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.

Hamilton's principal function for the Brownian motion of a particle and the Schrödinger–Langevin equation

1978 ◽  
Vol 56 (3) ◽  
pp. 311-320 ◽  
Author(s):  
M. Razavy
Keyword(s):  
Brownian Motion ◽  
Langevin Equation ◽  
Equations Of Motion ◽  
Dissipative System ◽  
Heat Bath ◽  
Linear Wave ◽  
Many Body ◽  
Formal Similarity ◽  
Linear Wave Equation ◽  
Frictional Forces

The Brownian motion of a particle coupled to a heat bath can be derived from an exactly solvable many-body system. This motion is governed by the Langevin equation in Newtonian mechanics, and by an operator equation formally identical to the Langevin equation when the system composed of the particle plus the heat bath is quantized. To get this formal similarity between the classical and the quantal equations of motion of the particle, the classical dissipative system is formulated in terms of a modified Hamilton–Jacobi equation and is then quantized using the Schrödinger method. The result is identical with the Schrödinger–Langevin equation that has been obtained by quantizing the entire system and then isolating the motion of the particle. The non-linear wave equation describing the motion of a particle subject to conservative and time-dependent forces as well as frictional forces has been applied to the problems of motion of a wave-packet, and of the scattering and trapping of heavy-ions.

Review Lecture. Calculations of nuclear structure

1972 ◽  
Vol 326 (1565) ◽  
pp. 199-213 ◽  
Keyword(s):  
Field Theory ◽  
Nuclear Structure ◽  
Single Particle ◽  
Transition Probabilities ◽  
Energy Levels ◽  
Nucleon Nucleon ◽  
Body System ◽  
Many Body ◽  
Nucleon Scattering ◽  
Body Interaction

The field theory of elementary particles has so far failed to predict the detailed form of the interaction between neutrons and protons (nucleons), but the nucleon-nucleon scattering experiments are now sufficiently complete that for most purposes the interaction may be taken as known. At the same time a wealth of data concerning energy levels, transition probabilities and so on is available for literally hundreds of nuclei. Such measurements reveal that nuclei have an extremely rich structure, with both single-particle and collective properties, illustrating almost every feature of a many-body system. It is the purpose of this talk to review the extent to which we are able to understand these properties on the basis of the known two-body interaction. It will be shown how some features may be understood quite readily while others still pose fascinating problems.

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.

BERRY PHASE IN AN EFFECTIVE SU(1,1) SYSTEM

2002 ◽  
Vol 16 (21) ◽  
pp. 783-791
Author(s):  
YANHONG JIN ◽  
ZHIJIAN LI ◽  
J.-Q. LIANG
Keyword(s):  
Evolution Operator ◽  
Berry Phase ◽  
Dissipative System ◽  
Heat Bath ◽  
Additional Term ◽  
Time Dependent ◽  
Geometrical Meaning ◽  
Time Evolution Operator ◽  
Berry Phases ◽  
Additional Phase

We study the dynamics of a quantum system with a time-dependent Hamiltonian which is given by a linear combination of SU(1,1) generators and coupled with a heat bath. An effective Hamiltonian of this dissipative system is derived. With the help of a time-dependent gauge transformation, we obtain the exact solutions of the time-dependent Schrödinger equation, from which the time-evolution operator and the non-adiabatic and adiabatic Berry phases, which depend on time, are calculated explicitly. In the weak dissipation limit, an additional term besides the original Berry phase is found. The additional phase does not have a geometrical meaning due to the dissipation.

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