Quantum many-body system in presence of time-dependent potential and electric field

2017 ◽  
Vol 71 (1) ◽  
pp. 8-12 ◽  
Author(s):  
Hadi Sobhani ◽  
Hassan Hassanabadi
Keyword(s):  
Electric Field ◽  
Time Dependent ◽  
Body System ◽  
Many Body ◽  
Dependent Potential

The time-dependent electric current from a flame

1984 ◽  
Vol 393 (1805) ◽  
pp. 297-308 ◽  
Keyword(s):  
Differential Equation ◽  
Electric Field ◽  
Electric Current ◽  
Diffusion Flame ◽  
Time Dependent ◽  
Two Dimensional ◽  
Ionization Detector ◽  
Flame Ionization ◽  
Dependent Potential ◽  
Ionization Detectors

An earlier static treatment of the electric current from the diffusion flame in a flame ionization detector has been extended to include time-dependent currents. The nonlinear differential equation describing the electric field in the space outside the flame has been solved analytically for a class of problems in which a time-dependent potential difference is switched on after a static current has been established. Both one- and two-dimensional geometrical configurations are considered. The results could be useful in suggesting new experiments on flame ionization detectors.

Wave equation for dissipative motion

1991 ◽  
Vol 69 (10) ◽  
pp. 1225-1232 ◽  
Author(s):  
M. Razavy
Keyword(s):  
Wave Equation ◽  
Single Particle ◽  
Equations Of Motion ◽  
Dissipative System ◽  
Heat Bath ◽  
Initial Position ◽  
Time Dependent ◽  
Reduced Form ◽  
Body System ◽  
Many Body

From a quantized many-body system a wave equation for the motion of a particle linearly coupled to a heat bath is derived. The effective Hamiltonian describing the motion of the single particle is explicitly time dependent, and for a quadratic potential, has a simple dependence on the initial position and momentum of the particle. For the case of dissipative harmonic motion, a time-dependent wave equation is derived and the ground-state wave function is determined. It is also shown that if the equations of motion for the many-body system is Galilean invariant, the reduced form of equation of motion for the single particle is not. However a generalized form of transformation for the position and momentum operators, to a coordinate system moving with constant velocity, is obtained, which reduces to the Galilean transformation when the coupling to the dissipative system is turned off.

The symmetry group of the quantum harmonic oscillator in an electric field

Open Physics ◽  
2008 ◽  
Vol 6 (3) ◽  
Author(s):  
Juan Lejarreta ◽  
Jose Cerveró
Keyword(s):  
Schrödinger Equation ◽  
Electric Field ◽  
Harmonic Oscillator ◽  
Schrodinger Equation ◽  
Group Structure ◽  
Time Dependent ◽  
Frequency Function ◽  
General Group ◽  
Dependent Potential ◽  
The Relationship

AbstractIn this paper we present two results. First, we derive the most general group of infinitesimal transformations for the Schrödinger Equation of the general time-dependent Harmonic Oscillator in an electric field. The infinitesimal generators and the commutation rules of this group are presented and the group structure is identified. From here it is easy to construct a set of unitary operators that transform the general Hamiltonian to a much simpler form. The relationship between squeezing and dynamical symmetries is also stressed. The second result concerns the application of these group transformations to obtain solutions of the Schrödinger equation in a time-dependent potential. These solutions are believed to be useful for describing particles confined in boxes with moving boundaries. The motion of the walls is indeed governed by the time-dependent frequency function. The applications of these results to non-rigid quantum dots and tunnelling through fluctuating barriers is also discussed, both in the presence and in the absence of a time-dependent electric field. The differences and similarities between both cases are pointed out.

SPIN CLUSTER AS A QUBIT: ROBUST AGAINST DISSIPATION OF THERMAL RADIATION FIELDS

2005 ◽  
Vol 19 (15n17) ◽  
pp. 2481-2485 ◽  
Author(s):  
XIAO-FEI SU ◽  
SHUN-JIN WANG
Keyword(s):  
Magnetic Field ◽  
Thermal Radiation ◽  
Time Evolution ◽  
Logic Gate ◽  
Time Dependent ◽  
Body System ◽  
Many Body ◽  
Spin Cluster ◽  
Radiation Fields ◽  
Qubit System

A spin cluster of 3 spin 1/2 particles has been studied as a qubit system. A time dependent magnetic field is applied to control the time evolution of the cluster. The lowest energy level of the cluster has the total spin 1/2 separated far away from the excited states and can be used as a qubit register. The universal 1-qubit logic gate can be constructed from the time evolution operator of the non-autonomous many-body system, and the 6 basic 1-qubit gates can be realized by adjusting the applied time dependent magnetic field. As a many-body system, this qubit system is expected to be robust against the dissipation effect of the thermal radiation fields from the environment.

scholarly journals Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 984
Author(s):  
Regina Finsterhölzl ◽  
Manuel Katzer ◽  
Andreas Knorr ◽  
Alexander Carmele
Keyword(s):  
Time Evolution ◽  
Nearest Neighbor ◽  
Matrix Product ◽  
Body System ◽  
Many Body ◽  
Initial State ◽  
Matrix Product States ◽  
Open Quantum ◽  
Many Body Systems ◽  
The Many

This paper presents an efficient algorithm for the time evolution of open quantum many-body systems using matrix-product states (MPS) proposing a convenient structure of the MPS-architecture, which exploits the initial state of system and reservoir. By doing so, numerically expensive re-ordering protocols are circumvented. It is applicable to systems with a Markovian type of interaction, where only the present state of the reservoir needs to be taken into account. Its adaption to a non-Markovian type of interaction between the many-body system and the reservoir is demonstrated, where the information backflow from the reservoir needs to be included in the computation. Also, the derivation of the basis in the quantum stochastic Schrödinger picture is shown. As a paradigmatic model, the Heisenberg spin chain with nearest-neighbor interaction is used. It is demonstrated that the algorithm allows for the access of large systems sizes. As an example for a non-Markovian type of interaction, the generation of highly unusual steady states in the many-body system with coherent feedback control is demonstrated for a chain length of N=30.

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