504 research outputs found
Phase transition in the Higgs model of scalar dyons
In the present paper we investigate the phase transition
"Coulomb--confinement" in the Higgs model of abelian scalar dyons -- particles
having both, electric and magnetic , charges. It is shown that by dual
symmetry this theory is equivalent to scalar fields with the effective squared
electric charge e^{*2}=e^2+g^2. But the Dirac relation distinguishes the
electric and magnetic charges of dyons. The following phase transition
couplings are obtained in the one--loop approximation:
\alpha_{crit}=e^2_{crit}/4\pi\approx 0.19,
\tilde\alpha_{crit}=g^2_{crit}/4\pi\approx 1.29 and \alpha^*_{crit}\approx
1.48.Comment: 16 pages, 2 figure
Nonlinear Bogolyubov-Valatin transformations and quaternions
In introducing second quantization for fermions, Jordan and Wigner
(1927/1928) observed that the algebra of a single pair of fermion creation and
annihilation operators in quantum mechanics is closely related to the algebra
of quaternions H. For the first time, here we exploit this fact to study
nonlinear Bogolyubov-Valatin transformations (canonical transformations for
fermions) for a single fermionic mode. By means of these transformations, a
class of fermionic Hamiltonians in an external field is related to the standard
Fermi oscillator.Comment: 6 pages REVTEX (v3: two paragraphs appended, minor stylistic changes,
eq. (39) corrected, references [10]-[14], [36], [37], [41], [67]-[69] added;
v4: few extensions, references [62], [63] added, final version to be
published in J. Phys. A: Math. Gen.
Anderson Localization of Bogolyubov Quasiparticles in Interacting Bose-Einstein Condensates
We study the Anderson localization of Bogolyubov quasiparticles in an
interacting Bose-Einstein condensate (with healing length \xi) subjected to a
random potential (with finite correlation length \sigma_R). We derive
analytically the Lyapunov exponent as a function of the quasiparticle momentum
k and we study the localization maximum k_{max}. For 1D speckle potentials, we
find that k_{max} is proportional to 1/\xi when \xi is much larger than
\sigma_R while k_{max} is proportional to 1/\sigma_R when \xi is much smaller
than \sigma_R, and that the localization is strongest when \xi is of the order
of \sigma_R. Numerical calculations support our analysis and our estimates
indicate that the localization of the Bogolyubov quasiparticles is accessible
in current experiments with ultracold atoms.Comment: published version (no significant changes compared to last version
Localization of Bogoliubov quasiparticles in interacting Bose gases with correlated disorder
We study the Anderson localization of Bogoliubov quasiparticles (elementary
many-body excitations) in a weakly interacting Bose gas of chemical potential
subjected to a disordered potential . We introduce a general mapping
(valid for weak inhomogeneous potentials in any dimension) of the Bogoliubov-de
Gennes equations onto a single-particle Schr\"odinger-like equation with an
effective potential. For disordered potentials, the Schr\"odinger-like equation
accounts for the scattering and localization properties of the Bogoliubov
quasiparticles. We derive analytically the localization lengths for correlated
disordered potentials in the one-dimensional geometry. Our approach relies on a
perturbative expansion in , which we develop up to third order, and we
discuss the impact of the various perturbation orders. Our predictions are
shown to be in very good agreement with direct numerical calculations. We
identify different localization regimes: For low energy, the effective
disordered potential exhibits a strong screening by the quasicondensate density
background, and localization is suppressed. For high-energy excitations, the
effective disordered potential reduces to the bare disordered potential, and
the localization properties of quasiparticles are the same as for free
particles. The maximum of localization is found at intermediate energy when the
quasicondensate healing length is of the order of the disorder correlation
length. Possible extensions of our work to higher dimensions are also
discussed.Comment: Published versio
Maximal width of the separatrix chaotic layer
The main goal of the paper is to find the {\it absolute maximum} of the width
of the separatrix chaotic layer as function of the frequency of the
time-periodic perturbation of a one-dimensional Hamiltonian system possessing a
separatrix, which is one of the major unsolved problems in the theory of
separatrix chaos. For a given small amplitude of the perturbation, the width is
shown to possess sharp peaks in the range from logarithmically small to
moderate frequencies. These peaks are universal, being the consequence of the
involvement of the nonlinear resonance dynamics into the separatrix chaotic
motion. Developing further the approach introduced in the recent paper by
Soskin et al. ({\it PRE} {\bf 77}, 036221 (2008)), we derive leading-order
asymptotic expressions for the shape of the low-frequency peaks. The maxima of
the peaks, including in particular the {\it absolute maximum} of the width, are
proportional to the perturbation amplitude times either a logarithmically large
factor or a numerical, still typically large, factor, depending on the type of
system. Thus, our theory predicts that the maximal width of the chaotic layer
may be much larger than that predicted by former theories. The theory is
verified in simulations. An application to the facilitation of global chaos
onset is discussed.Comment: 18 pages, 16 figures, submitted to PR
Bare vs effective pairing forces. A microscopic finite-range interaction for HFB calculations in coordinate space
We propose a microscopic effective interaction to treat pairing correlations
in the channel. It is introduced by recasting the gap equation
written in terms of the bare force into a fully equivalent pairing problem.
Within this approach, the proposed interaction reproduces the pairing
properties provided by the realistic force very accurately. Written in
the canonical basis of the actual Bogolyubov transformation, the force takes
the form of an off-shell in-medium two-body matrix in the superfluid phase
multiplied by a BCS occupation number . This interaction is finite
ranged, non local, total-momentum dependent and density dependent. The factor
emerging from the recast of the gap equation provides a natural
cut-off and makes zero-range approximations of the effective vertex meaningful.
Performing such an approximation, the roles of the range and of the density
dependence of the interaction can be disentangled. The isoscalar and isovector
density-dependences derived ab-initio provide the pairing force with a strong
predictive power when extrapolated toward the drip-lines. Although finite
ranged and non local, the proposed interaction makes HFB calculations of finite
nuclei in coordinate space tractable. Through the two-basis method, its
computational cost is of the same order as for a zero-range force.Comment: 43 pages, 13 figures. Published versio
Bogolyubov-Hartree-Fock approach to studying the QCD ground state
The quark's behaviour while influenced by a strong stochastic gluon field is
analyzed. An approximate procedure for calculating the effective Hamiltonian is
developed and the corresponding ground state within the Hartree-Fock-Bogolyubov
approach is found. The comparative analysis of various Hamiltonian models is
given and transition to the chiral limit in the Keldysh model is discussed in
detail.Comment: 18 pages, 4 figures, new version of the manuscrip
Universality of Cluster Dynamics
We have studied the kinetics of cluster formation for dynamical systems of
dimensions up to interacting through elastic collisions or coalescence.
These systems could serve as possible models for gas kinetics, polymerization
and self-assembly. In the case of elastic collisions, we found that the cluster
size probability distribution undergoes a phase transition at a critical time
which can be predicted from the average time between collisions. This enables
forecasting of rare events based on limited statistical sampling of the
collision dynamics over short time windows. The analysis was extended to
L-normed spaces () to allow for some amount of
interpenetration or volume exclusion. The results for the elastic collisions
are consistent with previously published low-dimensional results in that a
power law is observed for the empirical cluster size distribution at the
critical time. We found that the same power law also exists for all dimensions
, 2D L norms, and even for coalescing collisions in 2D. This
broad universality in behavior may be indicative of a more fundamental process
governing the growth of clusters
Spin transfer and current-induced switching in antiferromagnets
We present theoretical description of the precessional switching processes
induced by simultaneous application of spin-polarized current and external
magnetic field to antiferromagnetic component of the "pinned" layer. We found
stability ranges of different static and dynamic regimes. We showed the
possibility of steady current-induced precession of antiferromagnetic vector
with frequency that linearly depends on the bias current. Furthermore, we found
an optimal duration of current pulse required for switching between different
orientations of antiferromagnetic vector and current and field dependence of
switching time. Our results reveal the difference between dynamics of ferro-
and antiferromagnets subjected to spin transfer torques.Comment: 7 pages, 4 figure
Generation of linear waves in the flow of Bose-Einstein condensate past an obstacle
The theory of linear wave structures generated in Bose-Einstein condensate
flow past an obstacle is developed. The shape of wave crests and dependence of
amplitude on coordinates far enough from the obstacle are calculated. The
results are in good agreement with the results of numerical simulations
obtained earlier. The theory gives a qualitative description of experiments
with Bose-Einstein condensate flow past an obstacle after condensate's release
from a trap.Comment: 11 pages, 3 figures, to be published in Zh. Eksp. Teor. Fi
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