The current density order based on the Ginzburg-Landau description

The goal of this survey is to deduce the grandeurs, or the set of grandeurs, from which is derived simultaneously as a linear combination of densities of states, current density matrix and the reduced entropy, according to the general fact that the logarithm of the distribution is additive fir...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Datum:	2007
Hauptverfasser:	Bousnane, Z., Merabtine, N., Benslama, M., Bousaad, F.
Format:	Artikel
Sprache:	English
Veröffentlicht:	Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України 2007
Schriftenreihe:	Semiconductor Physics Quantum Electronics & Optoelectronics
Online Zugang:	http://dspace.nbuv.gov.ua/handle/123456789/117804
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!
Назва журналу:	Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:	The current density order based on the Ginzburg-Landau description / Z. Bousnane, N. Merabtine, M. Benslama, F. Bousaad // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2007. — Т. 10, № 1. — С. 97-100. — Бібліогр.: 2 назв. — англ.

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine

id	irk-123456789-117804
record_format	dspace
spelling	irk-123456789-1178042017-05-27T03:04:22Z The current density order based on the Ginzburg-Landau description Bousnane, Z. Merabtine, N. Benslama, M. Bousaad, F. The goal of this survey is to deduce the grandeurs, or the set of grandeurs, from which is derived simultaneously as a linear combination of densities of states, current density matrix and the reduced entropy, according to the general fact that the logarithm of the distribution is additive first integral. In this perspective, we introduce the notations, which gives to the logarithm of the distribution as the quaternionic picture of the operatorial transcriptions, this must follow the behaviour of a canonical distribution through the interval of the transitions. It seems that the nonreproducibility is caused essentially by the fact of absolute separability of dimensions between the observed and observer. The reduced entropy will suggest the inner displaying of observer, the invariance of unsymmetric order parameter products will be an expression of reproducibility. We must have a displaying of such products over inner dimensions, allowing to translate a limit of the displaying of stationary levels of macroscopic bodies over inner distances. Iˆ is the parity operator and will act under respect or violation of products as uncertainties, Jˆ is representing measurement process decomposing layers, sublayers and orbitals according to the thresholds logics answering how cold will be felt to transgress the conventional univoc filling rules, Kˆ represents measurement process realising the centesimal entropy depth penetration. The introduction of such notations will be justified by the fact that the ρ -distribution, introduced as an unsymmetric product of order parameters, is defined per pavement – pavement as defined by J.H. Poincaré. 2007 Article The current density order based on the Ginzburg-Landau description / Z. Bousnane, N. Merabtine, M. Benslama, F. Bousaad // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2007. — Т. 10, № 1. — С. 97-100. — Бібліогр.: 2 назв. — англ. 1560-8034 PACS 74.25.Bt http://dspace.nbuv.gov.ua/handle/123456789/117804 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
description	The goal of this survey is to deduce the grandeurs, or the set of grandeurs, from which is derived simultaneously as a linear combination of densities of states, current density matrix and the reduced entropy, according to the general fact that the logarithm of the distribution is additive first integral. In this perspective, we introduce the notations, which gives to the logarithm of the distribution as the quaternionic picture of the operatorial transcriptions, this must follow the behaviour of a canonical distribution through the interval of the transitions. It seems that the nonreproducibility is caused essentially by the fact of absolute separability of dimensions between the observed and observer. The reduced entropy will suggest the inner displaying of observer, the invariance of unsymmetric order parameter products will be an expression of reproducibility. We must have a displaying of such products over inner dimensions, allowing to translate a limit of the displaying of stationary levels of macroscopic bodies over inner distances. Iˆ is the parity operator and will act under respect or violation of products as uncertainties, Jˆ is representing measurement process decomposing layers, sublayers and orbitals according to the thresholds logics answering how cold will be felt to transgress the conventional univoc filling rules, Kˆ represents measurement process realising the centesimal entropy depth penetration. The introduction of such notations will be justified by the fact that the ρ -distribution, introduced as an unsymmetric product of order parameters, is defined per pavement – pavement as defined by J.H. Poincaré.
format	Article
author	Bousnane, Z. Merabtine, N. Benslama, M. Bousaad, F.
spellingShingle	Bousnane, Z. Merabtine, N. Benslama, M. Bousaad, F. The current density order based on the Ginzburg-Landau description Semiconductor Physics Quantum Electronics & Optoelectronics
author_facet	Bousnane, Z. Merabtine, N. Benslama, M. Bousaad, F.
author_sort	Bousnane, Z.
title	The current density order based on the Ginzburg-Landau description
title_short	The current density order based on the Ginzburg-Landau description
title_full	The current density order based on the Ginzburg-Landau description
title_fullStr	The current density order based on the Ginzburg-Landau description
title_full_unstemmed	The current density order based on the Ginzburg-Landau description
title_sort	current density order based on the ginzburg-landau description
publisher	Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
publishDate	2007
url	http://dspace.nbuv.gov.ua/handle/123456789/117804
citation_txt	The current density order based on the Ginzburg-Landau description / Z. Bousnane, N. Merabtine, M. Benslama, F. Bousaad // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2007. — Т. 10, № 1. — С. 97-100. — Бібліогр.: 2 назв. — англ.
series	Semiconductor Physics Quantum Electronics & Optoelectronics
work_keys_str_mv	AT bousnanez thecurrentdensityorderbasedontheginzburglandaudescription AT merabtinen thecurrentdensityorderbasedontheginzburglandaudescription AT benslamam thecurrentdensityorderbasedontheginzburglandaudescription AT bousaadf thecurrentdensityorderbasedontheginzburglandaudescription AT bousnanez currentdensityorderbasedontheginzburglandaudescription AT merabtinen currentdensityorderbasedontheginzburglandaudescription AT benslamam currentdensityorderbasedontheginzburglandaudescription AT bousaadf currentdensityorderbasedontheginzburglandaudescription
first_indexed	2025-07-08T12:49:36Z
last_indexed	2025-07-08T12:49:36Z
_version_	1837083108173676544
fulltext	Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 1. P. 97-100. © 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 97 PACS 74.25.Bt The current density order based on the Ginzburg-Landau description Z. Bousnane1, N. Merabtine2, M. Benslama2, F. Bousaad1 1Physics Department, Faculty of Science, University of Batna, 05000 Algeria 2Electromagnetism and Telecommunication Laboratory, Electronics Department, Faculty of Engineering, University of Constantine, 25000 Algeria Corresponding author: malekbenslama@hotmail.com Abstract. The goal of this survey is to deduce the grandeurs, or the set of grandeurs, from which is derived simultaneously as a linear combination of densities of states, current density matrix and the reduced entropy, according to the general fact that the logarithm of the distribution is additive first integral. In this perspective, we introduce the notations αβαβ ++Ψ SK̂jĴÎ 2 , which gives to the logarithm of the distribution as the quaternionic picture of the operatorial transcriptions, this must follow the behaviour of a canonical distribution through the interval of the transitions. It seems that the nonreproducibility is caused essentially by the fact of absolute separability of dimensions between the observed and observer. The reduced entropy will suggest the inner displaying of observer, the invariance of unsymmetric order parameter products will be an expression of reproducibility. We must have a displaying of such products over inner dimensions, allowing to translate a limit of the displaying of stationary levels of macroscopic bodies over inner distances. Î is the parity operator and will act under respect or violation of products as uncertainties, Ĵ is representing measurement process decomposing layers, sublayers and orbitals according to the thresholds logics answering how cold will be felt to transgress the conventional univoc filling rules, K̂ represents measurement process realising the centesimal entropy depth penetration. The introduction of such notations will be justified by the fact that the ρ -distribution, introduced as an unsymmetric product of order parameters, is defined per pavement – pavement as defined by J.H. Poincaré. Keywords: current density order, pavement, superconductivity. Manuscript received 21.02.06; accepted for publication 26.03.07; published online 01.06.07. 1. Introduction The reduced entropy defining the eigenvalue is equivalent to say that the possible order parameters describing the superconductor state are recursive, the recursivity of the order parameter implies that among the whole micropossible configurations, over which displayed are the macropossible configurations; there exist configurations that seems to be displayed over an effective subset of configurations, thus the symmetry order in nature will be as follows: a) the real symmetries corresponding to the attitude of matter to the order; b) the nonreal symmetries corresponding to the possibilities let by this order to the space to accept the same order. These considerations above will allow us to realise limitations imposed to the GL description validity. 2. Distribution law As known in the statistical mechanics methods [1], and conformably to the natural character of grandeurs during a phase transitions ( ) ( ) αββαβαβα jρ divdivlnlnÎlnln 2 −Γ∆+Ψ= (1) Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 1. P. 97-100. © 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 98 with αββα j dt d divdiv2 −=Ψ is the effective continuity equation. The distribution function W∆ is given by ( ) Γ∆π s2 hρ (2) that gives the number of the macropossible states. Equation (1) is written ( ) ( ) αββαβαβα jΨIΓ - ρ divdivˆ∆lnlnlnln 2 −= , (3) and for the W function, we have ( ) ( ) ( ) .divdivÎ lnln - ∆∆lnln 2 αββα βαsβα j Γ 2π W −Ψ= =Γ∆⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ′ h (4) For the definition of the W function, we must have Γ′Γ∆∆ 1 ∼ ( )s2 hπ that stipulate an uncertainty principle as follows: Γ′Γ∆∆ 1 ∼ s 1 h . (5) The recursivity here permits the stability for Γ∆ and Γ′∆ , and we hear by this an interaction between micropossible configurations, permitting the emergence of homologous one, which having amplitudes and phases linearly homologous between them, which is equivalent to the interaction of micropossible configurations for emerging a news proportional to their images. When the macropossible configurations follow the same processes, this leads to the reproducibility. Taking Γ′Γ∆∆ ∼ s 1 h into account, equation (4) will be written ( ) αββαβα jdivdivÎ Wlnln 2 −Ψ=∆ . (6) The emergence of recursivity will be generated by Eq. (5). Γ∆ and Γ′∆ are the measurement results as a state numbers, which here are a conventional choice, if Γ∆ presents the states number of macropossible informing on real symmetries, Γ′∆ is linked to the recursive one. We write αβS as βα Γ′∆Γ∆ln with αβSS =0 , (7) which expresses the conservation law of the reduced entropy mean value. If this law is expressed as a function of one statistical weight, we have == αβSS0 – ( )Γ∆βα lnln . The normalized Sαβ is written as βααβS Γ∆∆Γ= ln 2 1 , on the other hand, we have Sαβ = k lnα ( k ∆Γβ ), and βααβS Γ∆∆Γ= ln must obey the physical equivalence, we then write ( )]lnklnk[ln 2 1 βαβα Γ∆+Γ∆∆Γ=αβ S . (8) When 00 == SSαβ , we have =Γ∆∆Γ βαln ( )Γ∆−= βkk lnln α . The reduced entropy that we introduce takes the meaning that the natural increasing of entropy through an interval of states is “suffocating“ by the dual increasing of entropy through an other interval of states. The ancient entropy was free, it was in accord with homogenous, isotropic space and uniform time. The limitations imposed to the entropy in our case are caused by the recursive character of the wave function generating the GL order parameter. 3. Description With the decreasing of temperature, the entropy of the two “candidates” wave functions will be represented as two recursive lens, making the action of “cold” as a reduced entropy. The cold as a classical being, it was considered, had generated the order parameter with asymptotic form that was a function of the coherence length Ψ ∼ ( ) ( )Tξ Si ebaη , , (9) where a and b are the Landau phenomenological parameters. ( )Tξ , the Landau coherence length, and S is the entropy linked to the free energy density by relations: ( ) 2ENTSEF Ψln∆−=−= , (10a) ( ) 2ln Ψ∆−=ϕ−= ETSEF , (10b) ( ) ∗ ∗ ∆ΨΨ∇ Ψ∇∆Ψ ∆−=ϕ−= lnE,NTSEF , (10c) where ( )NS is written in N-representation, ( )ϕS is written in ϕ -representation, and ( ),NS ϕ is acting operator bi-univoc transformation between N-representation and ϕ -representation. In this case, the entropies in two candidates wave functions are the entropies, suffocating each other exponentially to the extremal point, the entropies are Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 1. P. 97-100. © 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 99 chained with interaction making the birth of matrix elements, which are the first term of the states density development. For the normalized current density matrix elements, we write: 2 12 αββα−= Ψ jdivdiv dt d , (11) ( ) ( )dAAJAj βααβ ΨΨ= ∫ ˆ , (12) where dA is the differential of the potential. The operatorial transcription of the macroscopicity giving the distance between levels, we write αβ=∆ jSFe n S 0 0ˆ , (13) then we obtain αβαββα ∗ +−= ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ Ψ+∇ ∫ jSdtjdivdivAA c eie n S 0 2 1 0ˆ h . (14) By concerning the similitude laws for the second order transition, the action of 0ˆSe operator is equalling 4 2 Ψ b with αβjSn0 , physically it signifies that, for an eigenvalue 0S of the reduced entropy corresponding to the αβj element, the term 4Ψ is not mentioning a spatial extension except those permitted by the multiplier of 2 b . The constant multiplication here is the 4Ψ length scale coherence normalization. In our work, we have considered the nullity of entropy as an asymptotic behaviour of the entropies wave functions, because of its definition as represented by 0ˆSe with conjugate 0ˆ Se− . The computing origin of the reduced entropy, will began by a negative number which is −5.0396×10−15. 4. The entropy thermodynamical scale We shall show, at less, as a principle that it is possible to construct a thermodynamical scales of entropies, having one of the temperatures, with the fundamental definition ctedE T S += ∫ 1 , by defining a reduced temperature and identifying these two equations: αβ= SS0 and ctedE T S += ∫ 1 , we obtain 15100396.51 − αβ ⋅−= ∫ dE T S (16) Let us write the eigenvalue of reduced entropy as αβ=∆ jSFe n S 0 0ˆ , where F∆ is in the order of ( )αβ∆F , also the two eigenvalues as αβ=∆ jSFeS 10 0ˆ and αβ=∆ jSFeS 20 0ˆ , which leads to αβαβ −=∆ jSjSFeS 20102 1ˆ 0 . (17) According to the general rule of operators derivation, we have [ ]HeeHi t e SS S ˆˆˆˆˆ 00 0 −= ∂ ∂ h . If HSS == 2010 , we must have αβαβ − jSjSi 20102h , then αβαβ −= ∂ ∂ jSjSi t eS 20102 ˆ 0 h . (18) For the thermal equilibrium of second order realization, it is necessary that the reduced entropy matrix must be diagonalizable per pavement, we write ( ) ( )⎪ ⎩ ⎪ ⎨ ⎧ ⋅−= =ξ= = − α ∫ ∫ αβ 15 0 0 100396.5~,ˆ,for 0,ˆ,for dττTTξδSS dττTTδSS Sαβ It seems that the variation of coherence scale causes the birth of reduced entropy and, reversibly, ( ) ττξδ∫ dTT ,ˆ, is equivalent to measurement process giving the eigenvalue of reduced entropy, we say that ( ) ττξδ∫ dTT ,ˆ, has a lot of extremals. 5. Thermal equilibrium equation Per pavement, where is defined a fluctuating order parameter, respecting the operators differentiation rule, we rewrite [ ] FeHHeiF td ed SS S ∆−=∆ 00 0 ˆˆˆˆˆ h , ( ) ( ) =∆−∆=∆ FeHiFHeiF td ed SS S 00 0 ˆˆˆˆˆ hh Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 1. P. 97-100. © 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 100 ( ) ( )FeHiFHei SS ∆−∆= 00 ˆˆˆˆ hh , ( ) αβ−∆=∆⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ jSHiFHeiFe td d n SS 0 ˆˆˆˆ 00 hh , then we obtain the two equations of thermal equilibrium αβ−=∆⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − jSHiFHei td ed n S S 0 ˆˆˆˆ 0 0 hh . (19) In modulus, ( ) =∆ ⎪⎭ ⎪ ⎬ ⎫ ⎪⎩ ⎪ ⎨ ⎧ +⎟ ⎠ ⎞ ⎜ ⎝ ⎛−⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ − 2ˆˆˆˆˆ2ˆ 0000 FHeiHeie td de td d SSSS hh 2 02 )ˆ(1 αβ−= jSH n h . (20) 6. Conclusion concerning the thermal equilibrium representation To establish equation for thermal equilibrium by expressing the action of operator ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ − Hei td edi S S ˆˆˆ 0 0 hh on F∆ , this action permits the birth of current density matrix elements. This kind of identity is an equivalence between two operatorial writings, this equivalence concern the effect and not the cause. To establish a thermodynamical scale of entropies, this will be possible by expressing the normalized extremums of ( ) ττξ∫ τ τ dTT 2 1 ,ˆ, . τ expresses the normalized thermodynamical scales, obtained as an equivalence between τd Td ln and the ratios Ψ∇∆ΨΨ∇∆Ψ Ψ∇Ψ∇∆Ψ∆Ψ Ψ∇ΨΨ∇Ψ ∆ΨΨΨ∆Ψ ∗∗ ∗∗ ∗∗ ∗∗ , with the normalized conditions giving the equivalence between ∫ ′∆Ψ∆Ψ ∗ qdqdĴ and τ′ττ′∆∆Ψ∆Ψτ∆∆Ψ∆Ψ ∗∗∫∫ ddeS0ˆ , ∫ ′Ψ∇Ψ∇ ∗ qdqdĴ and τ′ττ′∆Ψ∇Ψ∇τ∆Ψ∇Ψ∇ ∗∗∫∫ ddeS0ˆ , ( ) 22 qdqdjjjj ′− ∆ΨΨ∇ Ψ∇∆Ψ αββγβγαβ∗ ∗ ∫ , and [ ] τ′ττ′∆∆Ψ∆Ψ−τ∆Ψ∇Ψ∇ ∗∗∫∫ ddeHHei SS 00 ˆˆˆˆ h . The coefficients of those equivalences are considered as the levels of normalizations. 5. General conclusion The recursivity based on the J.H. Poincarre per pavement concept is permitting to introduce a limitation against the character of measurement processes, and the nature of values, emerging as a result of measurement without measurement, meaning by this that the reduced displaying levels of systems in nature appears as a result of interaction between two displaying faculties observed under two different indetermination orders [1, 2]. References 1. L. Landau, E. Lifshits, Statistical physics. Edition MIR, Moscow, 1969. 2. L. Landau, E. Lifshits, Quantum mechanics. Edition MIR, Moscow, 1967.

The current density order based on the Ginzburg-Landau description

Institution

Ähnliche Einträge