An exactly solvable quench protocol for integrable spin models

Quantum quenches in continuum field theory across critical points are known to display different scaling behaviours in different regimes of the quench rate. We extend these results to integrable lattice models such as the transverse field Ising model on a one-dimensional chain and the Kitaev model on a two-dimensional honeycomb lattice using a nonlinear quench protocol which allows for exact analytical solutions of the dynamics. Our quench protocol starts with a finite mass gap at early times and crosses a critical point or a critical region, and we study the behaviour of one point functions of the quenched operator at the critical point or in the critical region as a function of the quench rate. For quench rates slow compared to the initial mass gap, we find the expected Kibble-Zurek scaling. In contrast, for rates fast compared to the mass gap, but slow compared to the inverse lattice spacing, we find scaling behaviour similar to smooth fast continuum quenches. For quench rates of the same order of the lattice scale, the one point function saturates as a function of the rate, approaching the results of an abrupt quench. The presence of an extended critical surface in the Kitaev model leads to a variety of scaling exponents depending on the starting point and on the time where the operator is measured. We discuss the role of the amplitude of the quench in determining the extent of the slow (Kibble-Zurek) and fast quench regimes, and the onset of the saturation.Comment: 54 pages, 13 figures; v2: added analytic argument for Kitaev mode

Reciprocity in the Hecke Groups

An element $g$ in a group $G$ is called \emph{reciprocal} if there exists $h \in G$ such that $g^{-1}=hgh^{-1}$. The reciprocal elements are also known as `real elements' or `reversible elements' in the literature. We classify the reciprocal elements and parametrize the reciprocal classes in the Hecke groups $\Gamma_p$ for $p\geq 3$. This generalizes a result by Sarnak for reciprocal elements in the modular group

Some Applications of Group Theoretic Rips Constructions to the Classification of von Neumann Algebras

In this paper we study various von Neumann algebraic rigidity aspects for the property (T) groups that arise via the Rips construction developed by Belegradek and Osin in geometric group theory \cite{BO06}. Specifically, developing a new interplay between Popa's deformation/rigidity theory \cite{Po07} and geometric group theory methods we show that several algebraic features of these groups are completely recognizable from the von Neumann algebraic structure. In particular, we obtain new infinite families of pairwise non-isomorphic property (T) group factors thereby providing positive evidence towards Connes' Rigidity Conjecture. In addition, we use the Rips construction to build examples of property (T) II$_1$ factors which posses maximal von Neumann subalgebras without property (T) which answers a question raised in an earlier version of \cite{JS19} by Y. Jiang and A. Skalski.Comment: 35 pages, preliminary version, comments welcom

Exactly Solvable Floquet Dynamics for Conformal Field Theories in Dimensions Greater than Two

We find classes of driven conformal field theories (CFT) in d+1 dimensions with d > 1, whose quench and floquet dynamics can be computed exactly. The setup is suitable for studying periodic drives, consisting of square pulse protocols for which Hamiltonian evolution takes place with different deformations of the original CFT Hamiltonian in successive time intervals. These deformations are realized by specific combinations of conformal generators with a deformation parameter $\beta$; the $\beta 1$) Hamiltonians can be unitarily related to the standard (L\"uscher-Mack) CFT Hamiltonians. The resulting time evolution can be then calculated by performing appropriate conformal transformations. For d <= 3 we show that the transformations can be easily obtained in a quaternion formalism; we use this formalism to obtain exact expressions for the fidelity, unequal-time correlator, and the energy density for the driven system for d = 3. Our results for a single square pulse drive cycle reveal qualitatively different behaviors depending on the value of $\beta$, with exponential decays characteristic of heating for $\beta > 1$, oscillations for $\beta < 1$ and power law decays for $\beta = 1$. When the Hamiltonians in one cycle involve generators of a single SL(2, R) subalgebra we find fixed points or fixed surfaces of the corresponding transformations. Successive cycles lead to either convergence to one of the fixed points, or oscillations, depending on the conjugacy class. This indicates that the system can be in different dynamical phases as we vary the parameters of the drive protocol. We also point out that our results are expected to hold for a broader class of QFTs that possesses an SL(2,C) symmetry with fields that transform as quasi-primaries under this. As an example, we briefly comment on celestial CFTs in this context.Comment: 32 pages, 10 figure

Gathering over Meeting Nodes in Infinite Grid

The gathering over meeting nodes problem asks the robots to gather at one of the pre-defined meeting nodes. The robots are deployed on the nodes of an anonymous two-dimensional infinite grid which has a subset of nodes marked as meeting nodes. Robots are identical, autonomous, anonymous and oblivious. They operate under an asynchronous scheduler. They do not have any agreement on a global coordinate system. All the initial configurations for which the problem is deterministically unsolvable have been characterized. A deterministic distributed algorithm has been proposed to solve the problem for the remaining configurations. The efficiency of the proposed algorithm is studied in terms of the number of moves required for gathering. A lower bound concerning the total number of moves required to solve the gathering problem has been derived

RESVERATROL PROTECTS WHOLE BODY HEAT STRESS-INDUCED TESTICULAR DAMAGE IN RAT MODEL

Objective: The local thermoregulation in testis is important for optimum spermatozoa development. Excessive heat hampers this regulation resulting in alteration of normal testicular function. The present investigation confirms the role of free radicals in hyperthermia induced oxidative damage in testis and elucidates the dose-dependent ameliorating effect of resveratrol (RSV) against testicular oxidative damage. The aim of the present investigation is also to observe the role of selective concentration of RSV on heat induced oxidative changes in the damaged tissue. Methods: 48 male Wister rats were exposed to hyperthermic condition for the past 7 days of the total 21 days of experiment. RSV was pre- and co-treated with heat stress daily in a dose-dependent manner (1 mg, 5 mg, and 10 mg/kg body weight) for 21days. Results: Reactive oxygen species level was estimated using flow cytometry. Enhancement of hepatotoxicity markers in serum, lipid peroxidation and decreasing antioxidant status in the testis homogenate demonstrated that the oxidative damage in heat exposed tissue. Conclusion: Histological study along with biochemical and molecular assessment of the redox balance of testicular tissue in the present study revealed that RSV significantly ameliorated the heat induced damage in testis. The findings suggest that RSV is an effective antioxidant polyphenolic compound that can protect testis against hyperthermia induced oxidative damage