Self-consistency equations for nonunitary phases of superfluid Fermi liquid with spin-triplet pairing in a magnetic field

The generalized Fermi-liquid approach is used (with taking into account of the spin-exchange Fermi-liquid interaction) for description of different nonunitary phases of neutral paramagnetic superfluid Fermi liquid (SFL) with spin-triplet pairing of the ³He type (and also for the dense superfluid pur...

Повний опис

Збережено в:

Бібліографічні деталі
Дата:	2001
Автор:	Tarasov, A.N.
Формат:	Стаття
Мова:	English
Опубліковано:	Національний науковий центр «Харківський фізико-технічний інститут» НАН України 2001
Назва видання:	Вопросы атомной науки и техники
Теми:	Quantum fluids
Онлайн доступ:	http://dspace.nbuv.gov.ua/handle/123456789/80050
Теги:	Додати тег Немає тегів, Будьте першим, хто поставить тег для цього запису!
Назва журналу:	Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:	Self-consistency equations for nonunitary phases of superfluid Fermi liquid with spin-triplet pairing in a magnetic field / A.N. Tarasov // Вопросы атомной науки и техники. — 2001. — № 6. — С. 356-359. — Бібліогр.: 13 назв. — англ.

Репозитарії

Digital Library of Periodicals of National Academy of Sciences of Ukraine

id	irk-123456789-80050
record_format	dspace
spelling	irk-123456789-800502015-04-10T03:02:51Z Self-consistency equations for nonunitary phases of superfluid Fermi liquid with spin-triplet pairing in a magnetic field Tarasov, A.N. Quantum fluids The generalized Fermi-liquid approach is used (with taking into account of the spin-exchange Fermi-liquid interaction) for description of different nonunitary phases of neutral paramagnetic superfluid Fermi liquid (SFL) with spin-triplet pairing of the ³He type (and also for the dense superfluid pure neutron matter (SNM) existing inside core of neutron stars) in a strong magnetic field. In particular, the systems of connected nonlinear integral equations for the order parameter and effective magnetic field are obtained on the basis of energy functional (with Landau exchange amplitudes F₀a≠0 and F₂a≠0 ) which is quadratic in distribution functions of quasiparticles for nonunitary phases of ³He - A₂ type for SFL (or SNM) in a strong static and uniform magnetic field at any temperatures 0 ≤ T ≤ Tc (Tc is the normal - superfluid transition temperature). 2001 Article Self-consistency equations for nonunitary phases of superfluid Fermi liquid with spin-triplet pairing in a magnetic field / A.N. Tarasov // Вопросы атомной науки и техники. — 2001. — № 6. — С. 356-359. — Бібліогр.: 13 назв. — англ. 1562-6016 PACS: 67.57.-z, 05.30.-d, 21.65.+f, 97.60.Jd http://dspace.nbuv.gov.ua/handle/123456789/80050 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
topic	Quantum fluids Quantum fluids
spellingShingle	Quantum fluids Quantum fluids Tarasov, A.N. Self-consistency equations for nonunitary phases of superfluid Fermi liquid with spin-triplet pairing in a magnetic field Вопросы атомной науки и техники
description	The generalized Fermi-liquid approach is used (with taking into account of the spin-exchange Fermi-liquid interaction) for description of different nonunitary phases of neutral paramagnetic superfluid Fermi liquid (SFL) with spin-triplet pairing of the ³He type (and also for the dense superfluid pure neutron matter (SNM) existing inside core of neutron stars) in a strong magnetic field. In particular, the systems of connected nonlinear integral equations for the order parameter and effective magnetic field are obtained on the basis of energy functional (with Landau exchange amplitudes F₀a≠0 and F₂a≠0 ) which is quadratic in distribution functions of quasiparticles for nonunitary phases of ³He - A₂ type for SFL (or SNM) in a strong static and uniform magnetic field at any temperatures 0 ≤ T ≤ Tc (Tc is the normal - superfluid transition temperature).
format	Article
author	Tarasov, A.N.
author_facet	Tarasov, A.N.
author_sort	Tarasov, A.N.
title	Self-consistency equations for nonunitary phases of superfluid Fermi liquid with spin-triplet pairing in a magnetic field
title_short	Self-consistency equations for nonunitary phases of superfluid Fermi liquid with spin-triplet pairing in a magnetic field
title_full	Self-consistency equations for nonunitary phases of superfluid Fermi liquid with spin-triplet pairing in a magnetic field
title_fullStr	Self-consistency equations for nonunitary phases of superfluid Fermi liquid with spin-triplet pairing in a magnetic field
title_full_unstemmed	Self-consistency equations for nonunitary phases of superfluid Fermi liquid with spin-triplet pairing in a magnetic field
title_sort	self-consistency equations for nonunitary phases of superfluid fermi liquid with spin-triplet pairing in a magnetic field
publisher	Національний науковий центр «Харківський фізико-технічний інститут» НАН України
publishDate	2001
topic_facet	Quantum fluids
url	http://dspace.nbuv.gov.ua/handle/123456789/80050
citation_txt	Self-consistency equations for nonunitary phases of superfluid Fermi liquid with spin-triplet pairing in a magnetic field / A.N. Tarasov // Вопросы атомной науки и техники. — 2001. — № 6. — С. 356-359. — Бібліогр.: 13 назв. — англ.
series	Вопросы атомной науки и техники
work_keys_str_mv	AT tarasovan selfconsistencyequationsfornonunitaryphasesofsuperfluidfermiliquidwithspintripletpairinginamagneticfield
first_indexed	2025-07-06T03:59:12Z
last_indexed	2025-07-06T03:59:12Z
_version_	1836868544316309504
fulltext	SELF-CONSISTENCY EQUATIONS FOR NONUNITARY PHASES OF SUPERFLUID FERMI LIQUID WITH SPIN-TRIPLET PAIRING IN A MAGNETIC FIELD A.N. Tarasov Institute for Theoretical Physics National Science Center "Kharkov Institute of Physics and Technology", Kharkov, Ukraine e-mail: antarasov@kipt.kharkov.ua The generalized Fermi-liquid approach is used (with taking into account of the spin-exchange Fermi-liquid inter- action) for description of different nonunitary phases of neutral paramagnetic superfluid Fermi liquid (SFL) with spin-triplet pairing of the He3 type (and also for the dense superfluid pure neutron matter (SNM) existing inside core of neutron stars) in a strong magnetic field. In particular, the systems of connected nonlinear integral equations for the order parameter and effective magnetic field are obtained on the basis of energy functional (with Landau ex- change amplitudes 00 ≠aF and 02 ≠aF ) which is quadratic in distribution functions of quasiparticles for nonunitary phases of 2 3 AHe − type for SFL (or SNM) in a strong static and uniform magnetic field at any temperatures cTT ≤≤0 ( cT is the normal - superfluid transition temperature). PACS: 67.57.-z, 05.30.-d, 21.65.+f, 97.60.Jd GENERAL DESCRIPTION OF THE METHOD This research is devoted to theoretical analysis of su- perfluid Fermi liquids (SFL) with spin-triplet pairing in a magnetic field. We consider a SFL consisting of elec- trically neutral fermions possessing a magnetic moment. Such SFL include, for example, the superfluid phases of He3 and the extreme limit of isospin-asymmetric nucle- ar matter, namely superfluid pure neutron matter (SNM) (existing inside core of neutron stars). These phases were studied by many authors on the basis of different methods (see, for example, the reviews [1,2] and mono- graphs [3-5]). The Fermi-liquid approach generalized to superfluid systems [6-8] was used in [9,10] to derive a system of coupled equations for the order parameter (OP), effect- ive magnetic field (EMF) and energy of quasiparticles of a superfluid Fermi liquid in the general case of spin- triplet pairing (spin of a pair is 1=s , orbital angular momentum l of a pair is an arbitrary odd number) in static uniform magnetic field, taking into account the Landau spin-exchange normal Fermi-liquid (NFL) inter- action at temperatures cTT ≤≤0 . In this research general equations from [9,10] are used for deriving the equations for the OP and EMF which are valid for nonunitary superfluid phases of 2 3 AHe − type (and SNM) with taking into account only the p-wave pairing interaction ( 1=s , 1=l ) and with 00 ≠aF , 02 ≠aF in the spin-exchange NFL interac- tion. We restrict ourselves to the case of thermodynamic equilibrium. To describe the equilibrium states of superfluid phases of He3 type in sufficiently strong static uniform magnetic field H we introduce the energy functional (EF) );,,( HggfE + for this SFL, which is invariant to phase transformations and rotations both in coordinate and spin spaces separately. The EF can be written in the form (for details see [8,9,10]) ).,()();();,,( 210 ++ ++= ggEfEHfEHggfE (1) Here 1212 aaSpf +≡ ρ and 1212 aaSpg ρ≡ , +++ ≡ 1212 aaSpg ρ are the normal and abnormal distribution functions (DF) for quasiparticles ( ρ is the statistical operator, + 1a and 1a are the creation and annihilation operators for Fermi quasiparticles in the state ≡1 11,sp , where 1p is the mo- mentum and 1s is the spin component along the quantiz- ation axis). Expression (1) contains the energy of noninteracting fermions ( He3 atoms or neutrons in the case of SNM) );(0 HfE in a magnetic field, the energy functional )(1 fE possessing the above mentioned symmetry prop- erties, which describes NFL interactions: ( ) ( ) ( ) ( )[∑ += 21 20211101 , 2 1 pp pppp fFf V fE ( ) ( ) ( ) ( ) ]221211 , ppppp αα fFf+ , (2) where we take into account the fact that in spatially ho- mogeneous case under investigation ( ) ( ) ( ) 212121 ,11012 ][ pppp δσδ αα ssss fff += (3) 100 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2001, № 6, p. 356-359. (V is the volume occupied by the SFL, ασ are the Pauli matrices, 3,2,1=α ). NFL functions ( )211 ,ppF and ( )212 ,ppF of interaction between quasiparticles (intro- duced by Landau) depend on the angle θ between 1p and 2p lying on the Fermi surface, and hence can be ex- panded into a series in Legendre polynomials: ( ) ( ) ( ) ( )θθ cos12 2,1 0 2,1 l l l PFlF ∑ ∞ = += . (4) Here, in accordance with [9,10], we have denoted by )( 2,1 lF the NFL Landau's amplitudes, but in the literature such amplitudes are usually symbolized by as lF , (see, e.g., [4,5,11]). Finally, the last term in (1), which satisfies the prop- erties of invariance listed above, can be chosen, for ex- ample, in a form quadratic in g , i.e. ( ) ( ) ( ) ( )2211 * 2 21 ,1, pppp pp αα gLg V ggE t∑=+ , (5) where ( ) ( ) ( )ppp −−== ααα σσ ggSp i g s 22 1 . Expression (5) contains abnormal Fermi-liquid function of interaction ( )21,pptL between quasiparticles leading to triplet pairing. In the following we shall take into ac- count only p-wave pairing between He3 atoms (or neut- rons), i.e. ( ) ( ) ( ) ,ˆˆ3, 1 2121 LLt pppp ⋅−= ( )( )01 >L . (6) The OP for superfluid phases of He3 type has the form in the spatially homogeneous case (see [9,10]) ( ) ( )( ) ,,,2 221 121 21 2 12 ppp −+ + ∆= ∂ ∂=∆ δσσ αα ssi g ggE ( ) ( )pp αα ∆−=−∆ . (7) The energy matrix for quasiparticles is defined as ( ) ( ) = ∂ ∂= + 21 12 ;,,; f HggfEHfε ( ) ( ) ( )[ ] 212121 ,11 ;; pppp δσξδε ββ ssss ff += , (8) where the function ( )pξ is associated with the effective magnetic field ( )pHeff inside SFL (or SNM) through formula [9,10]: ( ) ( )( ) ββ µξ pp effn H−≡ (9) ( nµ is the magnetic dipole moment of nuclei of He3 atom (or neutron)). From (5)-(7) it follows the equation for the OP: ( ) ( ) ( ) ( )pppp p ′′⋅−=∆ ∑ ′ αα g V L13 , (10) and from (2),(3) and (8),(9) we find the equation for ( )pαξ : ( ) ( ) ( )∑ ′ ′′+−= p pppp ααα µξ fF V Hn , 2 1 2 . (11) The general explicit expressions for abnormal and nor- mal DF ( )pαg and ( )pαf for quasiparticles of the so- called nonunitary phases of SFL (or SNM) with spin- triplet pairing in a strong magnetic field H and at cTT ≤≤0 have the following form [10]: ( ) =pαg [ ] ( ) ( ) ( )[ ] ( ) ( ) − − Φ−Φ       ∆⋅+∆= −+ +− pp vpvp 22 ,,2, 2 EE i nn  ξξβ αα ( ) ( )[ ]nn vpvp ,, 2 −+ Φ+Φ∆− α , (12) ( ) ( ) ( ) ( )[ ] ( ) ( ) − − Φ−Φ      ∆⋅∆+= −+ +−∗ pp vpvpp 22 ,,2Re 2 EE zf nn  ξβ α α α ( ) ( )[ ]nn v,pv,p 2 −+ α Φ+Φξ− + ( ) ( )[ ] ( ) ( )pp vpvp 22 ,, −+ −+ − Ψ−Ψ EE nn αβ . (13) Here the functions ( )p±E , which are the energies of the quasiparticles in the SFL (or SNM) (with spin projec- tions parallel and antiparallel to the magnetic field), have the following general form ( ) ( ) ( ) ( )pppp 222 γβα +±≡±E , (14) where ( ) ( ) ( ) ( )pppp 222 ξα ++∆≡ z  , ( ) ( ) ( ) ( ) ( )ppppp ααα ξηβ zl 2+≡ , ( ) ( ) ( )ppp ∆⋅≡  ξγ 2 , ( ) ( ) µε −≡ pz p , ( ) ( ) ( ) ( )[ ]pp p pl ∗∆×∆≡  η i , and )( pε is the kinetic energy of a quasiparticle, µ is the chemical potential. The value ( ) ( ) ( )ppp ∗∆×∆≡  η is nonzero for the nonunitary phases of SFL with triplet pairing. The functions ±Φ and ±Ψ in (12), (13) are giv- en by the formulas: ( ) ≡Φ ± nvp, ( ) ( ) ( )            ⋅−+     ⋅+≡ ±± ± T Eth T Eth E nn 224 1 vppvpp p , 101 ( ) ≡Ψ ± nvp, ( ) ( )            ⋅−−     ⋅+≡ ±± T Eth T Eth nn 224 1 vppvpp . (15) Here nv is the nornal component velocity of the SFL (we assume that the superfluid component is at rest, 0=sv ). We stress that in the derivation of formulas (12) and (13) we have not specified the structure of the energy functional );,,( HggfE + but have only assumed that it has certain invariance properties mentioned above. The universal formulas (12) and (13) for the anomalous ( )pαg and normal ( )pαf distribution functions of the quasiparticles are valid in the general case for arbitrary nonunitary ( 0≠η ) phases of a SFL (or SNM) (with 0≠nv but 0=sv ) with triplet pairing (with 1=s and l an arbitrary odd integer) in a sufficiently strong static uniform magnetic field with allowance for the Landau Fermi-liquid exchange interaction. EQUATIONS FOR THE ORDER PARAME- TER AND EFFECTIVE MAGNETIC FIELD Knowing the explicit form of the quasiparticle DFs for a specific choice of structure of the energy functional (e.g., see (1), (2) and (5)) we can obtain a system of cou- pled equations (from (10), (11)) for the order parameter ( )pα∆ (7) and effective magnetic field )(pH eff (9) for the different phases of the SFL (or SNM). Let us consider the nonunitary superfluid phase of 2 3 AHe − type in the case of triplet p -wave pairing. The order parameter for such phase has the form: ( ) ( ) ( ) ( )pp ˆˆˆ2 ψααα eidA −+ ∆+∆=∆ , ( ) ( ) jjj pnim ˆˆˆˆ +≡pψ , ppp ≡ˆ . (16) Here d̂ and ê are mutually orthogonal real unit vectors in spin space, 0ˆˆ =⋅ ed , 1ˆˆ 22 == ed ; m̂ and n̂ are mu- tually orthogonal real unit vectors in orbital space, 0ˆˆ =⋅ nm , 1ˆˆ 22 == nm . The structure of functions ( ) ( ) ( )( ) 2TTT ↓ ↓↑ ↑± ∆±∆≡∆ corresponds to the case of Cooper pairing in the states with spin projections, which are equal to 1 and –1 on the quantization axis H. In the nonunitary phase of the 1 3 AHe − type 0=∆ ↓ ↓ and in the limit of zero magnetic field the unitary phase ( )0=η of the AHe −3 type with 0∆≡∆=∆ ↓ ↓↑ ↑ is re- alized. Thus, in the case of the energy functional of SFL (or SNM) quadratic in the DFs of quasiparticles we have obtained the following system of equations for the func- tions ( )ξ,T+∆ and ( )ξ,T−∆ (from Eqs. (10), (12) and (16)): ( ) ( ) ( ) ( ) ( ) ( )∫    +Φ+Φ∆⋅=∆ −+++ 2 1ˆˆˆ 2 3ˆ 111 3 3 1 pppp ψ π ψ pdL + ( ) ( )     − Φ−Φ       ∆+     ++∆ −+ −+ +− 22 2 2 2 2 1 EE iz dedl ξξξξη , (17.a) ( ) ( ) ( ) ( ) ( ) ( )∫    Φ+Φ∆⋅=∆ −+−− 2 1ˆˆˆ 2 3ˆ 111 3 3 1 pppp ψ π ψ pdL + + ( ) ( )     − Φ−Φ       ∆+     −+∆ −+ −+ −+ 22 2 2 2 2 1 EE iz eedl ξξξξη . (17.b) Here all functions, which are inside the braces { } , de- pend on the vector 1p and we have introduced by defini- tion the functions ( ) ( )( )dpp ˆ⋅≡ ξξ  d , ( ) ( )( )epp ˆ⋅≡ ξξ  e and ( ) ( )( )lpp ⋅≡ ξξ  l . In deriving the equations for the effective magnetic field ( )pHeff inside the SFL (or SNM) it has been taken into account the expansion (4) of the normal function of Fermi-liquid exchange interaction ( )12 ,ppF into a series in Legendre polinomials, in which we kept only the ( )0 2F and ( )2 2F Landau exchange amplitudes, i.e. ( ) ( ) ( )2 212 0 212 )ˆ,ˆ(5, FPFF pppp +≈ , (we have set ( ) 02 =lF for ,6,4=l ). In the case when ( ) 02 2 ≠F the function ( )pξ  depends on the p and, gen- erally speaking, is not collinear to external magnetic field H . Utilizing the explicit expressions (13) for ( )pαf [10] we have obtained the following system of nonlinear inte- gral equations for the scalar functions ( )pdξ , ( )peξ and ( )plξ (in the case when both the normal and superfluid components of the SFL (or SNM) are at rest, i.e. with velocities 0=nv , 0=sv ): ( ) ( ) ( ) ( ) ( ) ( )Hpp ˆˆ2 22 2 00 2 ⋅Ω−Ω−= PFF dddξ , ( ) ( ) ( ) ( ) ( ) ( )Hpp ˆˆ2 22 2 00 2 ⋅Ω−Ω−= PFF eeeξ , (18) ( ) ( ) ( ) ( ) ( ) ( )Hpp ˆˆ2 22 2 00 2 ⋅Ω−Ω−−= PFFH llnl µξ . Here lH \|\| and unknown functions ( )0 aΩ and ( )2 aΩ ( { }leda ,,≡ ) are defined by the formulas: ( ) ( ) ( ) ( )∫ − ≡Ω 1 1 112 0 coscos 22 1 θκθ π aa d , ( ) ( ) ( ) ( ) ( )∫ − −≡Ω 1 1 11 2 12 2 cos1cos3cos 24 5 θκθθ π aa d . (19) We have introduced in the formulas (19) the following functions ( )1p̂aκ : ( ) ( )([ +≡ ∫ 1 2 0 1 2 11 max pzpdp p dd pξκ ) ( ) ( ) ( ) ( )( ) + − Φ−Φ ∆+ −+ −+ + 1 2 1 2 11 1 22 2 1 sin pp pp EE θ ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2000, №2. Серия: Ядерно-физические исследования (36), с. 3-6. 102 ( ) ( )( ) Φ+Φ+ −+ 112 1 pp , (20.a) ( ) ( )([ +≡ ∫ 1 2 0 1 2 11 max pzpdp p ee pξκ ) ( ) ( ) ( ) ( )( ) + − Φ−Φ ∆+ −+ −+ − 1 2 1 2 11 1 22 2 1 sin pp pp EE θ ( ) ( )( ) Φ+Φ+ −+ 112 1 pp , (20.b) ( ) ( ) ( ) ( ) ( ) ( )( )∫             + − Φ−Φ ≡ −+ −+ max 0 1 2 1 2 11 1 2 1 2 11 2 1 p ll EE pzpdp pp pp pξκ ( ) ( )( ) +  Φ+Φ+ −+ 112 1 pp ( ) ( ) ( ) ( ) ( )( )      − Φ−Φ∆∆+ −+ −+ −+ 1 2 1 2 11 1 2 1 2 1sin pp pp EE pz θ . (20.c) CONCLUSION Thus, for the description of the equilibrium proper- ties of the SFL (or SNM) in the case of spin-triplet pair- ing in the state with ( )pα∆ of the form (16) in a high static and uniform magnetic field it is necessary to solve the systems of connected nonlinear integral equations (17.a), (17.b) and (18) (with taking into account defini- tions (19) and (20.a-c)). In the general case at arbitrary temperatures from the interval cTT ≤≤0 these equa- tions cannot be solved analytically (but they can be solved, for example, by the using of the numerical meth- ods). These results generalize the work [12] (where Fer- mi-liquid corrections were neglected) and our previous work [13] (where only )0( 2F NFL exchange Landau am- plitude was taken into account). ACKNOWLEDGMENTS The author is grateful to S.V. Peletminskii and A.A. Yatsenko for their interest in this work and for use- ful discussions of the results. This work was supported in part by the STCU (Project №1480). REFERENCES 1. A.J. Leggett. A theoretical description of the new phases of liquid 3He // Rev. Mod. Phys. 1975, v. 47, №2, p. 331-414. 2. V.P. Mineev. Superfluid 3He. Introduction to the subject // Usp. Fiz. Nauk, 1983, v. 139, №2, p. 303-332 (in Russian). [Sov. Phys. Usp. 1983, v. 26, p. 160]. 3. P.N. Brusov and V.N. Popov. Superfluidity and Collective Properties of Quantum Liquids. M.: “Nauka”, 1988, 216 p. (in Russian). 4. D. Vollhardt and P. Wolfle. The Superfluid Phases of Helium 3. London: “Taylor and Francis”, 1990, 619 p. 5. W.P. Halperin and L.P. Pitaevskii (eds.). Helium Three. Amsterdam: “North Holland”, 1990, 994 p. 6. V.V. Krasil’nikov, S.V. Peletminskii, and A.A. Yatsenko. On the theory of a superfluid Fermi liquid // Physica A. 1990, v. 162, №3, p. 513-541. 7. A.I. Akhiezer, V.V. Krasil'nikov, S.V. Pelet- minskii, A.A. Yatsenko. Theory of superfluid Fermi liquid // Usp. Fiz. Nauk, 1993, v. 163, №2, p. 1-32 (in Russian). [Phys. Usp. 1993, v. 36, p. 5]. 8. A.I. Akhiezer, V.V. Krasil'nikov, S.V. Pelet- minskii, A.A. Yatsenko. Research on superfluidity and superconductivity on the basis of Fermi liquid concept // Phys. Rep. 1994, v. 245, №1-2, p. 1-110. 9. A.N. Tarasov. On the theory of superfluid Fermi liquid with spin-triplet pairing in a magnetic field // Fiz. Nizk. Temp. 1998, v. 24, №5, p. 429- 437 (in Russian). [Low Temp. Phys. 1998, v. 24, №5, p. 324-330]. 10. A.N. Tarasov. Some questions in the theory of a superfluid Fermi liquid with triplet pairing in a magnetic field // Fiz. Nizk. Temp. 2000, v. 26, №11, p. 1059-1066 (in Russian). [Low Temp. Phys., 2000, v. 26, №11, p. 785-790]. 11. D. Pines and Ph. Nozieres. The Theory of Quantum Liquids, New York: “Benjamin”, 1966. 12. Y. Hasegawa. Superfluid 3He in a magnetic field // Progr. Theor. Phys. 1980, v. 63, №3, p. 1040-1043. 13. A.N. Tarasov. About nonunitary phases of superfluid helium-3 in a magnetic field // Journal of Molecular Liquids. 2001, v. 93, №1-3, p. 87-90. 103 SELF-CONSISTENCY EQUATIONS FOR NONUNITARY PHASES OF SUPERFLUID FERMI LIQUID WITH SPIN-TRIPLET PAIRING IN A MAGNETIC FIELD A.N. Tarasov GENERAL DESCRIPTION OF THE METHOD EQUATIONS FOR THE ORDER PARAMETER AND EFFECTIVE MAGNETIC FIELD CONCLUSION acknowledgmentS

Self-consistency equations for nonunitary phases of superfluid Fermi liquid with spin-triplet pairing in a magnetic field

Репозитарії

Схожі ресурси