scholarly journals Time-dependent Hilbert spaces, geometric phases, and general covariance in quantum mechanics

2004 ◽  
Vol 320 (5-6) ◽  
pp. 375-382 ◽  
Author(s):  
Ali Mostafazadeh
Keyword(s):  
Quantum Mechanics ◽  
Hilbert Spaces ◽  
Time Dependent ◽  
General Covariance ◽  
Geometric Phases

Decoherence in Holonomic Quantum Computation

2006 ◽  
Vol 13 (03) ◽  
pp. 263-272 ◽  
Author(s):  
Giuseppe Florio
Keyword(s):  
Quantum Mechanics ◽  
Master Equation ◽  
Quantum Computation ◽  
Physical Model ◽  
Numerical Solutions ◽  
Operation Time ◽  
Time Dependent ◽  
Geometric Phases ◽  
Experimental Implementation ◽  
Finite Operation

Geometric phases are an interesting field of research in quantum mechanics. Recently both abelian and nonabelian geometric phases have been proposed as a useful resource for the experimental implementation of quantum computation. In this paper we focus on a particular physical model and study the effect of a bosonic bath on a class of holonomic transformations. We write a general master equation for time-dependent Hamiltonians and derive analytical and numerical solutions for the system considered. The fidelity is analyzed in the adiabatic and nonadiabatic regime. We also determine an optimal finite operation time for this class of gates.

scholarly journals A new approximation method for time-dependent problems in quantum mechanics

2005 ◽  
Vol 340 (1-4) ◽  
pp. 87-93 ◽  
Author(s):  
Paolo Amore ◽  
Alfredo Aranda ◽  
Francisco M. Fernández ◽  
Hugh Jones
Keyword(s):  
Quantum Mechanics ◽  
Approximation Method ◽  
Time Dependent ◽  
Time Dependent Problems

Energy and Momentum Eigenspectrum of the Hulthén-screened Cosine Kratzer Potential Using Proper Quantization Rule and SUSYQM Method

2021 ◽  
Author(s):  
Kaushal R Purohit ◽  
Rajendrasinh H PARMAR ◽  
Ajay Kumar Rai
Keyword(s):  
Quantum Mechanics ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Numerical Data ◽  
Time Dependent ◽  
Quantization Rule ◽  
Approximation Approach ◽  
Momentum Spectra ◽  
Energy And Momentum ◽  
Three Dimensional Space

Abstract Using the Qiang-Dong proper quantization rule (PQR) and the supersymmetric quantum mechanics approach, we obtained the eigenspectrum of the energy and momentum for time independent and time dependent Hulthen-screened cosine Kratzer potentials. For the suggested time independent Hulthen-screened cosine Kratzer potential, we solved the Schrodinger equation in D dimensions (HSCKP). The Feinberg-Horodecki equation for time-dependent Hulthen-screened cosine Kratzer potential was also solved (tHSCKP). To address the inverse square term in the time independent and time dependent equations, we employed the Greene-Aldrich approximation approach. We were able to extract time independent and time dependent potentials, as well as their accompanying energy and momentum spectra. In three-dimensional space, we estimated the rotational vibrational (RV) energy spectrum for many homodimers ($H_2, I_2, O_2$) and heterodimers ($MnH, ScN, LiH, HCl$). We also used the recently introduced formula approach to obtain the relevant eigen function. We also calculated momentum spectra for the dimers $MnH$ and $ScN$. The method is compared to prior methodologies for accuracy and validity using numerical data for heterodimer $LiH, HCl$ and homodimer $I_2, O_2,H_2$. The calculated energy and momentum spectra are tabulated and analysed.

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 Gravity as entanglement, entanglement as gravity

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Reference Frame ◽  
Common Sense ◽  
Reference Frames ◽  
General Covariance ◽  
The Universe

A generalized and unifying viewpoint to both general relativity and quantum mechanics and information is investigated. It may be described as a generaliztion of the concept of reference frame from mechanics to thermodynamics, or from a reference frame linked to an element of a system, and thus, within it, to another reference frame linked to the whole of the system or to any of other similar systems, and thus, out of it. Furthermore, the former is the viewpoint of general relativity, the latter is that of quantum mechanics and information.Ciclicity in the manner of Nicolas Cusanus (Nicolas of Cusa) is complemented as a fundamental and definitive property of any totality, e.g. physically, that of the universe. It has to contain its externality within it somehow being namely the totality. This implies a seemingly paradoxical (in fact, only to common sense rather logically and mathematically) viewpoint for the universe to be repesented within it as each one quant of action according to the fundamental Planck constant.That approach implies the unification of gravity and entanglement correspondiing to the former or latter class of reference frames. An invariance, more general than Einstein's general covariance is to be involved as to both classes of reference frames unifying them. Its essence is the unification of the discrete and cotnitinuous (smooth). That idea underlies implicitly quantum mechanics for Bohr's principle that it study the system of quantum microscopic entities and the macroscopic apparatus desribed uniformly by the smmoth equations of classical physics.e

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