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Archive for the ‘2008 Volume 3’ Category
Non-dissipative diffusion in classical and quantum systems
Zahid Zakir [1]
Abstract
The theory of non-dissipative diffusion is constructed on an example of diffusion of a light particle in a dilute medium of heavy particles and it is shown that in low dissipative systems there are specific effects of non-dissipativity similar to quantum effects. In a non-dissipativity region mean energy of the light particle is conserved and processes are described by two non-linear diffusion equations with forward and backward time derivatives. Then these two diffusion equations are linearized and give one linear Schrödinger equation for complex amplitudes of probability. As a result, in the non-dissipative classical diffusion should be added probability amplitudes and there holds the superposition principle for these amplitudes. A mean square length of free passage and a mean square momentum define an elementary phase volume and a diffusion constant and they obey the uncertainty relations. It is shown that the formalism of quantum mechanics describes the classical non-dissipative diffusion with a homogeneous diffusion constant and that quantum mechanics is only a particular case when the elementary phase volume of free passage is universal and equal to the Planck constant.
PACS: 02.50.Ey, 03.65.Ta , 05.40.Jc,
Key words: stochastic processes, quantum mechanics, Brownian motion
Vol. 3, No 3, p. 16 – 35, v1, 29 August 2008
Online: TPAC: 2798-011 v2, 28 September 2012; DOI: 10.9751/TPAC.2798-011
Download pdf 932 kb
[1] Centre for Theoretical Physics and Astrophyics, Tashkent, Uzbekistan
zahidzakir@theor-phys.org
Quantization of strings without anomaly in spacetime of arbitrary dimensionality
Zahid Zakir [1]
Abstract
New method of C-symmetric quantization, strongly following to the restrictions of discrete symmetries of systems, is applied to quantization of closed boson strings. It is shown that the chiral symmetry restrictions exclude a zero-point energy of the string modes. It then leads to the theory of the relativistic strings without conformal anomaly, which can be quantized consistently in a spacetime of arbitrary dimensionality.
PACS: 11.25.-w, 12.10.-g,
Key words: strings, quantization, conformal anomaly, discrete symmetries
Vol. 3, No 2, p. 9 – 15, v1, 30 June 2008
Online: TPAC: 2738-010 v2, 28 September 2012; DOI: 10.9751/TPAC.2738-010
Download pdf 355 kb
[1] Centre for Theoretical Physics and Astrophyics, Tashkent, Uzbekistan
zahidzakir@theor-phys.org
Quantization of relativistic fields without zero-point energy
2. Vector and spinor fields
Zahid Zakir [1]
Abstract
The new method of C- and CP-symmetric quantization of complex fields is applied for spinor, complex vector and electromagnetic fields. It is shown that the constraints imposed by requirements of discrete symmetries on bilinear products of creation-annihilation operators lead to operators of observables in a normal-ordered form without a zero-point energy and a zero-point charge.
PACS: 03.70. + k, 11.30.Er
Key words: quantization, charge conjugation, parity
Vol. 3, No 1, p. 1 – 8, v1, 4 March 2008
Online: TPAC: 2620-009 v2, 28 September 2012; DOI: 10.9751/TPAC.2620-009
Download pdf 468 kb
[1] Centre for Theoretical Physics and Astrophyics, Tashkent, Uzbekistan
zahidzakir@theor-phys.org
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