New model for systems of mesoscopic Josephson junctions

Quantum fluctuations of the phases of the order parameter in two-dimensional arrays of mesoscopic Josephson junctions and their effect on the destruction of superconductivity in the system are investigated by means of a quantum-cosine model that is free of the incorrect application of the phase operator. The proposed model employs trigonometric phase operators and makes it possible to study arrays of small superconducting granules, pores containing superfluid helium, or Josephson junctions in which the average number of particles n ₀ (effective bosons, He atoms, and so on) is small, and the standard approach employing the phase operator and the particle number operator as conjugate operators is inapplicable. There is a large difference in the phase diagrams between arrays of macroscopic and mesoscopic objects for n ₀<5 and U<J (U is the characteristic interaction energy of the particles per granule and J is the Josephson coupling constant). Re-entrant superconductivity phenomena are discussed. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 10, 649–654 (25 November 1997)     

Marginal Distributions of Wigner Function in a Mesoscopic L-C Circuit at Finite Temperature and Thermal Wigner Operator

Wigner function in phase space has its physical meaning as marginal probability distribution in coordinate space and momentum space respectively, here we endow the Wigner function with a new physical meaning, i.e., its marginal distributions’ statistical average for q ²/(2C) and p ²/(2L) are the energy stored in capacity and in inductance of a mesoscopic L-C circuit at finite temperature, respectively. PACS numbers: 03.65.-w, 73.21.-b     

On the dimensionality of superconductivity in cuprate superconductors

The question of the dimensionality of superconductivity is considered within the framework of a model of superconductivity via asymmetric, delocalized “crystalline” π orbitals (analogous to the corresponding molecular orbitals) extending along chains of covalently bonded copper and oxygen ions. It is shown that superconductivity is preceded by a separation of the bonds in the CuO₂ layer into covalent and ionic bonds with ordering of the covalent bonds into chains. Such an ordering facilitates the formation of a crystalline π orbital lowering the crystal energy by the resonance energy of the π bond and is therefore favored. The superconducting current is created by non-dissipative motion of π-electron pairs along the asymmetric, “crystalline” π orbitals extending along chains of covalently bonded copper and oxygen ions, in the presence of an ionic bond between neighboring chains extending through the easily polarizable O²⁻ ions. This ionic bond correlates the motion of the electron pairs along all the π orbitals and stabilizes the superconducting state. Only in this sense is the apparent “onedimensionality” of superconductivity in cuprate superconductors to be understood. Zh. Tekh. Fiz. 68, 82–84 (November 1998)     

Towards a manifestly supersymmetric formulation of N = 8 supergravity on a light-cone superspace

N = 8 supergravity is formulated in the light-cone gauge. An unconstrained superfield defined on a light-cone superspace is constructed from the component formulation. The light-cone superspace is spanned by Grassmann coordinates which belong to the spinor representation of SO(7), a subgroup of the transverse SO(9).     

Berezinians,Exterior Powers and Recurrent Sequences

We study power expansions of the characteristic function of a linear operator A in a p|q-dimensional superspace V. We show that traces of exterior powers of A satisfy universal recurrence relations of period q. ‘Underlying’ recurrence relations hold in the Grothendieck ring of representations of GL(V). They are expressed by vanishing of certain Hankel determinants of order q+1 in this ring, which generalizes the vanishing of sufficiently high exterior powers of an ordinary vector space. In particular, this allows to express the Berezinian of an operator as a ratio of two polynomial invariants. We analyze the Cayley–Hamilton identity in a superspace. Using the geometric meaning of the Berezinian we also give a simple formulation of the analog of Cramer’s rule Mathematics Subject Classification (2000): 15A15, 58A50, 81R99 To the memory of Felix Alexandrovich Berezin     

Quantum orientational melting and the phase diagram of a mesoscopic system

The “phase diagram” of a two-dimensional mesoscopic system of bosons is investigated. An example of such a system is a system of indirect magnetoexcitons in semiconductor double quantum dots. Quantum Monte Carlo calculations show the existence of quantum orientational melting. At zero (quite low) temperature, as quantum fluctuations of the particles intensify, two quantum disordering phenomena occur with increasing de Boer parameter q. First, at q≈10⁻³ the system passes to a radially ordered but orientationally disordered state, where different shells of a cluster rotate relative to one another. Then at q≈0.16 a transition to a superfluid state occurs. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 11, 817–822 (10 December 1998)     

Electron phonon interactions and superconductivity in α ′ -TTF[Pd(dmit)2]2

A simple model is developed to understand superconductivity in α ^′ -TTF[Pd(dmit)₂]₂. We include electron-intra molecular and intermolecular phonon interactions as the mechanism of superconductivity. Intramolecular vibrations included are the eight symmetric A_g modes of the Pd(dmit)₂ molecule. Intermolecular vibrations included are the longitudinal acoustic and transverse acoustic (LA and TA) modes of the Pd(dmit)₂ column. All the electron-phonon coupling constants are calculated from first principles. We find that largest el-intramolecular vibration coupling is to the A_g mode with the highest frequency (1449 cm^-1). The el-intermolecular coupling to the LA mode is found to be larger than the total el-intramolecular couplings. We also find el-(TA)phonon coupling to be at least an order of magnitude smaller than el-(LA)phonon coupling. Estimate of superconducting transition temperature is comparable to experimental result. We also provide a detailed discussion, employing the results of recent numerical calculations on two-chain Hubbard model and the specific material parameters, on the relative importance of el-ph and Coulomb-origin mechanisms of superconductivity in α ^′ -TTF[Pd(dmit)₂]₂ and TTF[Ni(dmit) ₂ ] ₂ . Received 29 March 2001 and Received in final form 7 August 2001     

Influence of structural disorder on the current-voltage characteristic of a quasi-one-dimensional tunnel junction

The influence of the subbarrier impurity scattering of tunneling electrons on the current-voltage characteristic of a quasi-one-dimensional insulator layer with weak structural disorder (a small impurity concentration) is considered in the one-electron approximation at T=0. An expansion in powers of the impurity concentration gives the form of the current-voltage characteristic and the conditions for small mesoscopic fluctuations of the static tunneling conductance of such a layer in the cases of resonant and nonresonant tunneling. Zh. éksp. Teor. Fiz. 113, 1522–1530 (April 1998)     

Employment of curvilinear coordinates in ab initio calculations of insulators using pseudopotentials

The standard ab initio scheme for calculating the structure of crystals using nonlocal pseudopotentials is modified for use in curvilinear coordinates. A method for solving the Poisson equation for the Coulomb potential in a curved space in the k representation is found. It is shown in the example of calculations for crystals of insulators having an NaCl structure that the employment of a curved space permits a very significant decrease in the required size of the basis set. Fiz. Tverd. Tela (St. Petersburg) 41, 241–246 (February 1999)     

How different are the supermanifolds of Rogers and DeWitt?

A DeWitt supermanifold always has the structure of a vector bundle over an ordinary spacetime manifold, whereas a Rogers supermanifold is not so restricted. Corresponding to the vector space fibers of the DeWitt supermanifold, a Rogers supermanifold has a foliation by submanifolds, or leaves, parametrized by soul coordinates only. We show that the universal covering space of any leaf always admits a flat metric. If the covering space is complete in this metric, it must in fact be a vector space. We combine this result with known theorems about foliations to give conditions under which a compact Rogers supermanifold with a single even dimension is necessarily a quotient space of flat superspace. We also show that a supermanifold defined by a polynomial equation in flat superspace is always of the DeWitt type. Finally, we exhibit new supermanifold structures forR ² and the 2-torus which show that the foliation of a Rogers supermanifold can be quite exotic.Enrico Fermi Fellow. Research supported by the NSF: PHY 83-01221, and the Department of Energy: DE AC02-82-ER-40073     

Competition between nuclear ferromagnetism and superconductivity

A qualitative theory of nuclear magnetism against a background of superconductivity in metals is proposed. Even though the superconducting transition temperature is much higher than the nuclear ordering temperature, nuclear ferromagnetism can partially or completely destroy superconductivity. An experimental method of determining the effective electron-nuclear spin-spin interaction constant for superconductors is discussed. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 10, 772–775 (25 May 1997)     

Superconductivity in the presence of fermion condensation

Fermion condensation (FC) is studied within the density functional theory. FC can fulfill the role of a boundary, separating the region of strongly interacting electron liquid from the region of strongly correlated electron liquid. Consideration of the superconductivity in the presence of FC shows that, under certain circumstances, at temperatures above T _c the superconductivity vanishes and the superconducting gap smoothly transforms into a pseudogap. The pseudogap occupies only a part of the Fermi surface, and one that shrinks with increasing temperature and vanishes at T=T*, and the single-particle excitations of the gapped area of the Fermi surface have a width γ ∼(T-T _c ). Pis’ma Zh. éksp. Teor. Fiz. 68, No. 6, 491–496 (25 September 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Pseudogap and symmetry of superconducting order parameter in cuprates

The phase diagram, nature of the normal state pseudogap, type of the Fermi surface, and behavior of the superconducting gap in various cuprates are discussed in terms of a correlated state with valence bonds. The variational correlated state, which is a band analogue of the Anderson (RVB) states, is constructed using local unitary transformations. Formation of valence bonds causes attraction between holes in the d-channel and corresponding superconductivity compatible with antiferromagnetic spin order. Our calculations indicate that there is a fairly wide range of doping with antiferromagnetic order in isolated CuO₂ planes. The shape of the Fermi surface and phase transition curve are sensitive to the value and sign of the hopping interaction t′ between diagonal neighboring sites. In underdoped samples, the dielectrization of various sections of the Fermi boundary, depending on the sign of t′, gives rise to a pseudogap detected in photoemission spectra for various quasimomentum directions. In particular, in bismuth-and yttrium-based ceramics (t′>0), the transition from the normal state of overdoped samples to the pseudogap state of underdoped samples corresponds to the onset of dielectrization on the Brillouin zone boundary near k=(0,π) and transition from “large” to “small” Fermi surfaces. The hypothesis about s-wave superconductivity of La-and Nd-based ceramics has been revised: a situation is predicted when, notwithstanding the d-wave symmetry of the superconducting order parameter, the excitation energy on the Fermi surface does not vanish at all points of the phase space owing to the dielectrization of the Fermi boundary at k _x=± k _y. The model with orthorhombic distortions and two peaks on the curve of T _c versus doping is discussed in connection with experimental data for the yttrium-based ceramic. Zh. éksp. Teor. Fiz. 115, 649–674 (February 1999)     

Feynman-Kac and feynman formulas for evolution pseudodifferential equations in superspace

In the paper, evolution pseudodifferential equations in the space of superanalytic functions (X) of an infinite-dimensional argument with symbols in the space (Y) of Fourier supertransforms of distributions on the dual superspace are considered. For these equations, the “weak” Cauchy problem is posed and the existence theorem for the solutions of this problem is proved. The main result of the paper is the theorem concerning the representation of solutions of the “weak” Cauchy problem by the Feynman path integral in the phase superspace (the Feynman-Kac formula). The Feynman integral is understood in the sequential sense. Thus, the Feynman formula becomes an immediate consequence of the Feynman-Kac formula.     

Supercooling in a system of two superconductors

Supercooling in the transition of a type I superconductor to the superconducting state in contact with another superconductor whose critical temperature is higher has been measured. Using aluminum as a test material, it has been demonstrated that at temperatures below the critical temperature T _c and magnetic fields below the critical field H _c(T), aluminum remains in a metastable normal state, in spite of its contact with another superconductor. This means that it is not possible to generate a thermodynamic instability in a superconductor’s electronic system through the “proximity effect” with another superconductor whose critical temperature is higher. This experimental observation demonstrates a radical difference between surface superconductivity, which certainly generates instability in normal electronic states, and superconductivity induced by the proximity effect near a junction with another superconductor. Zh. éksp. Teor. Fiz. 112, 1119–1131 (September 1997)     

Ambient space formulations and statistical mechanics of holonomically constrained Langevin systems

The most classic approach to the dynamics of an n-dimensional mechanical system constrained by d independent holonomic constraints is to pick explicitly a new set of (n − d) curvilinear coordinatesparametrizingthe manifold of configurations satisfying the constraints, and to compute the Lagrangian generating the unconstrained dynamics in these (n − d) configuration coordinates. Starting from this Lagrangian an unconstrained Hamiltonian H(q,p) on 2(n−d) dimensional phase space can then typically be defined in the standard way via a Legendre transform. Furthermore, if the system is in contact with a heat bath, the associated Langevin and Fokker-Planck equations can be introduced. Provided that an appropriate fluctuation-dissipation condition is satisfied, there will be a canonical equilibrium distribution of the Gibbs form exp(−βH) with respect to the flat measure dqdp in these 2(n − d) dimensional curvilinear phase space coordinates. The existence of (n − d) coordinates satisfying the constraints is often guaranteed locally by an implicit function theorem. Nevertheless in many examples these coordinates cannot be constructed in any tractable form, even locally, so that other approaches are of interest. In ambient space formulations the dynamics are defined in the full original n-dimensional configuration space, and associated 2n-dimensional phase space, with some version of Lagrange multipliers introduced so that the 2(n − d) dimensional sub-manifold of phase space implied by the holonomic constraints and their time derivative, is invariant under the dynamics. In this article we review ambient space formulations, and explain that for constrained dynamics there is in fact considerable freedom in how a Hamiltonian form of the dynamics can be constructed. We then discuss and contrast the Langevin and Fokker-Planck equations and their equilibrium distributions for the different forms of ambient space dynamics.     

Dissipative Josephson effect in S/N/S structure with vanishingly weak Josephson coupling

A mesoscopic S/N/S structure is studied theoretically. It is shown that a Josephson effect can occur in the structure even if the distance between the superconductors is much larger than the correlation length ξ N(T) and the Josephson coupling is negligibly weak. This effect arises if an additional current I flows along the normal conductor. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 9, 624–629 (10 November 1996)