scholarly journals Invariant Quantum States of Quadratic Hamiltonians

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 634
Author(s):  
Viktor V. Dodonov
Keyword(s):  
Covariance Matrices ◽  
Quantum States ◽  
Time Dependent ◽  
General Solutions ◽  
Quadratic Hamiltonians ◽  
Invariant Quantum

The problem of finding covariance matrices that remain constant in time for arbitrary multi-dimensional quadratic Hamiltonians (including those with time-dependent coefficients) is considered. General solutions are obtained.

scholarly journals Gaussian quantum states can be disentangled using symplectic rotations

2021 ◽  
Vol 111 (3) ◽  
Author(s):  
Maurice A. de Gosson
Keyword(s):  
Quantum State ◽  
Covariance Matrices ◽  
Quantum States ◽  
Weyl Quantization ◽  
Symplectic Transformation ◽  
Metaplectic Operator

AbstractWe show that every Gaussian mixed quantum state can be disentangled by conjugation with a passive symplectic transformation, that is a metaplectic operator associated with a symplectic rotation. The main tools we use are the Werner–Wolf condition on covariance matrices and the symplectic covariance of Weyl quantization. Our result therefore complements a recent study by Lami, Serafini, and Adesso.

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 A CLASS OF QUANTUM STATES WITH CLASSICAL-LIKE EVOLUTION

1994 ◽  
Vol 08 (29) ◽  
pp. 1823-1831 ◽  
Author(s):  
SALVATORE DE MARTINO ◽  
SILVIO DE SIENA ◽  
FABRIZIO ILLUMINATI
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Coherent States ◽  
Quantum States ◽  
Time Dependent ◽  
Stationary States ◽  
Oscillator Potential ◽  
Classical Motion ◽  
Stochastic Formulation ◽  
New States

In the framework of the stochastic formulation of quantum mechanics we derive non-stationary states for a class of time-dependent potentials. The wave packets follow a classical motion with constant dispersion. The new states define a possible extension of the harmonic oscillator coherent states. As an explicit application, we study a sestic oscillator potential.

EXACT QUANTUM STATES OF AN INVERTED PENDULUM UNDER TIME-DEPENDENT GRAVITATION

2004 ◽  
Vol 19 (24) ◽  
pp. 4165-4172 ◽  
Author(s):  
I. A. PEDROSA ◽  
I. GUEDES
Keyword(s):  
Exact Solutions ◽  
Inverted Pendulum ◽  
Quantum States ◽  
Wave Functions ◽  
Time Dependent ◽  
Invariant Method ◽  
Exact Quantum ◽  
Generalized Time

We discuss the Lewis and Riesenfeld invariant method for cases where the invariant has continuous eigenvalues and use it to find the Schrödinger wave functions of an inverted pendulum under time-dependent gravitation. As a particular case, we consider an inverted pendulum with exponentially increasing mass and constant gravitation. We also obtain the exact solutions for a generalized time-dependent inverted pendulum.

scholarly journals Entangling power of permutation-invariant quantum states

2005 ◽  
Vol 72 (3) ◽  
Author(s):  
Vladislav Popkov ◽  
Mario Salerno ◽  
Gunter Schütz
Keyword(s):  
Quantum States ◽  
Invariant Quantum
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