Related papers: Possible large-N transitions for complex Wilson lo…
To model a complex system intrinsically separated by a barrier, we use two random Hamiltonians, coupled to each other either by a tunneling matrix element or by an intermediate transition state. We study that model in the universal limit of…
Buildup and switching mechanisms of solitons in complex nonlinear systems are fundamentally important dynamical regimes. Using a novel strongly nonlinear optical system,the work reveals a new buildup scenario for soliton molecules , which…
We uncover a novel dynamical quantum phase transition, using random matrix theory and its associated notion of planar limit. We study it for the isotropic XY Heisenberg spin chain. For this, we probe its real-time dynamics through the…
The dynamics of several light filaments (spatial optical solitons) propagating in an optically nonlinear and non-local random medium is investigated using the paradigms of the physics of complexity. Cluster formation is interpreted as a…
We introduce a new topological effect involving interference of two meson loops, manifesting a path-independent topological area dependence. The effect also draws a connection between quark confinement, Wilson-loops and topological…
We describe phase transitions in the heavy quark potential in planar gauge theories having wrapped D5-brane string duals. A new phase transition, previously unnoticed in these models, is driven by the source of a large dimension operator.…
In this thesis we consider four dimensional N=2 superconformal field theories, in presence of line defects such as Wilson loops. In this set up, using supersymmetric localization, we compute many observables, such as the vacuum expectation…
The phase structure of the generalized Yang--Mills theories is studied, and it is shown that {\it almost} always, it is of the third order. As a specific example, it is shown that all of the models with the interaction $\sum_j…
Eigenvalues of a Wilson loop operator are gauge invariant and their distribution undergoes a transition at infinite N as the size of the loop is changed. We study this transition using the average characteristic polynomial associated with…
We formulate and study a class of U(N)-invariant quantum mechanical models of large normal matrices with arbitrary rotation-invariant matrix potentials. We concentrate on the U(N) singlet sector of these models. In the particular case of…
An equation for the quantum average of the gauge invariant Wilson loop in non-commutative Yang-Mills theory with gauge group U(N) is obtained. In the 't Hooft limit, the equation reduces to the loop equation of ordinary Yang-Mills theory.…
Quantum phase transitions between the magnetically ordered and disordered states are studied for the two-dimensional antiferromagnetic quantum spin systems with ladder, plaquette, and mixed-spin structures. Starting with properly chosen…
Hybrid dynamical systems characterized by discrete switching of smooth dynamics have been used to model various rhythmic phenomena. However, the phase reduction theory, a fundamental framework for analyzing the synchronization of…
We present an analytic proof of the existence of phase transition in the large $N$ limit of certain random noncommutaitve geometries. These geometries can be expressed as ensembles of Dirac operators. When they reduce to single matrix…
Nonlinear diffusion is studied in the presence of multiplicative noise. The nonlinearity can be viewed as a ``wall'' limiting the motion of the diffusing field. A dynamic phase transition occurs when the system ``unbinds'' from the wall.…
Various light-matter interactions lead to diverse phase diagram structures in superradiant phase transition (SPT) studies. Such systems consist of multiqubit and multimode with anisotropic couplings, one- and two-photon interactions, Stark…
Some recent work on the thermodynamic behavior of the matrix model of M-theory on a pp-wave background is reviewed. We examine a weak coupling limit where computations can be done explicitly. In the large N limit, we find a phase transition…
We characterize the limiting fluctuations of traces of several independent Wigner matrices and deterministic matrices under mild conditions. A CLT holds but in general the families are not asymptotically free of second order and the…
Linear systems under the influence of nonlinear and random linear perturbations, and with random initial and boundary conditions, are discussed. The notion of states of a system is substituted by the notion of the generating vectors for…
We study an exactly solvable model of monitored dynamics in a system of $N$ spin-$1/2$ particles with pairwise all-to-all noisy interactions, where each spin is constantly perturbed by weak measurements of the spin component in a random…