Friction and dissipative phenomena in quantum mechanics

Kostin, M. D.

doi:10.1007/bf01010029

Cited by 113 publications

(42 citation statements)

References 5 publications

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“…(4) in the Schrödinger-Langevin equation (Kostin 1972(Kostin , 1975Davidson 1979). A logarithmic Schrödinger-Langevin equation is also derived (Nassar 1985).…”

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confidence: 99%

Nonlinear Theory of Quantum Brownian Motion

Tsekov

2008

Int J Theor Phys

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A nonlinear theory of quantum Brownian motion in classical environment is developed based on a thermodynamically enhanced nonlinear Schrödinger equation. The latter is transformed via the Madelung transformation into a nonlinear quantum Smoluchowski-like equation, which is proven to reproduce key results from quantum and classical physics. The application of the theory to a free quantum Brownian particle results in a nonlinear dependence of the position dispersion on time, being quantum generalization of the Einstein law of Brownian motion. It is shown that the time of decoherence for the transition from quantum to classical diffusion is proportional to the square of the thermal de Broglie wavelength divided by the Einstein diffusion constant.Brownian motion is the permanent irregular movement of a particle immersed in a medium. Its rigorous description requires joint consideration of the coupled dynamics of the Brownian particle and the medium, usually referred as thermal bath. Fundamental problems appear in the Brownian motion theory if the quantum effects become important. For instance, at time larger than the classical momentum relaxation time the Brownian motion of a quantum particle in a classical environment is regularly described by the classical Einstein law

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“…(4) in the Schrödinger-Langevin equation (Kostin 1972(Kostin , 1975Davidson 1979). A logarithmic Schrödinger-Langevin equation is also derived (Nassar 1985).…”

mentioning

confidence: 99%

Nonlinear Theory of Quantum Brownian Motion

Tsekov

2008

Int J Theor Phys

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“…The wave function contains all the information of the quantum system. In 1972, Kostin derived the Schrödinger-Langevin equation for a Brownian particle interacting with a thermal bath [7,8]. The wave function of the Brownian particle satisfies the nonlinear TDSE including a dissipative potential and a random potential…”

Section: Schrödinger-langevin Equation With Linear Dissipationmentioning

confidence: 99%

“…This potential is also called the energy dissipation operator, causing the quantum system to lose energy [8]. The system and the environment are linked through the phenomenological friction coefficient γ, and this term brings frictional and thermal effects into the system.…”

Section: Schrödinger-langevin Equation With Linear Dissipationmentioning

confidence: 99%

“…(5) [1,8,13]. First, the norm of the wave function is conserved; thus, the dissipative potential does not change the normalization of the wave function.…”

Section: Schrödinger-langevin Equation With Linear Dissipationmentioning

confidence: 99%

“…In 1972, Kostin derived the Schrödinger-Langevin equation for a Brownian particle interacting with a thermal bath [7,8]. In this approach, a dissipative potential and a random potential are incorporated into the timedependent Schrödinger equation (TDSE), and these terms describe the thermal and statistical influence of the environment.…”

Section: Introductionmentioning

confidence: 99%

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Trajectory approach to the Schrödinger–Langevin equation with linear dissipation for ground states

Chou

2015

Annals of Physics

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On the Three Dimensional Reduction of the Kustaanheimo‐Stiefel Transformation

Papp¹

1989

Annalen der Physik

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The Kustaanheimo-Stiefel [l] symmetry transformation x = {xi) -+ u = {u,], definetl by = Uf -u; -. : + 4 , 93 = 2(u,u2 -u3u4), 5 3 = 2(u,u3 + U274)r where j = 1, 2, 3 and iy = I, 2, 3, 4, has received much a of (1) the Hamiltoniaii ---= E ,P 1 -P ten ion 2-51. WI h he help of the three dimensional ( N = N1 = 3 ) hydrogen atom has been converted into the one of a related four-dimensional ( N = N , = 4) harmonic oscillator: 2F2 = 212 -4u2E = 48.( 3 ) The Corresponding eigenavlues have been displayed to the right. This conversion is implied by the, interconnection [ 2, 41 T A , = r A , + G R 2 , 1 1 in which ~~_ ( u , a ; -u , a ; ; + u , a~-u , a~) y = o .This latter equation has the meaning of a superselection rule relying on the singlevaluedness of the state function y ( u ) . A generalization of (I) for N l = 5 and N , = 8 has also been proposed [B, 71. Above r = 1x1 = u2, ai = a/axi = i& and a: = a/au, = iGa. The corresponding Laplace-operators read A , = Ziat and A , = Za a:', whereas the conjugated momenta have been denoted by p i and vx, respectively. I n this paper we shall analyse (1) by considering, this time, constant u,-values such that aiu4 = 0. We shall then prove that (1) enables us to convert (2) into the Hamiltoniaii of a related three-dimensional harmonic oscillator, now with a constraint generated by the selection of constant u,-values. Note that conversions concerning power-potentials [8-121 as well as other cases have also been discussed before.

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Friction and dissipative phenomena in quantum mechanics

Cited by 113 publications

References 5 publications

Nonlinear Theory of Quantum Brownian Motion

Nonlinear Theory of Quantum Brownian Motion

Trajectory approach to the Schrödinger–Langevin equation with linear dissipation for ground states

On the Three Dimensional Reduction of the Kustaanheimo‐Stiefel Transformation

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