CONTROL OF QUANTUM ROTOR WITH SPIN-1/2

2012 ◽  
Vol 26 (04) ◽  
pp. 1150021
Author(s):  
ALEXANDRE G. M. SCHMIDT ◽  
BRUNO N. MARTINS
Keyword(s):  
Magnetic Flux ◽  
Wave Packet ◽  
Time Evolution ◽  
Time Dependent ◽  
Starting Position ◽  
Switching Times

In this work, we study the time evolution of a quantum rotor with spin-1/2 interacting with a time-dependent magnetic flux. Choosing an adequate magnetic flux and applying it at certain special switching times ti and tf, we show how to drive a wave-packet from a starting position to a final one maximizing its probability.

On the dynamics of a time-dependent mesoscopic LC circuit with a negative inductance

2016 ◽  
Vol 30 (12) ◽  
pp. 1650122 ◽  
Author(s):  
I. A. Pedrosa ◽  
E. Nogueira ◽  
I. Guedes
Keyword(s):  
Magnetic Flux ◽  
Wave Packet ◽  
Operator Method ◽  
Invariant Operator ◽  
Time Dependent ◽  
Expectation Values ◽  
Gaussian States ◽  
Faraday’S Law ◽  
Uncertainty Product ◽  
Lc Circuit

We discuss the problem of a mesoscopic LC circuit with a negative inductance ruled by a time-dependent Hermitian Hamiltonian. Classically, we find unusual expressions for the Faraday’s law and for the inductance of a solenoid. Quantum mechanically, we solve exactly the time-dependent Schrödinger equation through the Lewis and Riesenfeld invariant operator method and construct Gaussian wave packet solutions for this time-dependent LC circuit. We also evaluate the expectation values of the charge and the magnetic flux in these Gaussian states, their quantum fluctuations and the corresponding uncertainty product.

CONTROLLING THE QUANTUM ROTOR WITH A TIME-DEPENDENT MAGNETIC FLUX

2009 ◽  
Vol 23 (14) ◽  
pp. 1731-1742 ◽  
Author(s):  
ALEXANDRE G. M. SCHMIDT ◽  
BRUNO N. MARTINS
Keyword(s):  
Magnetic Flux ◽  
External Field ◽  
Wave Packet ◽  
Tracking Control ◽  
Time Dependent ◽  
First Case ◽  
Piecewise Continuous ◽  
The One ◽  
Wave Packet Revival ◽  
Bang Bang Control

We study the possibility of controlling a quantum rotor interacting with a time-dependent external field, namely, using a continuous or a piecewise continuous (bang-bang control) magnetic flux. Using the exact eigenfunctions we show how to steer a wave-packet constructed as a superposition of these eigenstates. In the first case we show how to steer a Gaussian wave-packet (GWP) to two other positions: one of them which would not be realized if the evolution were free, and the second is the one where wave-packet revival takes place. In the piecewise approach we implement a kind of tracking control, i.e. before steering it to the final target we achieve another given GWP.

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 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.

Time-dependent wave-packet approach to the quantum transport of carbon nanotubes with vacancies

2007 ◽  
Vol 601 (22) ◽  
pp. 5266-5269 ◽  
Author(s):  
Hiroyuki Ishii ◽  
Nobuhiko Kobayashi ◽  
Kenji Hirose
Keyword(s):  
Carbon Nanotubes ◽  
Wave Packet ◽  
Quantum Transport ◽  
Time Dependent

scholarly journals Spin-Orbit Entanglement in Time Evolution of Radial Wave Packets in Hydrogenic Systems

2004 ◽  
Vol 11 (04) ◽  
pp. 401-409
Author(s):  
Marcin Turek ◽  
Piotr Rozmej
Keyword(s):  
Wave Packet ◽  
Time Evolution ◽  
Time Scale ◽  
Degrees Of Freedom ◽  
Wave Packets ◽  
Characteristic Time Scale ◽  
Radial Wave ◽  
Mean Values ◽  
Breathing Motion ◽  
Wave Packet Revival

Time evolution of radial wave packets built from the eigenstates of Dirac equation for a hydrogenic system is considered. Radial wave packets are constructed from the states of different n quantum numbers and the same lowest angular momentum. In general they exhibit a kind of breathing motion with dispersion and (partial) revivals. Calculations show that for some particular preparations of the wave packet one can observe interesting effects in spin motion, coming from inherent entanglement of spin and orbital degrees of freedom. These effects manifest themselves through some oscillations in the mean values of spin operators and through changes of spatial probability density carried by upper and lower components of the wave function. It is also shown that the characteristic time scale of predicted effects (called T ls ) is much smaller for radial wave packets than in other cases, reaching values comparable to (or even less than) the time scale for the wave packet revival.

A comparative study of time dependent quantum mechanical wave packet evolution methods

1992 ◽  
Vol 96 (3) ◽  
pp. 2077-2084 ◽  
Author(s):  
Thanh N. Truong ◽  
John J. Tanner ◽  
Piotr Bala ◽  
J. Andrew McCammon ◽  
Donald J. Kouri ◽  
...  
Keyword(s):  
Wave Packet ◽  
Comparative Study ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
Mechanical Wave ◽  
Quantum Mechanical Wave Packet

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.

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