2,782 research outputs found
Explicit Free Parameterization of the Modified Tetrahedron Equation
The Modified Tetrahedron Equation (MTE) with affine Weyl quantum variables at
N-th root of unity is solved by a rational mapping operator which is obtained
from the solution of a linear problem. We show that the solutions can be
parameterized in terms of eight free parameters and sixteen discrete phase
choices, thus providing a broad starting point for the construction of
3-dimensional integrable lattice models. The Fermat curve points parameterizing
the representation of the mapping operator in terms of cyclic functions are
expressed in terms of the independent parameters. An explicit formula for the
density factor of the MTE is derived. For the example N=2 we write the MTE in
full detail. We also discuss a solution of the MTE in terms of bosonic
continuum functions.Comment: 28 pages, 3 figure
Ground states of Heisenberg evolution operator in discrete three-dimensional space-time and quantum discrete BKP equations
In this paper we consider three-dimensional quantum q-oscillator field theory
without spectral parameters. We construct an essentially big set of eigenstates
of evolution with unity eigenvalue of discrete time evolution operator. All
these eigenstates belong to a subspace of total Hilbert space where an action
of evolution operator can be identified with quantized discrete BKP equations
(synonym Miwa equations). The key ingredients of our construction are specific
eigenstates of a single three-dimensional R-matrix. These eigenstates are
boundary states for hidden three-dimensional structures of U_q(B_n^1) and
U_q(D_n^1)$.Comment: 13 page
Comment on "Giant Nernst Effect due to Fluctuating Cooper Pairs in Superconductors" by M.N. Serbyn, M.A. Skvortsov, A.A. Varlamov, and V. Galitski
In a recent Letter, Serbyn et al. [A] investigated thermomagnetic effects
above the superconducting transition and generalized previous works for
arbitrary magnetic fields and temperatures. While the results of [A] have been
confirmed in [B], we have strong objections: (i) According to our results [C],
the linear response calculation does not require any correction from the
magnetization currents; (ii) The result of [A,B] is giant, because unlike the
normal Fermi liquid, it is of zero order in the particle-hole asymmetry.
Changing the interaction constant in the Cooper channel leads to ridiculously
large results even for nonsuperconducting metals; (iii)Derived in [A] the
Einstein-type relation for thermomagnetic coefficient contradicts to text-book
results.
[A] M.N. Serbyn, M.A. Skvortsov, A.A. Varlamov, V. Galitski, Phys. Rev. Lett.
102, 067001 (2009).
[B] K. Michaeli and A.M. Finkel'stein, EPL 86, 27007 (2009).
[C] A. Sergeev et al., Phys. Rev. B 77, 064501 (2008)
Quantum 2+1 evolution model
A quantum evolution model in 2+1 discrete space - time, connected with 3D
fundamental map R, is investigated. Map R is derived as a map providing a zero
curvature of a two dimensional lattice system called "the current system". In a
special case of the local Weyl algebra for dynamical variables the map appears
to be canonical one and it corresponds to known operator-valued R-matrix. The
current system is a kind of the linear problem for 2+1 evolution model. A
generating function for the integrals of motion for the evolution is derived
with a help of the current system. The subject of the paper is rather new, and
so the perspectives of further investigations are widely discussed.Comment: LaTeX, 37page
On invariance of specific mass increment in the case of non-equilibrium growth
It is the first time invariance of specific mass increments of crystalline
structures that co-exist in the case of non-equilibrium growth is grounded
using the maximum entropy production principle. Based on the hypothesis of the
existence of a universal growth equation, with the use of dimensional analysis,
an explicit form of the dependence of specific mass increment on time is
proposed. Applicability of the obtained results for describing growth in
animate nature is discussed.Comment: 5 page
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