Amplitude-squared squeezing in superposed coherent states

We study amplitude-squared squeezing of the Hermitian operator Z_θ=Z₁ cosθ+Z₂ sin θ, in the most general superposition state , of two coherent states and . Here operators Z_1,2 are defined by , a is annihilation operator, θ is angle, and complex numbers C_1,2 , α, β are arbitrary and only restriction on these is the normalization condition of the state . We define the condition for a state to be amplitude-squared squeezed for the operator Z_θ if squeezing parameter , where N=a⁺a and . We find maximum amplitude-squared squeezing of Z_θ in the superposed coherent state with minimum value 0.3268 of the parameter S for an infinite combinations with α- β= 2.16 exp [±i(π/4) + iθ/2], and with arbitrary values of (α+β) and θ. For this minimum value of squeezing parameter S, the expectation value of photon number can vary from the minimum value 1.0481 to infinity. Variations of the parameter S with different variables at maximum amplitude-squared squeezing are also discussed.     

Current-voltage characteristics of SIS structures with localized states in the material of the barrier layer

Elastic resonant tunneling through a single localized state in an insulating layer (I-layer) situated in the constriction zone between two thick superconducting electrodes is investigated theoretically, and the current-voltage characteristic (IVC) of the structure is calculated. The accompanying analysis leads to the prediction that an appreciable current can flow through the structure, not at |eV|=2Δ (Δ is the modulus of the order parameter of the superconducting electrodes) as in the case of an ordinary SIS junction, but at |eV|⩾Δ, and also that the IVC can acquire segments of negative differential resistance in the case of tunneling through a single localized state. Averaging of the IVC over an ensemble of localized states distributed uniformly throughout the volume of the I-layer and with respect to the energy near the chemical potential min the limit Γ₀/Δ≫1 (Γ₀ is the half-width of the resonance line of the localized state) produces a smaller excess current than in a junction of the SNS type. It is shown that the IVC’s exhibit a transition from an excess current to a deficit current as Γ₀ decreases in the high-voltage range. Zh. éksp. Teor. Fiz. 114, 687–699 (August 1998)     

Image states on beryllium surfaces with low indices

Using the self-consistent pseudopotential method, we have calculated the binding energy of the image states for the (0001) , and surfaces of beryllium. It is shown for the (0001) face that there exists a pronounced resonance image state with n=1 and energy −0.95 eV at the point of the surface Brillouin zone. In the surface, which has a wide band gap in the vicinity of the vacuum level, the calculated image state with n=1 at the point has energy −1.2 eV and is a surface state of gap type. For the face in the vicinity of the point band gaps are absent. However, the symmetry of the bulk states near the vacuum level enables the existence of a resonance image state with n=1 and energy −0.6 eV. Fiz. Tverd. Tela (St. Petersburg) 41, 935–940 (June 1999)     

Layered superconductors with anisotropic energy gap: specific heat and infrared absorption

New oxide superconductors with layered structure are expected to have anisotropic energy gap in the generalized BCS pairing theory. The gap parameter can be quite different for perpendicular to the plane of the layers as compared tok parallel to layer planes. Because of short coherence lengths ξ, quite small compared to the normal state carrier meanfree pathl, the effect of these anisotropies do not average out, as in many of the conventional superconductors. For a proper comparison of experimental results with the correct predictions of the pairing theory, a formulation is developed to obtain important physical quantities like specific heat and infrared absorption in the superconducting state of such anisotropic systems. This includes a brief account of the pairing theory generalized to layered crystals with arbitrary number of layers per unit cell, not necessarily equidistant. In an explicit model for the anisotropy of the gap parameter ink-space, with a simple form for the nonspherical Fermi-surface, it is shown that the low-temperature specific heat can have even a linear or a power-law temperature-dependence in the superconducting state. Even if the gap parameter does not vanish anywhere, its smeared-out exponential temperature-dependence may be difficult to be distinguished experimentally from a power-law behaviour. Similarly, it is shown that in the case of appreciable anisotropy, infrared absorption can take place much below the in-plane gap parameter , wherek _t is the wavevector in the plane of the layers.     

Squeezed states of a particle in magnetic field

For a charged particle in a homogeneous magnetic field, we construct stationary squeezed states which are eigenfunctions of the Hamiltonian and the non-Hermitian operator , and Ŷ being the coordinates of the Larmor circle center and Φ is a complex parameter. In the family of the squeezed states, the quantum uncertainty in the Larmor circle position is minimal. The wave functions of the squeezed states in the coordinate representation are found and their properties are discussed. Besides, for arbitrary gauge of the vector potential we derive the symmetry operators of translations and rotations. Fiz. Tverd. Tela (St. Petersburg) 40, 1405–1412 (August 1998) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Quantum glass transition in a periodic long-range Josephson array

We show that the ground state of a periodic long-range Josephson array frustrated by a magnetic field is a glass for sufficiently large Josephson energies despite the absence of quenched disorder. Like superconductors, this glass state has non-zero phase stiffness and Meissner response; for lower Josephson energies the glass “melts” and the ground state loses its phase stiffness and becomes insulating. We find the critical scaling behavior near this quantum phase transition: the excitation gap vanishes as (J−J _c )², and the frequency-dependent magnetic susceptibility behaves as . Zh. éksp. Teor. Fiz. 116, 1450–1461 (October 1999) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

One-and-a-Half Quantum de Finetti Theorems

When n − k systems of an n-partite permutation-invariant state are traced out, the resulting state can be approximated by a convex combination of tensor product states. This is the quantum de Finetti theorem. In this paper, we show that an upper bound on the trace distance of this approximation is given by , where d is the dimension of the individual system, thereby improving previously known bounds. Our result follows from a more general approximation theorem for representations of the unitary group. Consider a pure state that lies in the irreducible representation of the unitary group U(d), for highest weights μ, ν and μ + ν. Let ξ_μ be the state obtained by tracing out U _ν. Then ξ_μ is close to a convex combination of the coherent states , where and is the highest weight vector in U _μ. For the class of symmetric Werner states, which are invariant under both the permutation and unitary groups, we give a second de Finetti-style theorem (our “half” theorem). It arises from a combinatorial formula for the distance of certain special symmetric Werner states to states of fixed spectrum, making a connection to the recently defined shifted Schur functions [1]. This formula also provides us with useful examples that allow us to conclude that finite quantum de Finetti theorems (unlike their classical counterparts) must depend on the dimension d. The last part of this paper analyses the structure of the set of symmetric Werner states and shows that the product states in this set do not form a polytope in general.     

Existence of excited states for a nonlinear Dirac field

We prove the existence of infinitely many stationary states for the following nonlinear Dirac equation $$i\gamma ^\mu \partial _\mu \psi - m\psi + (\bar \psi \psi )\psi = 0.$$ Seeking for eigenfunctions splitted in spherical coordinates leads us to analyze a nonautonomous dynamical system inR ². The number of eigenfunctions is given by the number of intersections of the stable manifold of the origin with the curve of admissible datum. This proves the existence of infinitely many stationary states, ordered by the number of nodes of each component.     

One-and two-front states of equilibrium in a thin superconducting film

Two-phase states of equilibrium of a thin superconducting film carrying a current under conditions of convective heat exchange at the free surface of the film are studied. It is shown that for a classical superconductor the two-phase state of the film remains a single-front state over a wide range of parameters of the system. For high-T _c superconductors there exists a maximum value of the Steckl number above which weakly nonequilibrium stationary states can only be multifront states. The solutions of the boundary-value problem modeling a two-front state of equilibrium are investigated, and the conditions under which they obtain are examined. Zh. Tekh. Fiz. 68, 84–87 (March 1998)     

The four states of the Massless neutrino with pauli coupling by Spin-Gauge invariance

The Pauli coupling is introduced for four-component neutrino states and related to local T ⁴SU(2,2) spin-gauge (not internal symmetry) transformations applied to the massless Dirac equation. The well-known left-right asymmetry for free neutrino helicity states is generalised and discussed for Pauli-coupled neutrinos. An explicit exact solution is obtained for Pauli-coupled neutrino equations in an external free radiation field by the use of the above local spin-gauge transformations. It is also suggested that local SL(2, C)SU(2,2) spin-gauge transformations can be used to obtain models of neutral currents for neutrinos.     

Multiplicativity of Completely Bounded p-Norms Implies a New Additivity Result

We prove additivity of the minimal conditional entropy associated with a quantum channel Φ, represented by a completely positive (CP), trace-preserving map, when the infimum of S(γ₁₂) − S(γ₁) is restricted to states of the form . We show that this follows from multiplicativity of the completely bounded norm of Φ considered as a map from L ₁ → L _p for L _p spaces defined by the Schatten p-norm on matrices, and give another proof based on entropy inequalities. Several related multiplicativity results are discussed and proved. In particular, we show that both the usual L ₁ → L _p norm of a CP map and the corresponding completely bounded norm are achieved for positive semi-definite matrices. Physical interpretations are considered, and a new proof of strong subadditivity is presented.     

Modular construction of special mixed quantum states

For a homogeneous quantum network of N subsystems with n levels each we consider separable generalized Werner states. A generalized Werner state is defined as a mixture of the totally mixed state and an arbitrary pure state : with a mixture coefficient . For this density operator to be separable, will have an upper bound . Below this bound one should alternatively be able to reproduce by a mixture of entirely separable input-states. For this purpose we introduce a set of modules, each contributing elementary coherence properties with respect to a generalized coherence vector. Based on these there exists a general step-by-step mixing process for any . For being a cat-state it is possible to define an optimal process, which produces states right up to the separability boundary ( ).Received: 3 December 2002, Published online: 29 July 2003PACS: 03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bells inequalities, GHZ states, etc.) - 03.67.-a Quantum information - 03.65.-w Quantum mechanics     

Superconducting states of the cylinder with a single vortex in magnetic field according to the Ginzburg-Landau theory

Self-consistent solutions of the nonlinear Ginzburg-Landau (GL) equations are investigated numerically for a superconducting (SC) cylinder, placed in an axial magnetic field, with a single vortex on the axis (m=1). Two modes, which show the original state of the cylinder, SC or normal (s ₀ andn ₀), are studied. The field increase (FI) and the field decrease (FD) regimes are studied. The critical fields destroying the SC state withm=1 are found in both regimes. It is shown that in a cylinder of radiusR and GL-parameter ϰ, there exist a number of solutions depending only on the radial co-ordinater corresponding to different states such as M,e, d, p,i, n, ,n ^*, and the state diagram on the plane of the variables (ϰ,R) is described. The critical fields corresponding to intrastate transitions and the onset of hysteresis are obtained. The critical fieldH ₀(R) dividing the paramagnetic and diamagnetic states of the cylinder withm=1 is determined. The limiting fields of supercooling or superheating of the normal state at which the restoration of the SC state occurs are established. It is shown, that (in both casesm=1,0) there exist two critical parameters, and , which divide bulk SC into three groups (with and ), in accordance with the behavior in a magnetic field. The parameters and mark the boundary for the existence of a supercooled normal -state in FD-regime and a superheated SC M-state in FI-regime respectively. It is shown, that the value , which was claimed in a number of papers as related to type-I superconductors, is illusory. We regret to inform that Professor Gely Zharkov passed away on 9th July 2004.     

Mixing of pentaquark and molecular states

There are experimental evidences for the existence of narrow states Θ ⁺ and Θ _c with the same quantum numbers of and pentaquarks and also NK ^(*) and ND ^(*) molecular states. Their masses deviate from many theoretical estimates of the pure pentaquark and molecular states. In this work we study the possibility that the observed Θ ⁺ and Θ _c are mixtures of pure pentaquark and molecular states. The mixing parameters are in general related to non-perturbative QCD which are not calculable at present. We determine them by fitting data from known states and then generalize the mechanism to Θ _b to predict its mass and width. The mixing mechanism can also naturally explain the narrow width for Θ ⁺ and Θ _c through destructive interferences, even if the pure pentaquark and molecular states have much larger decay widths. We also briefly discuss the properties of the partner eigenstates of Θ ⁺ and Θ _c and the possibility of experimentally observe them. Moreover, probable consequences of multi-state mixing are also addressed. Received: 6 March 2005, Revised: 29 July 2005, Published online: 27 September 2005 An erratum to this article is available at .     

Low-temperature heat capacity of the mixed state of superconductors with anisotropic pairing

It is shown that in superconductors with anisotropic pairing the exponent of the power-law magnetic-field dependence of the low-temperature heat capacity of the mixed state depends strongly on the multiplicities of the zeros of the superconducting order parameter. As a result, an experimental determination of the corresponding power-law exponent makes it possible to judge not only the presence of zeros in the order parameter but also the multiplicities of these zeros. An expression is obtained for the spatially nonuniform quasiparticle density of states at low energies. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 5, 353–357 (10 March 1996)     

Invariant states in statistical mechanics

Mathematically we consider aC*-algebra , acted upon by the groupT of space-translations, which has an asymptotic abelian property. We analyse invariant states over . Physically this programme can be considered as a kinematical study of equilibrium states in statistical mechanics. Each invariant state can be uniquely decomposed into elementary invariant states (E-states). These elementary states have, amongst other characteristics, the physical property that space-averages of local observables are constants in the corresponding representations. In anE-state the discrete spectrum S _D of space-translations is additive which gives rise to the classificationE _I,E _II, andE _III corresponding to the three possibilities that S _D contains one point, a lattice of points, or a set with accumulation points. AnE _II-state can be uniquely decomposed into states (L-states) having a symmetry with respect to a closed subgroupT _L of (S _D and T _L are reciprocal lattices).L-states have properties with respect toT _L analogous to the properties ofE _I-states with respect toT. The decomposition intoL-states is the inverse process of homogenizing a lattice state by smearing it over a lattice distance. The mathematical methods which we employ have more general applications.     

Superconductivity in impurity bands

We present a theory of superconductivity in doped insulators. In the magnetic metal state of the compound we obtain the self-consistency equations for the superconducting state in the spin-dependent impurity bands of both extended and localized states in the initial insulator gap. A BCS-type triplet pairing field is considered. We show that the superconducting gap in which single-electron extended states do not exist is overlapped by the distribution of the localized states. The formation of a latent superconducting gap is discussed in connection with the unusual properties of high-T _c compounds. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 5, 419–424 (10 March 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Spin susceptibility of neutron-irradiation-disordered YBa2Cu3O6.9 in the normal and superconducting states

The spin-spin relaxation rate ⁶³ T ₂ ⁻¹ of ⁶³Cu nuclei in CuO₂ layers is measured in the normal and superconducting states of the compound YBa₂Cu₃O_6.9 (T _c ^onset =94 K) subjected to radiation-induced disordering by a fast-neutron flux Φ to T _c ^onset =68 K (Φ=7×10¹⁸ cm⁻²) and T _c ^onset <4 K (Φ=12×10¹⁸ cm⁻²). It is found that as the structural disorder increases, the contribution of the indirect spin-spin interaction ⁶³ T _2G ⁻¹ , which is related to the value of the spin susceptibility at the boundary of the Brillouin zone of the copper planes χ_s(q={π/a; π/a}), decreases slightly at the transition to the superconducting state for the initial sample and remains unchanged for the weakly disordered sample. This behavior of the short-wavelength contribution to the spin susceptibility attests to the stability of the x ²−y ² symmetry of the energy gap against structural disorder, in accordance with proposed theoretical models of Cooper pairing for high-T _c cuprates. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 3, 172–177 (10 February 1998)     

Critical fields of a superconducting cylinder

The self-consistent solutions of the nonlinear Ginzburg-Landau equations, which describe the behavior of a superconducting mesoscopic cylinder in an axial magnetic field H (provided there are no vortices inside the cylinder), are studied. Different, vortex-free states (M-, e-, d-, p-), which exist in a superconducting cylinder, are described. The critical fields (H ₁, H ₂, H _p , H _i , H _r ), at which the first or second order phase transitions between different states of the cylinder occur, are found as functions of the cylinder radius R and the GL-parameter . The boundary , which divides the regions of the first and second order (s, n)-transitions in the icreasing field, is found. It is found that at R→∞ the critical value, is . The hysteresis phenomena, which appear when the cylinder passes from the normal to superconducting state in the decreasing field, are described. The connection between the self-consistent results and the linearized theory is discussed. It is shown that in the limiting case and R ≫ λ (λ is the London penetration length) the self-consistent solution (which correponds to the socalled metastable p-state) coincides with the analitic solution found from the degenerate Bogomolnyi equations. The reason for the existence of two critical GL-parameters and in, bulk superconductors is discussed. An erratum to this article is available at.