Numerical Simulation of Relaxation of Quantum Thermal Fluctuations

  • O. N. Golubjeva People’s Friendship University of Russia
  • S. V. Sidorov People’s Friendship University of Russia
  • V. G. Bar’yakhtar Institute of Magnetism, Nat. Acad. of Sci. of Ukraine
Keywords: (h, k)-dynamics, quantum thermostat, cold and warm vacua, effective action, self-diffusion, diffusion pressure energy density, drift and diffusion velocities, numerical analysis

Abstract

A generalization of quantum-mechanical equations expressed in the hydrodynamic form by introducing terms that involve the diffusion velocity at zero and finite temperatures, as well as the diffusion pressure energy in a warm vacuum, into the Lagrangian density has been proposed. It is used as a basis for constructing a system of equations similar to the Euler equations, but making allowance for quantum-mechanical and thermal effects, for the model of one-dimensional hydrodynamics. The equations obtained generalize the equations of the Nelson stochastic mechanics. A numerical analysis of the solutions of this system allowed a conclusion to be drawn about its validity for the description of the relaxation of quantum thermal fluctuations.

References

D. Forster, Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions (Perseus, Cambridge, MA, 1990).

A.D. Sukhanov and O.N. Golubjeva, Teor. Mat. Fiz. 160, 369 (2009).

R. Furth, Z. Phys. 81, 143 (1933).

A.D. Sukhanov, Teor. Mat. Fiz. 139, 129 (2004).

A.D. Sukhanov, Teor. Mat. Fiz., 148, 295 (2006).

http://dx.doi.org/10.4213/tmf2087

E. Nelson, Dynamical Theory of Brownian Motion (Princeton Univ. Press, Princeton, 1967).

Thermodynamics, edited by M. Tadashi (InTech, 2011).

R. Feynman, P. Leiton, and M. Sands, The Feynman Lectures on Physics, Vol. 3: Quantum Mechanics (AddisonWesley, Reading, MA, 1964).

D.I. Blokhintsev, Quantum Mechanics (Reidel, Dordrecht, 1964).

A.N. Kolmogoroff, Math. Ann. 104, 415 (1931); 108, 149 (1933).

I. Fenyes, Zs. Math. 132, 81 (1952).

O.N. Golubjeva and A.D. Sukhanov, Part. Nucl. Lett. 8, 1 (2011).

O.N. Golubjeva and A.D. Sukhanov, Canad. J. Phys. 92, 259 (2014).

R. Courant and K.O. Friedrichs, Supersonic Flow and Shock Waves (Interscience, New York, 1948).

Published
2019-01-10
How to Cite
Golubjeva, O., Sidorov, S., & Bar’yakhtar, V. (2019). Numerical Simulation of Relaxation of Quantum Thermal Fluctuations. Ukrainian Journal of Physics, 60(10), 1062. https://doi.org/10.15407/ujpe60.10.1062
Section
General problems of theoretical physics

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