Ground-state properties of one-dimensional anyon gases

We investigate the ground state of the one-dimensional interacting anyonic system based on the exact Bethe ansatz solution for arbitrary coupling constant ($0\leq c\leq \infty$) and statistics parameter ($0\leq \kappa \leq \pi$). It is shown that the density of state in quasi-momentum $k$ space and the ground state energy are determined by the renormalized coupling constant $c'$. The effect induced by the statistics parameter $\kappa$ exhibits in the momentum distribution in two aspects: Besides the effect of renormalized coupling, the anyonic statistics results in the nonsymmetric momentum distribution when the statistics parameter $\kappa$ deviates from 0 (Bose statistics) and $\pi$ (Fermi statistics) for any coupling constant $c$. The momentum distribution evolves from a Bose distribution to a Fermi one as $\kappa$ varies from 0 to $\pi$. The asymmetric momentum distribution comes from the contribution of the imaginary part of the non-diagonal element of reduced density matrix, which is an odd function of $\kappa$. The peak at positive momentum will shift to negative momentum if $\kappa$ is negative.Comment: 6 pages, 5 figures, published version in Phys. Rev.

κ\kappa-Deformed Statistics and Classical Fourmomentum Addition Law

We consider $\kappa$-deformed relativistic symmetries described algebraically by modified Majid-Ruegg bicrossproduct basis and investigate the quantization of field oscillators for the $\kappa$-deformed free scalar fields on $\kappa$-Minkowski space. By modification of standard multiplication rule, we postulate the $\kappa$-deformed algebra of bosonic creation and annihilation operators. Our algebra permits to define the n-particle states with classical addition law for the fourmomenta in a way which is not in contradiction with the nonsymmetric quantum fourmomentum coproduct. We introduce $\kappa$-deformed Fock space generated by our $\kappa$-deformed oscillators which satisfy the standard algebraic relations with modified $\kappa$-multiplication rule. We show that such a $\kappa$-deformed bosonic Fock space is endowed with the conventional bosonic symmetry properties. Finally we discuss the role of $\kappa$-deformed algebra of oscillators in field-theoretic noncommutative framework.Comment: LaTeX, 12 pages. V2: second part of chapter 4 changed, new references and comments added. V3: formula (14) corrected. Some additional explanations added. V4: further comments about algebraic structure are adde

Conformal Curves on WO3WO_3 Surface

We have studied the iso-height lines on the $\mathrm{WO_3}$ surface as a physical candidate for conformally invariant curves. We have shown that these lines are conformally invariant with the same statistics of domain walls in the critical Ising model. They belong to the family of conformal invariant curves called Schramm-Loewner evolution (or $SLE_{\kappa}$), with diffusivity of $\kappa \sim 3$. This can be regarded as the first experimental observation of SLE curves. We have also argued that Ballistic Deposition (BD) can serve as a growth model giving rise to contours with similar statistics at large scales.Comment: 4 pages, 6 figures. accepted in PR

Bose-Einstein Condensation in the Framework of κ\kappa-Statistics

In the present work we study the main physical properties of a gas of $\kappa$-deformed bosons described through the statistical distribution function $f_\kappa=Z^{-1}[\exp_\kappa (\beta({1/2}m v^2-\mu))-1]^{-1}$. The deformed $\kappa$-exponential $\exp_\kappa(x)$, recently proposed in Ref. [G.Kaniadakis, Physica A {\bf 296}, 405, (2001)], reduces to the standard exponential as the deformation parameter $\kappa \to 0$, so that $f_0$ reproduces the Bose-Einstein distribution. The condensation temperature $T_c^\kappa$ of this gas decreases with increasing $\kappa$ value, and approaches the $^{4}He(I)-^{4}He(II)$ transition temperature $T_{\lambda}=2.17K$, improving the result obtained in the standard case ($\kappa=0$). The heat capacity $C_V^\kappa(T)$ is a continuous function and behaves as $B_\kappa T^{3/2}$ for $TT_c^\kappa$, in contrast with the standard case $\kappa=0$, it is always increasing. Pacs: 05.30.Jp, 05.70.-a Keywords: Generalized entropy; Boson gas; Phase transition.Comment: To appear in Physica B. Two fig.p

Vortex dissipation and level dynamics for the layered superconductors with impurities

We study parametric level statistics of the discretized excitation spectra inside a moving vortex core in layered superconductors with impurities. The universal conductivity is evaluated numerically for the various values of rescaled vortex velocities $\kappa$ from the clean case to the dirty limit case. The random matrix theoretical prediction is verified numerically in the large $\kappa$ regime. On the contrary in the low velocity regime, we observe $\sigma_{xx} \propto \kappa^{2/3}$ which is consistent with the theoretical result for the super-clean case, where the energy dissipation is due to the Landau-Zener transition which takes place at the points called ``avoided crossing''.Comment: 10 pages, 4 figures, REVTeX3.

Kappa-deformed random-matrix theory based on Kaniadakis statistics

We present a possible extension of the random-matrix theory, which is widely used to describe spectral fluctuations of chaotic systems. By considering the Kaniadakis non-Gaussian statistics, characterized by the index {\kappa} (Boltzmann-Gibbs entropy is recovered in the limit {\kappa}\rightarrow0), we propose the non-Gaussian deformations ({\kappa} \neq 0) of the conventional orthogonal and unitary ensembles of random matrices. The joint eigenvalue distributions for the {\kappa}-deformed ensembles are derived by applying the principle maximum entropy to Kaniadakis entropy. The resulting distribution functions are base invarient as they depend on the matrix elements in a trace form. Using these expressions, we introduce a new generalized form of the Wigner surmise valid for nearly-chaotic mixed systems, where a basis-independent description is still expected to hold. We motivate the necessity of such generalization by the need to describe the transition of the spacing distribution from chaos to order, at least in the initial stage. We show several examples about the use of the generalized Wigner surmise to the analysis of the results of a number of previous experiments and numerical experiments. Our results suggest the entropic index {\kappa} as a measure for deviation from the state of chaos. We also introduce a {\kappa}-deformed Porter-Thomas distribution of transition intensities, which fits the experimental data for mixed systems better than the commonly-used gamma-distribution.Comment: 18 pages, 8 figure

The covariant and on-shell statistics in kappa-deformed spacetime

It has been a long-standing issue to construct the statistics of identical particles in $\kappa$-deformed spacetime. In this letter, we investigate different ideas on this problem. Following the ideas of Young and Zegers, we obtain the covariant and on-shell kappa two-particle state in 1+1 D in a simpler way. Finally, a procedure to get such state in higher dimension is proposed.Comment: 16 page