Invariants of linear combinations of transpositions

It is shown that for a one-parameter set H _N of linear combinations of N(N–1)/2 elementary transpositions {P _jk } (1j at arbitrary natural N3, one can construct a variety {I _m } (3mN) of operators which commute with H _N . Being applied to SU(n) spin representations of the permutation group, this proves the integrability of 1D periodic spin chains with elliptic short-range interaction.     

Formation and quenching mechanisms of excited particles in an oxygen-iodine laser medium

New values of a number of kinetic constants of processes proceeding in oxygen-iodine laser media are presented. The total probabilities of formation of I₂(X, 15 ≤ v ≤ 24) and I₂(X, 25 ≤ v ≤ 47) molecules in the course of quenching of I* atoms by I₂(X) are found to be 0.9 and 0.1, respectively. The quantum yield of singlet oxygen in the reaction O(¹ D) + N₂O → N₂ + O₂(a ¹Δ) is close to 100%. The quenching rate constants of I₂(A’) by O₂, H₂O, CO₂, I₂, and Ar and of I(² P _1/2) by O(³ P), O₃, NO₂, N₂O₄, and N₂O are presented.     

On Ruelle’s Construction of the Thermodynamic Limit for the Classical Microcanonical Entropy

In 1969 Ruelle published his construction of the thermodynamic limit, in the sense of Fisher, for the quasi-microcanonical entropy density of classical Hamiltonian N-body systems with stable and tempered pair interactions. Here, “quasi-microcanonical” refers to the fact that he discussed the entropy defined with a regularized microcanonical measure as ln (N!⁻¹ ∫ χ _{{ℰ−▵ℰ<H<ℰ}}d^6N X) rather than defined with the proper microcanonical measure as ln (N!⁻¹ ∫ δ(ℰ−H) d^6N X). Replacing δ(ℰ−H) by χ _{{ℰ−▵ℰ<H<ℰ}} seems to have become the standard procedure for rigorous treatments of the microcanonical ensemble hence. In this note we make a very elementary technical observation to the effect that Ruelle’s proof (still based on regularization) does establish the thermodynamic limit also for the entropy density defined with the proper microcanonical measure. We also show that with only minor changes in the proof the regularization of δ(ℰ−H) is actually not needed at all.     

Distribution of a Particle’s Position in the ASEP with the Alternating Initial Condition

In this paper we give the distribution of the position of a particle in the asymmetric simple exclusion process (ASEP) with the alternating initial condition. That is, we find ℙ(X _m (t)≤x) where X _m (t) is the position of the particle at time t which was at m=2k−1, k∈ℤ at t=0. As in the ASEP with step initial condition, there arises a new combinatorial identity for the alternating initial condition, and this identity relates the integrand of the integral formula for ℙ(X _m (t)≤x) to a determinantal form together with an extra product.     

On the Energy Growth of Some Periodically Driven Quantum Systems with Shrinking Gaps in the Spectrum

We consider quantum Hamiltonians of the form H(t)=H+V(t) where the spectrum of H is semibounded and discrete, and the eigenvalues behave as E _n ∼n ^α , with 0<α<1. In particular, the gaps between successive eigenvalues decay as n ^α−1. V(t) is supposed to be periodic, bounded, continuously differentiable in the strong sense and such that the matrix entries with respect to the spectral decomposition of H obey the estimate ‖V(t) _m,n ‖≤ε|m−n|^−p max {m,n}^−2γ for m≠n, where ε>0, p≥1 and γ=(1−α)/2. We show that the energy diffusion exponent can be arbitrarily small provided p is sufficiently large and ε is small enough. More precisely, for any initial condition Ψ∈Dom(H ^1/2), the diffusion of energy is bounded from above as 〈H〉 _Ψ (t)=O(t ^σ ), where . As an application we consider the Hamiltonian H(t)=|p| ^α +ε v(θ,t) on L ²(S ¹,dθ) which was discussed earlier in the literature by Howland.     

Quantum oscillations of the resistivity and hall coefficient and the quantum limit in Bi<Subscript>0.93</Subscript>Sb<Subscript>0.07</Subscript> alloys in a magnetic field along the trigonal axis

The dependences of the electrical resistivity ρ and the Hall coefficient R on the magnetic field have been measured for single-crystal samples of the n-Bi_0.93Sb_0.07 semiconductor alloys with electron concentrations in the range 1 × 10¹⁶ cm⁻³ < n < 2 × 10¹⁸ cm⁻³. It has been found that the measured dependences exhibit Shubnikov-de Haas quantum oscillations. The magnetic fields corresponding to the maxima of the quantum oscillations of the electrical resistivity are in good agreement with the calculated values of the magnetic fields in which the Landau quantum level with the number N intersects the Fermi level. The quantum oscillations of the Hall coefficient with small numbers are characterized by a significant spin splitting. In a magnetic field directed along the trigonal axis, the quantum oscillations of the resistivity ρ and the Hall coefficient R are associated with electrons of the three-valley semiconductor and are in phase with the magnetic field. In the case of a magnetic field directed parallel to the binary axis, the quantum oscillations associated both with electrons of the secondary ellipsoids in weaker magnetic fields and with electrons of the main ellipsoid in strong magnetic fields (after the overflow of electrons from the secondary ellipsoids to the main ellipsoid) are also in phase. In magnetic fields of the quantum limit ħω _c /2 ≥ E _F, the electrical conductivity increases with an increase in the magnetic field: σ₂₂(H) ∼ H ^k . A theoretical evaluation of the exponent in this expression for a nonparabolic semiconductor leads to values of k close to the experimental values in the range 4 ≤ k ≤ 4.6, which were obtained for samples of the semiconductor alloys with different electron concentrations. A further increase in the magnetic field results in a decrease of the exponent k and in the transition to the inequality σ₂₂(H) ≤ σ₂₁(H).     

Quantum information entropies of ultracold atomic gases in a harmonic trap

The position and momentum space information entropies of weakly interacting trapped atomic Bose–Einstein condensates and spin-polarized trapped atomic Fermi gases at absolute zero temperature are evaluated. We find that sum of the position and momentum space information entropies of these quantum systems containing N atoms confined in a D( ≤ 3)-dimensional harmonic trap has a universal form as S_t^(D) = N(a D - b lnN) S_\mathrm{t}^{(D)} = N(a D - b \ln N) , where a ≃ 2.332 and b = 2 for interacting bosonic systems and a ≃ 1.982 and b = 1 for ideal fermionic systems. These results obey the entropic uncertainty relation given by Beckner, Bialynicki-Birula and Myceilski.     

Quasi-long-range order in the random anisotropy Heisenberg model

The random field and random anisotropy N-vector models are studied with the functional renormalization group in 4−ε dimensions. The random anisotropy Heisenberg (N=3) model has a phase with an infinite correlation length at low temperatures and weak disorder. The correlation function of the magnetization obeys a power law 〈m(r ₁)m(r ₂)〉∼|r ₁−r ₂|^{− 0.62ε}. The magnetic susceptibility diverges at low fields as χ∼H ^−1+0.15ε. In the random field N-vector model the correlation length is finite at arbitrarily weak disorder for any N>3. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 2, 130–135 (25 July 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

The Current Distribution of the Multiparticle Hopping Asymmetric Diffusion Model

In this paper we treat the multiparticle hopping asymmetric diffusion model (MADM) on ℤ introduced by Sasamoto and Wadati in 1998. The transition probability of the MADM with N particles is provided by using the Bethe ansatz. The transition probability is expressed as the sum of N-dimensional contour integrals of which contours are circles centered at the origin with restrictions on their radii. By using the transition probability we find ℙ(x _m (t)=x), the probability that the mth particle from the left is at x at time t. The probability ℙ(x _m (t)=x) is expressed as the sum of |S|-dimensional contour integrals over all S⊂{1,…,N} with |S|≥m, and is used to give the current distribution of the system. The mapping between the MADM and the pushing asymmetric simple exclusion process (PushASEP) is discussed.     

Contribution of superconducting grains and grain boundaries to the magnetoresistance of ceramic YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7 − δ</Subscript> high-temperature superconductors in weak magnetic fields

The current-voltage characteristics of granular YBa₂Cu₃O_6.95 high-temperature superconductor samples have been measured at a temperature of 77.3 K in external transverse magnetic fields H _ext with a strength of up to H _ext ≈ 500 Oe for low transport current densities (0.1 A/cm² ≤ j ≤ 0.6 A/cm²). The current-voltage characteristics obtained have been used to construct dependences of the magnetoresistance ρ on the quantities j (ρ(j) _Hext=const) and H _ext(ρ(H _ext) _{j = const}). It has been revealed that the current and field dependences of the magnetoresistance exhibit anomalies at H _ext ≥ H _c1g , where H _c1g is the lower critical field of superconducting grains. A comparative analysis of the dependences ρ(j)H _{ext = const} and ρ(H _ext) _{j = const} has made it possible to develop concepts regarding the influence of the processes of redistribution of the magnetic field between grain boundaries and superconducting grains on the transport and galvanomagnetic properties of granular high-temperature superconductors. It has been established that the field dependences of the magnetoresistance exhibit specific features associated with the beginning of penetration of Josephson vortices into grain boundaries in the magnetic field H _c1J and with the breaking of a continuous chain of Josephson junctions in the magnetic field H _c2J .     

Maximum Solutions of Normalized Ricci Flow on 4-Manifolds

We consider the maximum solution g(t), t ∈ [0,  + ∞), to the normalized Ricci flow. Among other things, we prove that, if (M, ω) is a smooth compact symplectic 4-manifold such that and let g(t), t ∈ [0, ∞), be a solution to (1.3) on M whose Ricci curvature satisfies that |Ric(g(t))| ≤ 3 and additionally χ(M) = 3τ (M) > 0, then there exists an , and a sequence of points {x _j,k ∈ M}, j = 1, . . . , m, satisfying that, by passing to a subsequence,

EPR and optical absorption studies of Cu<Superscript>2+</Superscript> ions in [ZnPd(CN)<Subscript>4</Subscript>(C<Subscript>4</Subscript>H<Subscript>12</Subscript>N<Subscript>2</Subscript>O<Subscript>2</Subscript>)] single crystals

A Cu²⁺-doped single crystal of catena-trans-bis(N-(2-hydroxyethyl)-ethylenediamine) zinc(II)-tetra-m-cyanopaladate(II) [ZnPd(CN)₄(C₄H₁₂N₂O₂)] complex has been investigated by electron paramagnetic resonance (EPR) technique at room temperature. EPR spectra indicate that Cu²⁺ ions substitute for magnetically equivalent Zn²⁺ ions and form octahedral complexes in [ZnPd(CN)₄(C₄H₁₂N₂O₂)] hosts. The crystal field affecting the Cu²⁺ ion is nearly axial. The optical absorption studies show two bands at 322 nm (30864 cm⁻¹) and 634 nm (15337 cm⁻¹) which confirm the axial symmetry. The spin Hamiltonian parameters and the relevant wave function are determined.     

$\mathcal{CPT}$-Symmetric Discrete Square Well

In an addendum to the recent systematic Hermitization of certain N by N matrix Hamiltonians H ^(N)(λ) (Znojil in J. Math. Phys. 50:122105, 2009) we propose an amendment H ^(N)(λ,λ) of the model. The gain is threefold. Firstly, the updated model acquires a natural mathematical meaning of Runge-Kutta approximant to a differential PT\mathcal{PT}-symmetric square well in which P\mathcal{P} is parity. Secondly, the appeal of the model in physics is enhanced since the related operator C\mathcal{C} of the so called “charge” (the requirement of observability of which defines the most popular Bender’s metric Q = PC\Theta=\mathcal{PC}) becomes also obtainable (and is constructed here) in an elementary antidiagonal matrix form at all N. Last but not least, the original phenomenological energy spectrum is not changed so that the domain of its reality (i.e., the interval of admissible couplings λ∈(−1,1)) remains the same.     

np → ηd near threshold and the s -wave ηN amplitude

We calculate the process np → ηd near threshold using a separable potential model of the coupled ηN - πN - ππN subystems, and a relativistic three-body calculation for the ηd scattering amplitude. The ππN channels are represented by an effective σN channel, and we compare the case where the σ and π masses are related by m _σ = 2m _π and no width is considered, to another where the mass and width of the σ -meson are taken from ππ scattering data. The np → ηd cross-section can be well described up to about 60MeV by models where the real part of the ηN scattering length lies between 0.4≤Re(a _ηN)≤0.6 fm which allows us to determine the s -wave ηN scattering amplitude for -60≤E≤60 MeV.     

The 2<Superscript>1/3</Superscript> rule for magnetic susceptibility of gadolinium

The dependences of the magnetization M and the magnetic susceptibility χ = ∂M/∂H of pure gadolinium (the concentration of foreign impurities is lower than 0.1 wt %) on the temperature T and the magnetic field H have been measured using a Quantum Design MPMS-5XL SQUID magnetometer. In this material, inhomogeneities of the atomic structure should not lead to a nonuniform distribution of the magnetic characteristics (including the Curie temperature T _C) over the volume of the sample. The obtained dependences of M and χ have been used to investigate the possibility of suppressing magnetic inhomogeneities of other types by magnetic fields with a strength of up to 50 kOe. It has been assumed that these inhomogeneities are suppressed when the specific relationship, namely, the 2^1/3 rule is fulfilled. The rule relates the portions of the dependence χ(T, H) which at the temperature T = T _C and at the maximum in the curve χ(T) (T = T _m ) depend on H in accordance with the H ^2/3 law. It has been shown that the portions separated from the experimental curves χ(T _C, H) and χ(T _m , H) obey the 2^1/3 rule.     

Weak chaos and metastability in a symplectic system of many long-range-coupled standard maps

We introduce, and numerically study, a system of N symplectically and globally coupled standard maps localized in a d=1 lattice array. The global coupling is modulated through a factor r^-α, being r the distance between maps. Thus, interactions are long-range (nonintegrable) when 0≤α≤1, and short-range (integrable) when α>1. We verify that the largest Lyapunov exponent λ_M scales as λ_M ∝ N^-κ(α), where κ(α) is positive when interactions are long-range, yielding weak chaos in the thermodynamic limit N↦∞ (hence λ_M→0). In the short-range case, κ(α) appears to vanish, and the behaviour corresponds to strong chaos. We show that, for certain values of the control parameters of the system, long-lasting metastable states can be present. Their duration t_c scales as t_c ∝N^β(α), where β(α) appears to be numerically in agreement with the following behavior: β>0 for 0 ≤α< 1, and zero for α≥1. These results are consistent with features typically found in nonextensive statistical mechanics. Moreover, they exhibit strong similarity between the present discrete-time system, and the α-XY Hamiltonian ferromagnetic model.     

Magnetoexciton absorption in coupled quantum wells

A Mott exciton in coupled quantum wells in a transverse magnetic field H is considered. An expression for the exciton spectrum in an arbitrary magnetic field for large separations D between quantum wells containing an electron (e) and a hole (h) is given. The exciton spectrum in a strong magnetic field for different Landau levels at arbitrary D has been calculated. Changes in the parameter D/l, where is the magnetic length, cause rearrangement of the magnetoexciton dispersion curves ℰ(P), where P is the conserved “magnetic” momentum, which is a function of the separation between the electron and hole in the plane of the quantum wells. Off-center (“roton”) extrema occur only for D/l,<(D/l)_cr, where (D/l)_cr is a function of the exciton quantum numbers n and m. The magnetoexciton effective mass in states with magnetic quantum number m=0 monotonically increases with H and D, while in states with m≠0 it is a nonmonotonic function of D/l. The probability of generating an exciton in coupled quantum wells increases with H. Absorption of electromagnetic radiation due to transitions between excitonic levels in coupled quantum wells is discussed. For an exciton containing a heavy hole the oscillator strengths increase with H and the oscillator strengths decrease. Zh. éksp. Teor. Fiz. 112, 1791–1808 (November 1997)