13 research outputs found
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.
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
Quantum critical behavior and thermodynamics of the repulsive one-dimensional Hubbard model in a magnetic field
Even though the Hubbard model is one of the most fundamental models of highly
correlated electrons, analytical and numerical data describing its
thermodynamics at nonzero magnetization are relatively scarce. We present a
detailed investigation of the thermodynamic properties for the one dimensional
repulsive Hubbard model in the presence of an arbitrary magnetic field for all
values of the filling fraction and temperatures as low as
Our analysis is based on the system of integral equations derived in the
quantum transfer matrix framework. We determine the critical exponents of the
quantum phase transitions and also provide analytical derivations for some of
the universal functions characterizing the thermodynamics in the vicinities of
the quantum critical points. Extensive numerical data for the specific heat,
susceptibility, compressibility, and entropy are reported. The experimentally
relevant double occupancy presents an interesting doubly nonmonotonic
temperature dependence at intermediate values of the interaction strength and
also at large repulsion and magnetic fields close to the critical value. The
susceptibility in zero magnetic field has a logarithmic singularity at low
temperatures for all filling factors similar to the behavior of the same
quantity in the XXX spin chain. We determine the density profiles for a
harmonically trapped system and show that while the total density profile seems
to depend mainly on the value of chemical potential at the center of the trap
the distribution of phases in the inhomogeneous system changes dramatically as
we increase the magnetic field.Comment: 26 pages, 23 figures, RevTeX 4.