SU(1,1) LIE ALGEBRA APPLIED TO THE TIME-DEPENDENT QUADRATIC HAMILTONIAN SYSTEM PERTURBED BY A SINGULARITY

2004 ◽  
Vol 18 (26) ◽  
pp. 3429-3441 ◽  
Author(s):  
JEONG RYEOL CHOI ◽  
SEONG SOO CHOI
Keyword(s):  
Hamiltonian System ◽  
Probability Density ◽  
Lie Algebra ◽  
Time Evolution ◽  
Coherent States ◽  
Classical Trajectory ◽  
Quantum States ◽  
Time Dependent ◽  
Expectation Values ◽  
Quadratic Hamiltonian

We realized SU (1,1) Lie algebra in terms of the appropriate SU (1,1) generators for the time-dependent quadratic Hamiltonian system perturbed by a singularity. Exact quantum states of the system are investigated using SU (1,1) Lie algebra. Various expectation values in two kinds of the generalized SU (1,1) coherent states, that is, BG coherent states and Perelomov coherent states are derived. We applied our study to the CKOPS (Caldirola–Kanai oscillator perturbed by a singularity). Due to the damping constant γ, the probability density of the SU (1,1) coherent states for the CKOPS converged to the center with time. The time evolution of the probability density in SU (1,1) coherent states for the CKOPS are very similar to the classical trajectory.

scholarly journals Evaluation of time-dependent correlators after a local quench in iPEPS: hole motion in the t-J model

2020 ◽  
Vol 8 (2) ◽  
Author(s):  
Claudius Hubig ◽  
Annabelle Bohrdt ◽  
Michael Knap ◽  
Fabian Grusdt ◽  
Ignacio Cirac
Keyword(s):  
Real Time ◽  
Time Evolution ◽  
Correlation Functions ◽  
Spin Correlation ◽  
Quantum States ◽  
Time Dependent ◽  
Two Dimensional ◽  
Quantum Gas ◽  
Expectation Values ◽  
Equal Time

Infinite projected entangled pair states (iPEPS) provide a convenient variational description of infinite, translationally-invariant two-dimensional quantum states. However, the simulation of local excitations is not directly possible due to the translationally-invariant ansatz. Furthermore, as iPEPS are either identical or orthogonal, expectation values between different states as required during the evaluation of non-equal-time correlators are ill-defined. Here, we show that by introducing auxiliary states on each site, it becomes possible to simulate both local excitations and evaluate non-equal-time correlators in an iPEPS setting under real-time evolution. We showcase the method by simulating the t-Jt−J model after a single hole has been placed in the half-filled antiferromagnetic background and evaluating both return probabilities and spin correlation functions, as accessible in quantum gas microscopes.

scholarly journals Quantum Weak Invariants: Dynamical Evolution of Fluctuations and Correlations

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1219
Author(s):  
Zeyi Shi ◽  
Sumiyoshi Abe
Keyword(s):  
Time Evolution ◽  
Open Quantum System ◽  
Dynamical Evolution ◽  
Time Dependent ◽  
Von Neumann Entropy ◽  
Completely Positive Map ◽  
Expectation Values ◽  
Completely Positive ◽  
Temporal Asymmetry ◽  
Von Neumann

Weak invariants are time-dependent observables with conserved expectation values. Their fluctuations, however, do not remain constant in time. On the assumption that time evolution of the state of an open quantum system is given in terms of a completely positive map, the fluctuations monotonically grow even if the map is not unital, in contrast to the fact that monotonic increases of both the von Neumann entropy and Rényi entropy require the map to be unital. In this way, the weak invariants describe temporal asymmetry in a manner different from the entropies. A formula is presented for time evolution of the covariance matrix associated with the weak invariants in cases where the system density matrix obeys the Gorini–Kossakowski–Lindblad–Sudarshan equation.

Exact quantum theory of a time-dependent bound quadratic Hamiltonian system

1993 ◽  
Vol 48 (4) ◽  
pp. 2716-2720 ◽  
Author(s):  
Kyu Hwang Yeon ◽  
Kang Ku Lee ◽  
Chung In Um ◽  
Thomas F. George ◽  
Lakshmi N. Pandey
Keyword(s):  
Quantum Theory ◽  
Hamiltonian System ◽  
Time Dependent ◽  
Exact Quantum ◽  
Quadratic Hamiltonian

scholarly journals DYNAMICS OF GENERALIZED COHERENT STATES

1995 ◽  
Vol 09 (13) ◽  
pp. 823-828 ◽  
Author(s):  
SALVATORE DE MARTINO ◽  
SILVIO DE SIENA ◽  
FABRIZIO ILLUMINATI
Keyword(s):  
Coherent States ◽  
Wave Packets ◽  
Classical Trajectory ◽  
Feedback Mechanism ◽  
The State ◽  
Time Dependent ◽  
Generalized Coherent States ◽  
Classical Evolution

We show that generalized coherent states follow Schrödinger dynamics in time-dependent potentials. The normalized wave-packets follow a classical evolution without spreading; in turn, the Schrödinger potential depends on the state through the classical trajectory. This feedback mechanism with continuous dynamical re-adjustment allows the packets to remain coherent indefinitely.

Nonlinear time evolution of coherent states with observation of super revivals in a generalized isotonic oscillator

2014 ◽  
Vol 11 (04) ◽  
pp. 1450027
Author(s):  
V. Chithiika Ruby ◽  
P. Muruganandam ◽  
M. Senthilvelan
Keyword(s):  
Energy Spectrum ◽  
Time Evolution ◽  
Coherent States ◽  
Uncertainty Relation ◽  
Cubic Nonlinearity ◽  
Expectation Values ◽  
Ladder Operators ◽  
Deformed Oscillator ◽  
Fractional Revivals ◽  
Nonlinear Energy

In this paper, we investigate revival and super revivals of nonlinear coherent states while generating these states through the interaction of coherent states of a generalized isotonic oscillator with the nonlinear media during time evolution. We construct the f-deformed generalized isotonic oscillator which is a non-isochronous partner of the generalized isotonic oscillator. We connect these two nonlinear oscillators through deformed ladder operators. The generalized isotonic oscillator possesses linear energy spectrum whereas f-deformed generalized isotonic oscillator exhibits nonlinear energy spectrum. The presence of the cubic nonlinearity in the f-deformed oscillator motivates us to study revivals, super and fractional revivals of coherent states which are nonlinearly evolved. We also investigate time-dependent expectation values of uncertainties in certain canonically conjugate variables and demonstrate that at revival and super revival times the uncertainty relation attains its minimum value.

COLLAPSE AND REVIVAL EFFECT IN A MESOSCOPIC LC CIRCUIT

2004 ◽  
Vol 18 (08) ◽  
pp. 1217-1224 ◽  
Author(s):  
HAI-MEI LUO ◽  
YING-HUA JI ◽  
JIE LIU
Keyword(s):  
Time Evolution ◽  
Dynamic Behavior ◽  
Quantum State ◽  
Tunnel Junction ◽  
Coherent States ◽  
The State ◽  
Quantum States ◽  
Quantum Superposition ◽  
Coupling Energy ◽  
Lc Circuit

This paper studied the time evolution of quantum state in a mesoscopic LC circuit with the coupling energy caused by mesoscopic capacitor acting as a tunnel junction. It indicates that the state of the junction evolves into the quantum superposition of two coherent states and, in the state, nonclassical squeezing properties of the circuit appear. It also indicates that the dynamic behavior of the current shows collapse and revival phenomenon. The research in the paper will be helpful to miniaturize integrate circuits and electric components. It will be also important for the utilization of mesoscopic circuits to evolve the quantum states, which work as information carriers.

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