8,612 research outputs found

### Critical behavior of $U(n)$-$\chi^{4}$-model with antisymmetric tensor order parameter coupled with magnetic field

The critical behavior of $U(n)$-$\chi^{4}$-model with antisymmetric tensor
order parameter at charged regime is studied by means of the field theoretic
renormalization group at the leading order of $\varepsilon$-expansion (one-loop
approximation). It is shown that renormalization group equations have no
infrared attractive charged fixed points. It is also shown that anomalous
dimension of the order parameter in charged regime appears to be gauge
dependent.Comment: 6 pages; the talk presented at 19th International Seminar on High
Energy Physics "QUARKS-2016

### Bose-Einstein condensate in a rapidly rotating non-symmetric trap

A rapidly rotating Bose-Einstein condensate in a symmetric two-dimensional
harmonic trap can be described with the lowest Landau-level set of
single-particle states. The condensate wave function psi(x,y) is a Gaussian
exp(-r^2/2), multiplied by an analytic function f(z) of the complex variable z=
x+ i y. The criterion for a quantum phase transition to a non-superfluid
correlated many-body state is usually expressed in terms of the ratio of the
number of particles to the number of vortices. Here, a similar description
applies to a rapidly rotating non-symmetric two-dimensional trap with arbitrary
quadratic anisotropy (omega_x^2 < omega_y^2). The corresponding condensate wave
function psi(x,y) is a complex anisotropic Gaussian with a phase proportional
to xy, multiplied by an analytic function f(z), where z = x + i \beta_- y is a
stretched complex variable and 0< \beta_- <1 is a real parameter that depends
on the trap anisotropy and the rotation frequency. Both in the mean-field
Thomas-Fermi approximation and in the mean-field lowest Landau level
approximation with many visible vortices, an anisotropic parabolic density
profile minimizes the energy. An elongated condensate grows along the soft trap
direction yet ultimately shrinks along the tight trap direction. The criterion
for the quantum phase transition to a correlated state is generalized (1) in
terms of N/L_z, which suggests that a non-symmetric trap should make it easier
to observe this transition or (2) in terms of a "fragmented" correlated state,
which suggests that a non-symmetric trap should make it harder to observe this
transition. An alternative scenario involves a crossover to a quasi
one-dimensional condensate without visible vortices, as suggested by Aftalion
et al., Phys. Rev. A 79, 011603(R) (2009).Comment: 20 page

### Classical and relativistic dynamics of supersolids: variational principle

We present a phenomenological Lagrangian and Poisson brackets for obtaining
nondissipative hydrodynamic theory of supersolids. A Lagrangian is constructed
on the basis of unification of the principles of non-equilibrium thermodynamics
and classical field theory. The Poisson brackets, governing the dynamics of
supersolids, are uniquely determined by the invariance requirement of the
kinematic part of the found Lagrangian. The generalization of Lagrangian is
discussed to include the dynamics of vortices. The obtained equations of motion
do not account for any dynamic symmetry associated with Galilean or Lorentz
invariance. They can be reduced to the original Andreev-Lifshitz equations if
to require Galilean invariance. We also present a relativistic-invariant
supersolid hydrodynamics, which might be useful in astrophysical applications.Comment: 22 pages, changed title and content, added reference

### Fermions on one or fewer Kinks

We find the full spectrum of fermion bound states on a Z_2 kink. In addition
to the zero mode, there are int[2 m_f/m_s] bound states, where m_f is the
fermion and m_s the scalar mass. We also study fermion modes on the background
of a well-separated kink-antikink pair. Using a variational argument, we prove
that there is at least one bound state in this background, and that the energy
of this bound state goes to zero with increasing kink-antikink separation, 2L,
and faster than e^{-a2L} where a = min(m_s, 2 m_f). By numerical evaluation, we
find some of the low lying bound states explicitly.Comment: 7 pages, 4 figure

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