1,208 research outputs found
The Correlation Functions of the XXZ Heisenberg Chain for Zero or Infinite Anisotropy and Random Walks of Vicious Walkers
The XXZ Heisenberg chain is considered for two specific limits of the
anisotropy parameter: \Dl\to 0 and \Dl\to -\infty. The corresponding wave
functions are expressed by means of the symmetric Schur functions. Certain
expectation values and thermal correlation functions of the ferromagnetic
string operators are calculated over the base of N-particle Bethe states. The
thermal correlator of the ferromagnetic string is expressed through the
generating function of the lattice paths of random walks of vicious walkers. A
relationship between the expectation values obtained and the generating
functions of strict plane partitions in a box is discussed. Asymptotic estimate
of the thermal correlator of the ferromagnetic string is obtained in the limit
of zero temperature. It is shown that its amplitude is related to the number of
plane partitions.Comment: 22 pages, 1 figure, LaTe
Correlation Functions of XX0 Heisenberg Chain, q-Binomial Determinants, and Random Walks
The XX0 Heisenberg model on a cyclic chain is considered. The representation
of the Bethe wave functions via the Schur functions allows to apply the
well-developed theory of the symmetric functions to the calculation of the
thermal correlation functions. The determinantal expressions of the
form-factors and of the thermal correlation functions are obtained. The
q-binomial determinants enable the connection of the form-factors with the
generating functions both of boxed plane partitions and of self-avoiding
lattice paths. The asymptotical behavior of the thermal correlation functions
is studied in the limit of low temperature provided that the characteristic
parameters of the system are large enough.Comment: 27 pages, 2 figures, LaTe
Exactness of the Bogoliubov approximation in random external potentials
We investigate the validity of the Bogoliubov c-number approximation in the
case of interacting Bose-gas in a \textit{homogeneous random} media. To take
into account the possible occurence of type III generalized Bose-Einstein
condensation (i.e. the occurrence of condensation in an infinitesimal band of
low kinetic energy modes without macroscopic occupation of any of them) we
generalize the c-number substitution procedure to this band of modes with low
momentum. We show that, as in the case of the one-mode condensation for
translation-invariant interacting systems, this procedure has no effect on the
exact value of the pressure in the thermodynamic limit, assuming that the
c-numbers are chosen according to a suitable variational principle. We then
discuss the relation between these c-numbers and the (total) density of the
condensate
Master formula approach to broken chiral U(3)xU(3) symmetry
The master formula approach to chiral symmetry breaking proposed by Yamagishi
and Zahed is extended to the U_R(3)xU_L(3) group, in which effects of the
U_A(1) anomaly and the flavor symmetry breaking m_u \not= m_d \not= m_s are
properly contained. New identities for the gluon topological susceptibility and
pi^0, eta, eta' -> gamma^(*) gamma^(*) decays are derived, which exactly embody
the consequence from broken chiral symmetry in QCD without relying on any
unphysical limit.Comment: Version to appear in PRD, 25 page
Bogoliubov theory of Feshbach molecules in the BEC-BCS crossover
We present the Bogoliubov theory for the Bose-Einstein condensation of
Feshbach molecules in a balanced Fermi mixture. Because the Bogoliubov theory
includes (Gaussian) fluctuations, we can in this manner accurately incorporate
both the two-body and many-body aspects of the BEC-BCS crossover that occurs
near a Feshbach resonance. We apply the theory in particular to the very broad
Feshbach resonance in atomic Li-6 at a magnetic field of B_0 = 834 G and find
good agreement with experiments in that case. The BEC-BCS crossover for more
narrow Feshbach resonances is also discussed.Comment: 13 pages of RevTex and 12 Figures. Submitted for publication in
Physical review
Exact Nonperturbative Renormalization
We propose an exact renormalization group equation for Lattice Gauge
Theories, that has no dependence on the lattice spacing. We instead relate the
lattice spacing properties directly to the continuum convergence of the support
of each local plaquette. Equivalently, this is formulated as a convergence
prescription for a characteristic polynomial in the gauge coupling that allows
the exact meromorphic continuation of a nonperturbative system arbitrarily
close to the continuum limit.Comment: 12 page
Coupling running through the Looking-Glass of dimensional Reduction
The dimensional reduction, in a form of transition from four to two
dimensions, was used in the 90s in a context of HE Regge scattering. Recently,
it got a new impetus in quantum gravity where it opens the way to
renormalizability and finite short-distance behavior. We consider a QFT model
with running coupling defined in both the two domains of
different dimensionality; the \gbar(Q^2)\, evolutions being duly conjugated
at the reduction scale Beyond this scale, in the deep UV 2-dim
region, the running coupling does not increase any more. Instead, it {\it
slightly decreases} and tends to a finite value \gbar_2(\infty) \,< \,
\gbar_2(M^2)\, from above. As a result, the global evolution picture looks
quite peculiar and can propose a base for the modified scenario of gauge
couplings behavior with UV fixed points provided by dimensional reduction
instead of leptoquarks.Comment: 8 pages, 4 figures,Version to match the one which (besides the
Appendix) will appear in "Particles and Nuclei (PEPAN), Letters", v.7, No
6(162) 2010 pp 625-631. Slightly edited, one more reference and related
numerical estimate adde
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