Slow quench dynamics of the Kitaev model: anisotropic critical point and effect of disorder

We study the non-equilibrium slow dynamics for the Kitaev model both in the presence and the absence of disorder. For the case without disorder, we demonstrate, via an exact solution, that the model provides an example of a system with an anisotropic critical point and exhibits unusual scaling of defect density $n$ and residual energy $Q$ for a slow linear quench. We provide a general expression for the scaling of $n$ ($Q$) generated during a slow power-law dynamics, characterized by a rate $\tau^{-1}$ and exponent $\alpha$, from a gapped phase to an anisotropic quantum critical point in $d$ dimensions, for which the energy gap $\Delta_{\vec k} \sim k_i^z$ for $m$ momentum components ($i=1..m$) and $\sim k_i^{z'}$ for the rest $d-m$ components ($i=m+1..d$) with $z\le z'$: $n \sim \tau^{-[m + (d-m)z/z']\nu \alpha/(z\nu \alpha +1)}$ ($Q \sim \tau^{-[(m+z)+ (d-m)z/z']\nu \alpha/(z\nu \alpha +1)}$). These general expressions reproduce both the corresponding results for the Kitaev model as a special case for $d=z'=2$ and $m=z=\nu=1$ and the well-known scaling laws of $n$ and $Q$ for isotropic critical points for $z=z'$. We also present an exact computation of all non-zero, independent, multispin correlation functions of the Kitaev model for such a quench and discuss their spatial dependence. For the disordered Kitaev model, where the disorder is introduced via random choice of the link variables $D_n$ in the model's Fermionic representation, we find that $n \sim \tau^{-1/2}$ and $Q\sim \tau^{-1}$ ($Q\sim \tau^{-1/2}$) for a slow linear quench ending in the gapless (gapped) phase. We provide a qualitative explanation of such scaling.Comment: 10 pages, 11 Figs. v

Controlling the composition of a confined fluid by an electric field

Starting from a generic model of a pore/bulk mixture equilibrium, we propose a novel method for modulating the composition of the confined fluid without having to modify the bulk state. To achieve this, two basic mechanisms - sensitivity of the pore filling to the bulk thermodynamic state and electric field effect - are combined. We show by Monte Carlo simulation that the composition can be controlled both in a continuous and in a jumpwise way. Near the bulk demixing instability, we demonstrate a field induced population inversion in the pore. The conditions for the realization of this method should be best met with colloids, but being based on robust and generic mechanisms, it should also be applicable to some molecular fluids.Comment: 9 pages, 5 figure

Effect of random disorder and spin frustration on the reentrant spin glass phase and ferromagnetic phase in stage-2 Cu_{0.93}Co_{0.07}Cl_{2} graphite intercalation compound near the multicritical point

Stage-2 Cu$_{0.93}$Co$_{0.07}$Cl$_{2}$ graphite intercalation compound magnetically behaves like a reentrant ferromagnet near the multicritical point ($c_{MCP} \approx 0.96$). It undergoes two magnetic phase transitions at $T_{RSG}$ ($= 6.64 \pm 0.05$ K) and $T_{c}$ ($= 8.62 \pm 0.05$ K). The static and dynamic nature of the ferromagnetic and reentrant spin glass phase has been studied using DC and AC magnetic susceptibility. Characteristic memory phenomena of the DC susceptibility are observed at $T_{RSG}$ and $T_{c}$. The nonlinear AC susceptibility $\chi_{3}^{\prime}$ has a positive local maximum at $T_{RSG}$, and a negative local minimum at $T_{c}$. The relaxation time $\tau$ between $T_{RSG}$ and $T_{c}$ shows a critical slowing down: $\tau$ with $x = 13.1 \pm 0.4$ and $\tau_{0}^{*} = (2.5 \pm 0.5) \times 10^{-13}$ sec. The influence of the random disorder on the critical behavior above $T_{c}$ is clearly observed: $\alpha = -0.66$, $\beta = 0.63$, and $\gamma = 1.40$. The exponent of $\alpha$ is far from that of 3D Heisenberg model.Comment: 15 pages, 16 figures, submitted to Phys. Rev.

Causal Propagators for Algebraic Gauges

Applying the principle of analytic extension for generalized functions we derive causal propagators for algebraic non-covariant gauges. The so generated manifestly causal gluon propagator in the light-cone gauge is used to evaluate two one-loop Feynman integrals which appear in the computation of the three-gluon vertex correction. The result is in agreement with that obtained through the usual prescriptions.Comment: LaTex, 09 pages, no figure

Coulomb corrected eikonal description of the breakup of halo nuclei

The eikonal description of breakup reactions diverges because of the Coulomb interaction between the projectile and the target. This divergence is due to the adiabatic, or sudden, approximation usually made, which is incompatible with the infinite range of the Coulomb interaction. A correction for this divergence is analysed by comparison with the Dynamical Eikonal Approximation, which is derived without the adiabatic approximation. The correction consists in replacing the first-order term of the eikonal Coulomb phase by the first-order of the perturbation theory. This allows taking into account both nuclear and Coulomb interactions on the same footing within the computationally efficient eikonal model. Excellent results are found for the dissociation of 11Be on lead at 69 MeV/nucleon. This Coulomb Corrected Eikonal approximation provides a competitive alternative to more elaborate reaction models for investigating breakup of three-body projectiles at intermediate and high energies.Comment: 19 pages, 9 figures, accepted for publication in Phys. Rev.

Quark-Exchange Mechanism of γd→np\gamma d \to np Reaction At 2-6 GeV

Within the constituent quark model, we examine the extent to which the deuteron photo-disintegration at 2-6 GeV can be described by the quark-exchange mechanism. With the parameters constrained by the $np$ scattering, the calculated differential cross sections disagree with the data in both magnitude and energy-dependence. The results can be improved if we use a smaller size parameter for quark wavefunctions. We also find that the on-shell approximation used in a previous investigation is not accurateComment: To be published in the Proceeeding of Second Asia Pacific Conference on Few-Body Problems in Physics, Shanghai, China, August 27-30, 200

Commuting quantum transfer matrix approach to intrinsic Fermion system: Correlation length of a spinless Fermion model

The quantum transfer matrix (QTM) approach to integrable lattice Fermion systems is presented. As a simple case we treat the spinless Fermion model with repulsive interaction in critical regime. We derive a set of non-linear integral equations which characterize the free energy and the correlation length of $$ for arbitrary particle density at any finite temperatures. The correlation length is determined by solving the integral equations numerically. Especially in low temperature limit this result agrees with the prediction from conformal field theory (CFT) with high accuracy.Comment: 17 page

A New Symmetric Expression of Weyl Ordering

For the creation operator \adag and the annihilation operator $a$ of a harmonic oscillator, we consider Weyl ordering expression of (\adag a)^n and obtain a new symmetric expression of Weyl ordering w.r.t. \adag a \equiv N and a\adag =N+1 where $N$ is the number operator. Moreover, we interpret intertwining formulas of various orderings in view of the difference theory. Then we find that the noncommutative parameter corresponds to the increment of the difference operator w.r.t. variable $N$. Therefore, quantum (noncommutative) calculations of harmonic oscillators are done by classical (commutative) ones of the number operator by using the difference theory. As a by-product, nontrivial relations including the Stirling number of the first kind are also obtained.Comment: 15 pages, Latex2e, the title before replacement is "Orderings of Operators in Quantum Physics", new proofs by using a difference operator added, some references added, to appear in Modern Physics Letters