alternative to the complex models of Earth thermal behavior under time-changing conditions. We show the one-to-one relationship between changes in atmospheric properties and time-dependent changes in temperature and its distribution on Earth. The model accounts for convection and radiation, thermal inertia and changes in albedo (ρ) and greenhouse factor (γ). The constructal law is used as the principle that governs the evolution of flow configuration in time, and provides closure for the equations that describe the model. In the first part of the paper, the predictions are tested against the current thermal state of Earth. Next, the model showed that for two time-dependent scenarios, (δρ = 0.002; δγ = 0.011) and (δρ = 0.002; δγ = 0.005) the predicted equatorial and polar temperature increases and the time scales are (ΔTH = 1.16 K; ΔTL = 1.11 K; 104 years) and (0.41 K; 0.41 K; 57 years), respectively. In the second part, a continuous model of temperature variation was used to predict the thermal response of the Earth's surface for changes bounded by δρ = δγ and δρ = −δγ. The results show that the global warming amplitudes and time scales are consistent with those obtained for δρ = 0.002 and δγ = 0.005. The poleward heat current reaches its maximum in the vicinity of 35° latitude, accounting for the position of the Ferrel cell between the Hadley and Polar Cells.

QUANTUM AND THERMAL STATE FOR EXPONENTIALLY DAMPED HARMONIC OSCILLATOR WITH AND WITHOUT INVERSE QUADRATIC POTENTIAL

2002 ◽  
Vol 16 (09) ◽  
pp. 1341-1351 ◽  
Author(s):  
J. R. CHOI
Keyword(s):  
Harmonic Oscillator ◽  
Density Operator ◽  
Thermal State ◽  
Mechanical Energy ◽  
Invariant Operator ◽  
Diagonal Element ◽  
Quadratic Potential ◽  
Damped Harmonic Oscillator ◽  
Energy Expectation ◽  
Quantum Mechanical Energy

By taking advantage of dynamical invariant operator, we derived Schrödinger solution for exponentially damped harmonic oscillator with and without inverse quadratic potential. We investigated quantum mechanical energy expectation value, uncertainty relation, partition function and density operator of the system. The various expectation values in thermal state are calculated using the diagonal element of density operator.

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 Analysis of Novel Oscillations of Quantized Mechanical Energy in Mass-Accreting Nano-Oscillator Systems

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 153
Author(s):  
Jeong Ryeol Choi
Keyword(s):  
Quantum Theory ◽  
Hamiltonian Systems ◽  
Operator Theory ◽  
Mechanical Energy ◽  
Invariant Operator ◽  
The Other ◽  
Time Dependent ◽  
Mathematical Tool ◽  
Quantum Energy ◽  
Reasonable Explanation

Quantum characteristics of a mass-accreting oscillator are investigated using the invariant operator theory, which is a rigorous mathematical tool for unfolding quantum theory for time-dependent Hamiltonian systems. In particular, the quantum energy of the system is analyzed in detail and compared to the classical one. We focus on two particular cases; one is a linearly mass-accreting oscillator and the other is an exponentially mass-accreting one. It is confirmed that the quantum energy is in agreement with the classical one in the limit ℏ→0. We showed that not only the classical but also the quantum energy oscillates with time. It is carefully analyzed why the energy oscillates with time, and a reasonable explanation for that outcome is given.

WAVE FUNCTIONS OF TIME-DEPENDENT TWO COUPLED OSCILLATORS BY LEWIS–RIESENFELD METHOD

2006 ◽  
Vol 20 (09) ◽  
pp. 1087-1096 ◽  
Author(s):  
HONG-YI FAN ◽  
ZHONG-HUA JIANG
Keyword(s):  
Schrödinger Equation ◽  
Operator Theory ◽  
Coupled Oscillators ◽  
Coherent States ◽  
Schrodinger Equation ◽  
Invariant Operator ◽  
Wave Functions ◽  
Time Dependent ◽  
General Solutions ◽  
Eigenvectors And Eigenvalues

For the two time-dependent coupled oscillators model we derive its time-dependent invariant in the context of Lewis–Riesenfeld invariant operator theory. It is based on the general solutions to the Schrödinger equation which is obtained and turns out to be the superposition of the generalized atomic coherent states in the Schwinger bosonic realization. The energy eigenvectors and eigenvalues of the corresponding time-independent Hamiltonian are also obtained as a by-product.

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.

QUANTUM STATES WITH CONTINUOUS SPECTRUM FOR THE TIME-DEPENDENT HARMONIC OSCILLATOR WITH A SINGULAR PERTURBATION

2007 ◽  
Vol 21 (10) ◽  
pp. 585-593 ◽  
Author(s):  
JEONG RYEOL CHOI ◽  
JUN-YOUNG OH
Keyword(s):  
Singular Perturbation ◽  
Harmonic Oscillator ◽  
Continuous Spectrum ◽  
Unitary Operator ◽  
Energy Eigenvalue ◽  
Invariant Operator ◽  
Quantum States ◽  
Wave Functions ◽  
Time Dependent ◽  
Discrete Energy

The quantum states with continuous spectrum for the time-dependent harmonic oscillator perturbed by a singularity are investigated. This system does not oscillate while the system that has discrete energy eigenvalue does. Exact wave functions satisfying the Schrödinger equation for the system are derived using invariant operator and unitary operator together.

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.

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