Bound states and critical behavior of the Yukawa potential

We investigate the bound states of the Yukawa potential V (r)=−λexp(−αr)/r, using different algorithms: solving the Schr?dinger equation numerically and our Monte Carlo Hamiltonian approach. There is a critical α = α_C, above which no bound state exists. We study the relation between α_C and λ for various angular momentum quantum number l, and find in atomic units, α_C(l) = λ[A ₁ exp(−l/B ₁) + A ₂ exp(−l/B ₂)], with A ₁ = 1.020(18), B ₁ = 0.443(14), A ₂ = 0.170(17), and B ₂ = 2.490(180).     

Dissipation of a two-mode squeezed vacuum state in the single-mode amplitude damping channel

We explore how a two-mode squeezed vacuum state sechθ e^{a+b+ tanh θ} |00> evolves when it undergoes a singlemode amplitude dissipative channel with rate of decay κ. We find that in this process not only the squeezing parameter decreases, tanh θ → e^-κt tanh θ, but also the second-mode vacuum state evolves into a chaotic state exp{b⁺bln[1 - e^-2κt tanh² θ]}. The outcome state is no more a pure state, but an entangled mixed state.     

Deexcitation of K π = 0 2+ , 0 3+ , and 21/+ levels by M 1 transitions in nonspherical even-even nuclei

The signs of the experimental values of the multipole-mixture parameters δ are compared with the signs of ℛ = Σa _i μ _i for (2⁺0₂−2⁺0₁) and (2⁺0₃−2⁺0₁) transitions and with the signs of = Σa _i [(μ _i + μ _kν ) or (μ _kπ − 1/2)] for (2⁺2₁−2⁺0₁) transitions in nonspherical even-even nuclei, where a _i is the contribution of the ith pair of quasiparticles to the wave function for 2⁺0₂, 2⁺0₃, and 2⁺2₁ single-phonon states according to the quasiparticle-phonon model and μ is the magnetic moment for the corresponding Nilsson state. Original Russian Text ? A.M. Demidov, L.I. Govor, V.A. Kurkin, I.V. Mikhailov, 2009, published in Yadernaya Fizika, 2009, Vol. 72, No. 2, pp. 228–235.     

Baryon resonances in the mean field approach and a simple explanation of the Θ<Superscript>+</Superscript> pentaquark

We suggest to classify baryon resonances as single-quark states in a mean field, and/or as its collective excitations. Identifying the Roper resonance N(1440, 1/2⁺), the nucleon resonance N(1535, 1/2⁻), and the singlet hyperon Λ(1405, 1/2⁻) as single-quark excitations, we find that there must be an exotic S = +1 baryon resonance Θ⁺ (the “pentaquark”) with a mass about 1440 + 1535 − 1405 = 1570 MeV and spin-parity 1/2⁺. We argue that Θ⁺ is an analog of the Gamov-Teller excitation long known in nuclear physics.     

Classical spin liquid properties of the infinite-component spin vector model on a fully frustrated two dimensional lattice

Thermodynamic quantities and correlation functions (CFs) of the classical antiferromagnet on the checkerboard lattice are studied for the exactly solvable infinite-component spin-vector model, D↦∞. In contrast to conventional two-dimensional magnets with continuous symmetry showing extended short-range order at distances smaller than the correlation length, r ξ _c∝ exp(T ^*/T), correlations in the checkerboard-lattice model decay already at the scale of the lattice spacing due to the strong degeneracy of the ground state characterized by a macroscopic number of strongly fluctuating local degrees of freedom. At low temperatures, spin CFs decay as < >∝ 1/r ² in the range a ₀≪r≪ξ _c∝T ^-1/2, where a₀ is the lattice spacing. Analytical results for the principal thermodynamic quantities in our model are very similar with MC simulations, exact and analytical results for the classical Heisenberg model (D = 3) on the pyrochlore lattice. This shows that the ground state of the infinite-component spin vector model on the checkerboard lattice is a classical spin liquid. Received 16 November 2001 and Received in final form 12 February 2002     

One Dimensional Behavior of Singular N Dimensional Solutions of Semilinear Heat Equations

We consider u(x,t) a solution of u _t =Δu+|u| ^{p − 1} u that blows up at time T, where u:ℝ ^N ×[0, T)→ℝ, p>1, (N−2)p<N+2 and either u(0)≥ 0 or (3N−4)p<3N+8. We are concerned with the behavior of the solution near a non isolated blow-up point, as T−t→ 0. Under a non-degeneracy condition and assuming that the blow-up set is locally continuous and N−1 dimensional, we escape logarithmic scales of the variable T−t and give a sharper expansion of the solution with the much smaller error term (T−t)^{1, 1/2−η} for any η>0. In particular, if in addition p>3, then the solution is very close to a superposition of one dimensional solutions as functions of the distance to the blow-up set. Finally, we prove that the mere hypothesis that the blow-up set is continuous implies that it is C ^{1, 1/2−η} for any η>0. Received: 20 June 2001 / Accepted: 6 October 2001     

Transport theory of multiterminal hybrid structures

We derive a microscopic transport theory of multiterminal hybrid structures in which a superconductor is connected to several spin-polarized electrodes. We discuss the non-perturbative physics of extended contacts, and show that such contacts can be well represented by averaging out the phase of the electronic wave function. The intercontact Andreev reflection and elastic cotunneling conductances are identical if the phase can be averaged out, namely in the presence of at least one extended contact. The maximal conductance of a two-channel contact is proportional to (e ²/h)(a ₀/D)²exp[-D/ξ(ω^*)], where D is the distance between the contacts, a₀ the lattice spacing, ξ(ω) is the superconducting coherence length, and ω^* is the cross-over frequency between a perturbative regime ( ω < ω^*) and a non perturbative regime ( ω^* < ω < Δ). Received 18 June 2001 and Received in final form 17 January 2002     

Symmetry and boundness of four-particle coulomb systems

The problem of boundness of a ⁺ b ⁺ c ⁻ d ⁻ four-particle Coulomb systems (quadrions) is studied versus the masses of the particles involved. Inequalities that make it possible to deduce that, if some reference quadrions form a bound state, the same is true for a large number of quadrions formed by particles having various masses were derived. A compendium of calculations for energies of reference systems that possess various symmetries [positronium molecules (e ⁺ e ⁺ e ⁻ e ⁻) and quadrions of the a ⁺ b ⁺ b ⁻ b ⁻, a ⁺ b ⁺ a ⁻ b ⁻, and a ⁺ a ⁺ b ⁻ c ⁻ types] is given, and groups of bound asymmetric quadrions corresponding to them are determined. An inequality for kinetic energies of particles that makes it possible to find out, by using asymmetric reference systems, whether specific quadrions are bound is obtained. It is shown that the boundness of many quadrions is ensured by the boundness of respective three-particle systems. The entire body of the present results permits proving that, of the total number of 406 quadrions containing electrons, muons, pions, kaons, protons, deuterons, and tritons and their antiparticles, 227 quadrions are bound.     

Pseudovector heavy quarkonia in e + e −2 collisions

It is shown that BR(χ _b1(1 P)→e ⁺ e ⁻)≃3.3· 10⁻⁷ and BR(χ _c1(1 P)→e ⁺ e ⁻)≃10⁻⁸. This gives realistic possibilities for searching for the production of χ _b1(1 P) and ξ _c1(1 P) states in e ⁺ e ⁻ collisions, even on the present-day colliders, to say nothing of b and c-τ factories. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 8, 569–574 (25 April 1996)     

Tails in harnesses

We consider space- and time-uniformd-dimensional random processes with linear local interaction, which we call harnesses and which may be used as discrete mathematical models of random interfaces. Their components are rea random variablesa _s ^t , wheres ∈ Z ^d andt=0, 1, 2.,... At every time step two events occur: first, every component turns into a linear combination of itsN neighbors, and second, a symmetric random i.i.d. “noise”v is added to every component. For any σ ∈Z _d ⁺ define Δ_σ a′ _s as follows. If σ=(0,...,0), σ=(0,...,0), Δ_σ a _s ^t =a _s ^t . Then by induction, wheree _i is thed-dimensional vector, whoseith component is one and other components are zeros. Denote |σ| the sum of components of σ. Call a real random variable ϕ symmetric if it is distributed as −ϕ. For any symmetric random variable ϕpower decay or P-decay is defined as the supremum of thoser for which therth absolute moment of ϕ is finite. Convergence a.s., in probability and in law whent→∞ is examined in terms of P-decay(v): Ifd=1, σ=0 ord=2, σ=(0,0), Δ_σ a _s ^t diverges. In all the other cases: If P-decay(v)<(d+2)/(d+|σ|), Δ_σ a _s ^t diverges; if P-decay(v)>(d+2)/(d+|σ|), Δ_σ a _s ^t , converges and P-decay(ν) For any symmetric random variable ϕexponential decay or E-decay is defined as the supremum of thoser for which the expectation of exp(|x|^r) is finite. Let E-decay(v)>0. Whenever Δ_σ a _s ^t converges (that is, ifd>2 or |σ|>0: Ifd>2, E-decay(lima _s ^t )=min(E-decay(v),d+2/2); if |σ|=1, E-decay (lim Δ_σ a _s ^t )=min(E-decay(ν),d+2); if |σ| ⩾, E-decay (lim Δ_σ a _s ^t )=E-decay(ν).     

On the existence of four-particle Coulomb systems

Whether bound states of Coulomb systems composed of four particles with unit charges (quadrions), a ⁺ b ⁺ c ⁻ d ⁻, exist is demonstrated to be determined by the masses of the constituent particles. Relations that make it possible to establish the existence of a large number quadrions with different masses of the particles are derived. The energies of reference quadrions of different symmetry, a positronium molecule, a ⁺ a ⁺ a ⁻ a ⁻, a ⁺ b ⁺ a ⁻ b ⁻, a ⁺ b ⁺ a ⁻ b ⁻, and a ⁺ a ⁺ b ⁻ c ⁻, are determined and groups of stable asymmetric quadrions corresponding to them are identified. A relationship between the stability of a number of quadrions and three-particle systems (trions) was found. The results shows that, among all the 406 four-particle independent combinations of electrons, muons, pions, kaons, protons, deuterons, and tritium nuclei or their antiparticles, there are 227 bound quadrions.     

Stretched Exponential Fixation in Stochastic Ising Models at Zero Temperature

We study a class of continuous time Markov processes, which describes ± 1 spin flip dynamics on the hypercubic latticeℤ ^d , d≥ 2, with initial spin configurations chosen according to the Bernoulli product measure with density p of spins + 1. During the evolution the spin at each site flips at rate c= 0, or 0 < α≤ 1, or 1, depending on whether, respectively, a majority of spins of nearest neighbors to this site exists and agrees with the value of the spin at the given site, or does not exist (there is a tie), or exists and disagrees with the value of the spin at the given site. These dynamics correspond to various stochastic Ising models at 0 temperature, for the Hamiltonian with uniform ferromagnetic interaction between nearest neighbors. In case α= 1, the dynamics is also a threshold voter model. We show that if p is sufficiently close to 1, then the system fixates in the sense that for almost every realization of the initial configuration and dynamical evolution, each site flips only finitely many times, reaching eventually the state + 1. Moreover, we show that in this case the probability q(t) that a given spin is in state − 1 at time t satisfies the bound: for arbitrary ɛ > 0, q(t) ≤ exp(−t ^{(1/ d ) −ɛ}), for large t. In d= 2 we obtain the complementary bound: for arbitrary ɛ > 0, q(t) ≥ exp(−t ^{(1/2) +ɛ}), for large t. Received: 12 July 2001 / Accepted: 1 February 2002     

Exact Analytical Solution of the Schrödinger Equation for an N-Identical Body-Force System

A mathematical method is presented for solving the Schr?dinger equation for a system of identical body forces. The N-body forces are more easily introduced and treated within the hyperspherical harmonics. The problem of the N-body potential has been used at the level of both classical and quantum mechanics. The hypercentral interacting potential is assumed to depend on the hyperradius x = (ξ₁² + ξ₂² + ⋯ + ξ_N−1²)^1/2 only, where ξ₁,ξ₂,…,ξ_N−1 are Jacobi relative coordinates which are functions of N-particle relative positions r₁₂,r₂₃,…,r_N1. The problem of the harmonic oscillator and the Coulomb-type potential has been widely studied in different contexts. Using the N-body potential V(x) = ax² + bx − (c/x) as an example, and assuming an ansatz for the eigenfunction, an exact analytical solution of the Schr?dinger equation for an N-body system in three dimensions is obtained. This method is also applicable to some other types of potentials for N-identical interacting particles.     

Synchrotron and annihilation channels for axion production in an external electromagnetic field

We consider axion formation processes in the synchrotron (e ⁻→e ⁻ a) and annihilation (e ⁻ e ⁺→a) channels in a constant crossed field F _μν F^μν=Fμν*F ^μν =0, which approximates constant fields of other configurations in the ultrarelativistic asymptotic limit. The probability and intensity of axion emission are obtained, and we analyze the energy and field asymptotics. A comparison with the characteristic neutrino channel yields the constraints on the axion mass and the energy scale for Peccei-Quinn symmetry breaking. Possible astrophysical applications are discussed. Zh. éksp. Teor. Fiz. 112, 25–31 (July 1997)     

Asymptotic Properties of Solutions to 3-Particle Schrödinger Equations

We construct a generalized Fourier transformation ℱ(λ) associated with the 3-body Schr?dinger operator H=−Δ+Σ ^a V ^a (x ^a ) and characterize all solutions of (H−λ)u= 0 in the Agmon–H?rmander space ℬ^* as the image of ℱ(λ)^*. These stationary solutions admit asymptotic expansions in ℬ^* in terms of spherical waves associated with scattering channels. Received: 20 September 2000 / Accepted: 20 May 2001     

Monte-Carlo optimization of correlated helium wave function

A new type of correlated wave function for the normal helium is proposed in the form:ψ(r₁, r₂)=Σc _mφ_m withφ _m=exp]−α(r ₁+r ₂)]/(br ₁₂+a) ^m wherea, b, α are non-linear variational parameters. Optimizing these parameters by the Monte-Carlo technique, an energy eigen-value of −2.903645(a.u.) is obtained withonly three terms in the basis expansion alongwith satisfactory cusp condition, compared to the essentially exact non-relativistic value of −2.903724 as given by Freundet al (Phys. Rev. A29, 980 (1984)).     

An improved model for band tail states inn-type degenerate semiconductors

Summary Using two screened donor potential energy models and a wave vectork-positionr uncertainty relation, the results of the exponential band tail states, inn-type degenerate semiconductors, obtained in our previous paper, are improved. The second-order cumulant or the correlation functionW (ϱ,E) is expressed as a function of the total donor concentration ϱ and total carrier energyE. Near band edges, the conduction and valence band tails are, respectively, proportional to exp [E/E ₀(ϱ)] and exp [−E/E ₀(ϱ)], whereE ₀(ϱ) is the energy characteristic of the appropriate band tail, in good accordance with those experimentally obtained by Pankove. Far below the conduction band edge, our result of the conduction band tail is proportional to exp [−BE ² exp [A ]], whereA andB are the functions of ϱ, which is reduced to zero more rapidly in comparison with the corresponding result obtained by Halperin and Lax (i.e. exp [−|E| ⁿ , wheren varies between 1/2 and 2). To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Three-dimensional correlated-fermion phase separation from analysis of the geometric mean of the individual susceptibilities

A quasi-Gaussian approximation scheme is formulated to study the strongly correlated imbalanced Fermions thermodynamics, where the mean-field theory is not applicable. The non-Gaussian correlation effects are understood to be captured by the statistical geometric mean of the individual susceptibilities. In the three-dimensional unitary fermions ground state, a universal nonlinear scaling transformation relates the physical chemical potentials with the individual Fermi kinetic energies. For the partial polarization phase separation to full polarization, the calculated critical polarization ratio is δ _C = [1−(1−ξ)^6/5]/[1+(1−ξ)^6/5] ≐ 0.34. ξ = 4/9 gives the ratio of the symmetric ground state energy density to that of the ideal fermion gas. Supported by the National Natural Science Foundation of China (Grant Nos. 10875050 and 10675052), the Fund of Central China Normal University, and the Foundation of Ministry of Education of China (Grant No. IRT0624)     

Collective bands of the positive parity states inf 7/2 shell nuclei

Collective bands of the positive parity states in odd-A f _7/2 shell nuclei are described in the framework of deformed Hartree-Fock theory by projecting states from lowest energy intrinsic states with (d ₃ ^2/−1 f ₇ ^2/n+1 ) one hole configurations. In the calculation empirical (d _3/2 −f _7/2)² effective matrix elements have been used to test the tacit assumptions of the Bansal and French model.