Upper bound to the spin correlation function of the n-vector model with random anisotropic interactions

We obtain an upper bound to the spin correlation function in the thermodynamic limit of the zero external field limit for the n-vector model with random anisotropic interactions. We find a sufficient condition for disappearance of the spontaneous long-range order.     

On the P- and T-nonconserving nuclear moments

The contribution of virtual excitations of paired nucleons to T-nonconserving nuclear moments caused by T-odd nuclear forces is shown to be comparable to the contribution of the external nucleon. Taking into account the contribution of paired nucleons in the ¹²⁹Xe nucleus allows one to extract from atomic experiments the best limit on the P- and T-nonconserving nucleon-nucleon interactions. This limit approaches, by its implications, the limit on the neutron dipole moment. In the case of the P-nonconserving, but T-invariant, anapole nuclear moment the external nucleon's excitations dominate.     

Random Ising model in the magnetic field at T = 0: I. The distribution of the effective fields

The integral equation for the distribution function of the effective fields in the random Ising model in the finite external field is solved exactly at zero temperature in the one-dimensional case for 1) dilute ferromagnet, 2) dilute antiferromagnet and 3) ±J model. The ground state characteristics of these systems are obtained. In particular the effective fields in the ±J model are shown to have a triangular distribution in the zero external field limit.     

Spontaneous supersymmetry breaking in matrix models from the viewpoints of localization and Nicolai mapping

In the previous work, it was shown that, in supersymmetric (matrix) discretized quantum mechanics, inclusion of an external field twisting the boundary condition of fermions enables us to discuss spontaneous breaking of supersymmetry (SUSY) in the path-integral formalism in a well-defined way. In the present work, we continue investigating the same systems from the points of view of localization and Nicolai mapping. The localization is studied by changing of integration variables in the path integral, which is applicable whether or not SUSY is explicitly broken. We examine in detail how the integrand of the partition function with respect to the integral over the auxiliary field behaves as the auxiliary field vanishes, which clarifies a mechanism of the localization. In SUSY matrix models, we obtain a matrix-model generalization of the localization formula. In terms of eigenvalues of matrix variables, we observe that eigenvalues' dynamics is governed by balance of attractive force from the localization and repulsive force from the Vandermonde determinant. The approach of the Nicolai mapping works even in the presence of the external field. It enables us to compute the partition function of SUSY matrix models for finite N (N is the rank of matrices) with arbitrary superpotential at least in the leading nontrivial order of an expansion with respect to the small external field. We confirm the restoration of SUSY in the large-N limit of a SUSY matrix model with a double-well scalar potential observed in the previous work.     

Conductance peaks in open quantum dots

We present a simple measure of the conductance fluctuations in open ballistic chaotic quantum dots, extending the number of maxima method originally proposed for the statistical analysis of compound nuclear reactions. The average number of extreme points (maxima and minima) in the dimensionless conductance T as a function of an arbitrary external parameter Z is directly related to the autocorrelation function of T(Z). The parameter Z can be associated with an applied gate voltage causing shape deformation in quantum dot, an external magnetic field, the Fermi energy, etc. The average density of maxima is found to be <ρ(Z)>=α(Z)/Z(c), where α(Z) is a universal constant and Z(c) is the conductance autocorrelation length, which is system specific. The analysis of <ρ(Z)> does not require large statistic samples, providing a quite amenable way to access information about parametric correlations, such as Z(c).     

Vertex correction of the anisotropic magnetic impurities to the spin polarization of 2D electron gas

In terms of Kubo's formula and Green's function method, for the two-dimensional electron gas (2DEG) with Rashba spin-orbit coupling (SOC), we study the spin polarization due to the effect from magnetic impurities with anisotropic spin dependent delta type coupling to electrons when an external dc electric field in plane is applied. The vertex correction of impurities in ladder approximation is carried out in the limit of EF?1/τ, Δ. We find that the strength of spin polarization can be significantly modified by vertex correction and the spin polarization is relevant to the anisotropy coefficient γ, but the direction of net spin polarization cannot be changed.     

Non-Abelian Chern-Simons particles in an external magnetic field

The quantum mechanics and thermodynamics of SU(2) non-Abelian Chern-Simons particles (non-Abelian anyons) in an external magnetic field are addressed. We derive the N-body Hamiltonian in the (anti-) holomorphic gauge when the Hilbert space is projected onto the lowest Landau level of the magnetic field. In the presence of an additional harmonic potential, the N-body spectrum depends linearly on the coupling (statistics) parameter. We calculate the second virial coefficient and find that in the strong magnetic field limit it develops a step-wise behavior as a function of the statistics parameter, in contrast to the linear dependence in the case of Abelian anyons. For small enough values of the statistics parameter we relate the N-body partition functions in the lowest Landau level to these of SU(2) bosons and find that the cluster (and virial) coefficients dependence on the statistics parameter cancels.     

On the possibility of corona initiation near a conducting drop nonlinearly vibrating in an external electrostatic field

An analytical asymptotic expression for the field strength near an ideal incompressible electrically conducting liquid drop nonlinearly vibrating in external electrostatic field E ₀ is found in an order of 5/2 in a small parameter. The small parameter here is the amplitude of deformation of the spherical shape of the drop. It is found that the strength of the electric field resulting at the tops of the drop exceeds the corona-initiating field even if E ₀ is one order of magnitude lower than the value at which the drop becomes unstable against the induced charge (that is, at such values of E ₀ as are observed in storm clouds in full-scale experiments).     

Oscillations of echo amplitude in glasses in a magnetic field induced by nuclear dipole-dipole interaction

The influence of a magnetic field on the dipole echo amplitude in glasses (at temperatures of about 10 mK) induced by the dipole-dipole interaction of nuclear spins has been theoretically studied. It has been shown that a change in the mutual position of nuclear spins at tunneling and the Zeeman energy E _H of their interaction with the external magnetic field lead to a nonmonotonic magnetic-field dependence of the dipole echo amplitude. The approximation that the nuclear dipole-dipole interaction energy E _d is much smaller than the Zeeman energy has been found to be valid in the experimentally important cases. It has been shown that the dipole echo amplitude in this approximation may be described by a simple universal analytic function independent of the microscopic structure of the two-level systems. An excellent agreement of the theory with the experimental data has been obtained without fitting parameters (except for the unknown echo amplitude).     

Direct measurement of the nuclear magnetic dipole moment of Ho165 with the atomic beam magnetic resonance method

With an atomic beam magnetic resonance apparatus four rf transitions between different Zeeman levels of the⁴ I _15/2 ground state of Ho¹⁶⁵ have been measured in an external magnetic field of about 3000 Gauss. The interaction between the nuclear magnetic dipole moment and the external field could be deduced from these measurements. Because the magnetic field was measured by calibration transitions in K³⁹, Rb⁸⁵ and Rb⁸⁷, the following value could be determined for the nuclear magnetic dipole moment: μ _I (Ho¹⁶⁵)=4.094(44) μ _n (uncorrected for diamagnetic shielding). Thegj-factor of the ground state of Ho¹⁶⁵ was measured to begj(⁴ I _15/2, Ho¹⁶⁵)=1.1951445(40).     

Electromagnetic properties of massive neutrinos

The vertex function for a virtual massive neutrino is calculated in the limit of soft real photons. A method based on employing the neutrino self-energy operator in a weak external electromagnetic field in the approximation linear in the field is developed in order to render this calculation of the vertex function convenient. It is shown that the electric charge and the electric dipole moment of the real neutrino are zero; only the magnetic moment is nonzero for massive neutrinos. A fourth-generation heavy neutrino of mass not less than half of the Z-boson mass is considered as a massive neutrino.     

Bistability of radiation force on N-atom system

We consider a system with N two-level atoms in a cavity, interacting with an external radiation field. Using Ehrenfest's theorem the radiation force on the N-atom system is studied as a function of the external radiation field. In a certain parameter region we are able to show that the radiation force can be bistable     

Studies of the nuclear inertia in fission and heavy-ion reactions

On the basis of the non-self-consistent cranking model we study some aspects of the nuclear inertia of interest in fission and heavy-ion reactions. First, we consider in the adiabatic limit the inertia for a doubly closed-shell nucleus in a deformed spheroidal harmonic-oscillator single-particle potential plus a small perturbation. When expressed in terms of a coordinate that describes the deformation of the nuclear matter distribution, the inertia for small oscillations about a spherical shape is exactly equal to the incompressible, irrotational value. For large distortions it deviates from the incompressible, irrotational value by up to about ±1 % away from level crossings. Second, in order to study the dependence of the inertia upon a level crossing, we consider in detail two levels of the above system. This is done both in the adiabatic limit and for large collective velocities. At level crossings the adiabatic inertia relative to the deformation of the matter distribution diverges as 1/|ΔV|, where |ΔV| is the magnitude of the perturbation. However, for large collective velocities the contribution to the inertia from a level crossing is less than 4|ΔV|r²_m, where r_m is the collective velocity of the matter distribution. Although we have not considered the effect of large velocities on the remaining levels of the many-body system or the effect of a statistical ensemble of states, some of our results suggest that for high excitation energies and moderately large collective velocities the nuclear inertia approaches approximately the irrotational value.     

Axial-vector anomaly for Dirac-Kähler fermions on the lattice

The axial-vector current of Dirac-Kähler fermions on the lattice is studied. We consider a U(1) gauge theory in two dimensions as well as an SU(N) gauge theory in four dimensions. Using a short-distance expansion of the fermion propagator in an external gauge field, we show that the correct anomaly is reproduced in the continuum limit.     

The quantum acoustomagnetoelectric field in a quantum well with a parabolic potential

The acoustomagnetoelectric (AME) field in a quantum well with a parabolic potential (QWPP) has been studied in the presence of an external magnetic field. The analytic expression for the AME field in the QWPP is obtained by using the quantum kinetic equation for the distribution function of electrons interacting with external phonons. The dependence of the AME field on the temperature T of the system, the wavenumber q of the acoustic wave and external magnetic field B for the specific AlAs/GaAs/AlAs is achieved by using a numerical method. The problem is considered for both cases: The weak magnetic field region and the quantized magnetic field region. The results are compared with those for normal bulk semiconductor and superlattices to show the differences, and we use the quantum theory to calculate the AME field in the QWPP.     

Fission instability of nuclei at very high angular momenta

Deformation energy surfaces at high angular momenta ($\text{I ≧ 30?}$) are calculated for different nuclear shapes characterized by the deformation β and a neck parameter r. This parametrization has the advantage that it is a natural extension of the Bohr-Mottelson shape parameters β and γ. This choice allows one to study the neck degree of freedom near the fission instability at high angular momenta and also the sudden change of the nuclear shape from an oblate deformation (β > 0; γ = ?60°) to a prolate one (β > 0, γ = 0°) which gives rise to the so called giant backbending (g.b.b.). The deformation energy surface is calculated using the Strutinsky approach with the rotating liquid-drop model (RLDM) and the shell corrections based on a cranked Saxon-Woods potential. The heights of the first and, if present, the second barrier are studied at γ = 0° as a function of the total angular momentum for even mass rare earth and actinide nuclei. The critical angular momenta at which the fission barriers vanish are often higher than that predicted by the RLDM.     

The Quantum and Klein-Gordon Oscillators in a Non-commutative Complex Space and the Thermodynamic Functions

In this work we study the quantum and Klein-Gordon oscillators in a non-commutative complex space. We show that a particle described by such oscillators behaves similarly as an electron with spin in a commutative space in an external uniform magnetic field. Therefore the wave-function $\psi (z,\bar{z} )$ takes values in C ⁴, spin up, spin down, particle, antiparticle, a result which is obtained by the Dirac theory. We obtain the energy levels by exact solutions. We also derive the thermodynamic functions associated to the partition function, and show that the non-commutativity effects are manifested in energy at the high temperature limit.     

Nonlinear sigma model and the origin of geometric frustration on curved manifolds

Classical Heisenberg spins considered on an elastic two-dimensional curved manifold in the continuum limit correspond to the nonlinear σ model. If the corresponding Euler-Lagrange (EL) equations support a soliton solution, a mismatch of length scales induces geometrical frustration in the region of the soliton which is relieved by a deformation of the manifold in the region of the soliton. We illustrate the origin of this elastic effect in four different cases: (i) A single soliton on a circular cylinder with anisotropic spin-spin coupling, (ii) a soliton lattice on a circular cylinder with isotropic spin-spin coupling, (iii) a single soliton on an elliptic cylinder, and (iv) a circular cylinder in an external axial magnetic field. For the first three cases the EL equation is the sine-Gordon equation while for the last case it is the double sine-Gordon equation. Geometrical frustration results whenever the solution of the EL equation does not satisfy the self-dual equations of Bogomol’nyi which are a necessary condition to reach the minimum energy configuration in each homotopy class.     

Non-equilibrium Dynamics of an Infinite Range XY Model in an External Field

We study the XY model with infinite range interactions in an external magnetic field. The simulations show that in the thermodynamic limit this model does not relax to the thermodynamic equilibrium—instead it becomes trapped in a non-ergodic out-of-equilibrium state. We show how the relaxation towards this non-equilibrium state can be studied using the properties of the collisionless Boltzmann (Vlasov) equation.     

Statistical theory of nuclear reactions and the Gaussian orthogonal ensemble

Using methods developed in field theory and statistical mechanics, especially in the context of the Anderson model as generalised by Wegner, a novel approach to the statistical theory of nuclear reactions is developed. A finite set of N bound states, coupled to each other by an ensemble of Gaussian orthogonal matrices, is considered and coupled to a set of channels via fixed coupling matrix elements. The ensemble average and the variance of the elements of the nuclear scattering matrix are evaluated, using the method of a generating function combined with the replica trick, followed by the Hubbard-Stratonovitch transformation and a modified loop expansion. In the limit N → ∞, it is shown quite generally that, aside from a trivial dependence on average S-matrix elements, the variance depends only on the transmission coefficients, and that the correlation width of a pair of S-matrix elements is given by a universal function of the transmission coefficients. A modified loop expansion yields an asymptotic series valid for strong absorption. The terms in this series are partly novel, and partly coincide with results obtained earlier in the framework of a model which did not take account of the GOE eigenvalue fluctuations. This suggests that average cross sections are mainly sensitive to the stiffness of the GOE spectrum. Fluctuation properties are also derived, and the link to Ericson fluctuation theory is established.