Quantum Dynamics: Resonance and a Quantum Flip-Flop

2021 ◽  
pp. 135-159
Author(s):  
Duncan G. Steel
Keyword(s):  
Time Evolution ◽  
Quantum Dynamics ◽  
Classical System ◽  
Time Dependent ◽  
Full Time ◽  
Flip Flop ◽  
Quantum Bit ◽  
Lc Circuit ◽  
Oscillating Potential ◽  
Potential Energy Term

This chapter begins the discussion of the time evolution of an active quantum system. From the earlier chapters, time dependent physics has been observed through the presence of the time evolution of the phase of each eigenstate. The Hamiltonian itself is time independent. This represents the same kind of evolution of a classical system like the vibration of a tuning fork when it has been struck or the oscillation of an LC circuit if the capacitor is charged to some voltage and then the switch is closed. In the quantum case, the Hamiltonian has also been time independent. The time evolution evolves according the full-time dependent Schrödinger equation, depending only on a single initial condition of the state vector or wave function and the corresponding time evolution of the phase factor for each eigenstate. However in this chapter, we consider the case of when there is a time dependent Hamiltonian such as a sinewave generator or laser. As in the case of resonant tunneling, we see the importance in dynamics of resonant coupling. With an oscillating potential energy term, we see the presence of Rabi oscillations in the probability amplitude of a two-state system on resonance, which can be viewed as a quantum flip-flop between two states of a quantum bit (qubit).

A Refined Speed Limit for the Imaginary-Time Schrödinger Equation

2020 ◽  
Vol 27 (02) ◽  
pp. 2050010
Author(s):  
Jie Sun ◽  
Songfeng Lu
Keyword(s):  
Schrödinger Equation ◽  
Quantum Dynamics ◽  
Schrodinger Equation ◽  
Time Dependent ◽  
Uncertainty Relations ◽  
Speed Limit ◽  
Full Time ◽  
Imaginary Time ◽  
Full Solution ◽  
The One

Recently, Kieu proposed a new class of time-energy uncertainty relations for time-dependent Hamiltonians, which is not only formal but also useful for actually evaluating the speed limit of quantum dynamics. Inspired by this work, Okuyama and Ohzeki obtained a similar speed limit for the imaginary-time Schrödinger equation. In this paper, we refine the latter one to make it be further like that of Kieu formally. As in the work of Kieu, only the initial states and the Hamiltonians, but neither the instantaneous eigenstates nor the full time-dependent wave like functions, which would demand a full solution for a time-dependent system, are required for our optimized speed limit. It turns out to be more helpful for estimating the speed limit of an actual quantum annealing driven by the imaginary-time Schrödinger equation. For certain case, the refined speed limit given here becomes the only useful tool to do this estimation, because the one given by Okuyama and Ohzeki cannot do the same job.

DYNAMICS OF MOLECULAR MAGNET Fe8 INTERACTING WITH AN INJECTING SPIN-POLARIZED ELECTRON

2004 ◽  
Vol 18 (11) ◽  
pp. 479-483
Author(s):  
GUO-FENG ZHANG ◽  
YIN WEN ◽  
YING-FANG GAO ◽  
JIU-QING LIANG ◽  
QI-WEI YAN
Keyword(s):  
Time Evolution ◽  
Nuclear Spin ◽  
Quantum Dynamics ◽  
Interaction Strength ◽  
Time Dependent ◽  
Molecular Magnet ◽  
Schrodinger Equations ◽  
Spin States ◽  
Schrödinger Equations ◽  
Spin Polarized

Quantum dynamics time evolution of a molecular magnet Fe 8 interacting with an electron nuclear spin is studied by solving the time-dependent Schrödinger equations. It is found that the variation of Fe 8 magnetization and the nuclear spin crucially depends on the interaction strength. The time evolution of the entanglement between the injecting electron and Fe 8 is evaluated. It is observed that the entanglement oscillates in time and is tightly related to the spin variation of the injecting electron. From these characteristics, the technique for the reversing and read-out of Fe 8 spin states is suggested.

Alternative approach to time evolution of quantum systems

2020 ◽  
Vol 33 (4) ◽  
pp. 358-366
Author(s):  
Mustafa Erol
Keyword(s):  
Potential Energy ◽  
Time Evolution ◽  
Current Theory ◽  
Quantum Systems ◽  
Time Dependent ◽  
Standard Theory ◽  
Energy Term ◽  
Wave Nature ◽  
Alternative Approach ◽  
Potential Energy Term

This study focuses on the temporal evolution of quantum systems based on epistemological and ontological arguments and reconsiders some fundamental concepts of quantum theory. Initially, the time dependent Schrödinger wave equation (TDSWE) is criticized for the lack of a potential energy term and thereafter, a novel time dependent momentum operator is defined which eventually leads to an alternative TDSWE, including a potential energy term that remains in harmony with current theory. The wave nature is then generally examined by comparing time evolutions of classical and Schrödinger waves, dissimilarities then carefully inspected and ultimately a novel second order TDSWE is suggested. Finally, time evolution of the probability density is discussed in light of this new approach, and additionally some further insights and conclusions are briefly outlined that conform with the standard theory.

scholarly journals London superconductor and time-varying mesoscopic LC circuits

2021 ◽  
Vol 67 (5 Sep-Oct) ◽  
pp. 1-6
Author(s):  
Inácio de Almeida Pedrosa ◽  
Luciano Nascimento
Keyword(s):  
Magnetic Flux ◽  
Harmonic Oscillator ◽  
Quantum Dynamics ◽  
Time Dependent ◽  
Time Varying ◽  
Expectation Values ◽  
Fock States ◽  
Damped Harmonic Oscillator ◽  
Constant Rate ◽  
Lc Circuit

In this work we study the classical and quantum dynamics of a London superconductor and of a time-dependent mesoscopic or nanoscale LC circuit by assuming that the inductance and capacitance vary exponentially with time at constant rate. Surprisingly, we find that the behavior of these two systems are equivalent, both classically and quantum mechanically, and can be mapped into a standard damped harmonic oscillator which is described by the Caldirola-Kanai Hamiltonian. With the aid of the dynamical invariant method and Fock states, we solve the time-dependent Schr\"odinger equation associated with this Hamiltonian and calculate some important physical properties of these systems such as expectation values of the charge and magnetic flux, their variances and the respective uncertainty principle.

scholarly journals The time-dependent angular analysis of Bd → KSℓℓ, a new benchmark for new physics

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Sébastien Descotes-Genon ◽  
Martín Novoa-Brunet ◽  
K. Keri Vos
Keyword(s):  
Time Evolution ◽  
Form Factors ◽  
New Physics ◽  
Time Dependent ◽  
Angular Analysis ◽  
Time Dependent Analysis ◽  
Tensor Operators

Abstract We consider the time-dependent analysis of Bd→ KSℓℓ taking into account the time-evolution of the Bd meson and its mixing into $$ {\overline{B}}_d $$ B ¯ d . We discuss the angular conventions required to define the angular observables in a transparent way with respect to CP conjugation. The inclusion of time evolution allows us to identify six new observables, out of which three could be accessed from a time-dependent tagged analysis. We also show that these observables could be obtained by time-integrated measurements in a hadronic environment if flavour tagging is available. We provide simple and precise predictions for these observables in the SM and in NP models with real contributions to SM and chirally flipped operators, which are independent of form factors and charm-loop contributions. As such, these observables provide robust and powerful cross-checks of the New Physics scenarios currently favoured by global fits to b → sℓℓ data. In addition, we discuss the sensitivity of these observables with respect to NP scenarios involving scalar and tensor operators, or CP-violating phases. We illustrate how these new observables can provide a benchmark to discriminate among the various NP scenarios in b → sμμ. We discuss the extension of these results for Bs decays into f0, η or η′.

scholarly journals Chaos in time-dependent variational approximations to quantum dynamics

1998 ◽  
Vol 57 (2) ◽  
pp. 1489-1498 ◽  
Author(s):  
Fred Cooper ◽  
John Dawson ◽  
Salman Habib ◽  
Robert D. Ryne
Keyword(s):  
Quantum Dynamics ◽  
Time Dependent ◽  
Variational Approximations

scholarly journals Coagulation Processes with Gibbsian Time Evolution

2012 ◽  
Vol 49 (03) ◽  
pp. 612-626
Author(s):  
Boris L. Granovsky ◽  
Alexander V. Kryvoshaev
Keyword(s):  
Stochastic Process ◽  
Recurrence Relation ◽  
Time Evolution ◽  
Nonnegative Function ◽  
Gibbs Distribution ◽  
Time Dependent ◽  
Explicit Solutions ◽  
Gibbs Distributions ◽  
Giant Cluster ◽  
Positive Integers

We prove that a stochastic process of pure coagulation has at any timet≥ 0 a time-dependent Gibbs distribution if and only if the rates ψ(i,j) of single coagulations are of the form ψ(i;j) =if(j) +jf(i), wherefis an arbitrary nonnegative function on the set of positive integers. We also obtain a recurrence relation for weights of these Gibbs distributions that allow us to derive the general form of the solution and the explicit solutions in three particular cases of the functionf. For the three corresponding models, we study the probability of coagulation into one giant cluster by timet> 0.

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