462 research outputs found
Anti-Symmetrically Fused Model and Non-Linear Integral Equations in the Three-State Uimin-Sutherland Model
We derive the non-linear integral equations determining the free energy of
the three-state pure bosonic Uimin-Sutherland model. In order to find a
complete set of auxiliary functions, the anti-symmetric fusion procedure is
utilized. We solve the non-linear integral equations numerically and see that
the low-temperature behavior coincides with that predicted by conformal field
theory. The magnetization and magnetic susceptibility are also calculated by
means of the non-linear integral equation.Comment: 16 pages, 6 figure
Exact probability distribution functions for Parrondo's games
We consider discrete time Brownian ratchet models: Parrondo's games. Using
the Fourier transform, we calculate the exact probability distribution
functions for both the capital dependent and history dependent Parrondo's
games. We find that in some cases there are oscillations near the maximum of
the probability distribution, and after many rounds there are two limiting
distributions, for the odd and even total number of rounds of gambling. We
assume that the solution of the aforementioned models can be applied to
portfolio optimization.Comment: 5 pages, 3 figure
Universality and quantum criticality of the one-dimensional spinor Bose gas
We investigate the universal thermodynamics of the two-component
one-dimensional Bose gas with contact interactions in the vicinity of the
quantum critical point separating the vacuum and the ferromagnetic liquid
regime. We find that the quantum critical region belongs to the universality
class of the spin-degenerate impenetrable particle gas which, surprisingly, is
very different from the single-component case and identify its boundaries with
the peaks of the specific heat. In addition, we show that the compressibility
Wilson ratio, which quantifies the relative strength of thermal and quantum
fluctuations, serves as a good discriminator of the quantum regimes near the
quantum critical point. Remarkably, in the Tonks-Girardeau regime the universal
contact develops a pronounced minimum, reflected in a counterintuitive
narrowing of the momentum distribution as we increase the temperature. This
momentum reconstruction, also present at low and intermediate momenta, signals
the transition from the ferromagnetic to the spin-incoherent Luttinger liquid
phase and can be detected in current experiments with ultracold atomic gases in
optical lattices.Comment: 5+2 pages, RevTeX 4.
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