Related papers: A (2+1)-dimensional Gaussian field as fluctuations…
The system of interacting spinless fermions hopping on a two-leg ladder exhibits a series of quantum phase transitions when subjected to an external magnetic field. At half filling, these are either U(1) Gaussian phase transitions between…
The quantum random walk has been much studied recently, largely due to its highly nonclassical behavior. In this paper, we study one possible route to classical behavior for the discrete quantum walk on the line: the presence of decoherence…
We study the dynamics of 2+1 dimensional theories with ${\cal N}=1$ supersymmetry. In these theories the supersymmetric ground states behave discontinuously at co-dimension one walls in the space of couplings, with new vacua coming in from…
The extremely fascinating behaviors of the quantum walks of particles, which differ much from the classical counterparts, have attracted many physicists. Here we investigate another interesting part of the quantum walks, that is the quantum…
We study the fuzzy spaces (as special examples of noncommutative manifolds) with their quasicoherent states in order to find their pertinent metrics. We show that they are naturally endowed with two natural "quantum metrics" which are…
We introduce and analyze a one-dimensional quantum walk with two time-independent rotations on the coin. We study the influence on the property of quantum walk due to the second rotation on the coin. Based on the asymptotic solution in the…
We consider the time-independent scattering theory for time evolution operators of one-dimensional two-state quantum walks. The scattering matrix associated with the position-dependent quantum walk naturally appears in the asymptotic…
In this article, we prove a lower bound for the fluctuations of symmetric random walks on dynamic random environments in dimension $1 + 1$ in the perturbative regime where the walker is weakly influenced by the environment. We suppose that…
This paper is concerned with the quantum theory of noncommutative scalar fields in two dimensional space time. It is shown that the noncommutativity originates from the the deformation of symplectic structures. The quantization is performed…
The staggered quantum walk is a type of discrete-time quantum walk model without a coin which can be generated on a graph using particular partitions of the graph nodes. We design Hamiltonians for potential realization of the staggered…
In this paper we analyze the behavior of quantum random walks. In particular we present several new results for the absorption probabilities in systems with both one and two absorbing walls for the one-dimensional case. We compute these…
Discrete quantum walks are dynamical protocols for controlling a single quantum particle. Despite of its simplicity, quantum walks display rich topological phenomena and provide one of the simplest systems to study and understand…
Studying the geometry generated by Gaussian and Gaussian- related random fields via their excursion sets is now a well developed and well understood subject. The purely non-Gaussian scenario has, however, not been studied at all. In this…
We consider quantum random walks in an infinite-dimensional phase space constructed using Weyl representation of the coordinate and momentum operators in the space of functions on a Hilbert space which are square integrable with respect to…
Following our earlier analyses of nonstandard continuum quantum field theories, we study here gapped systems in 3+1 dimensions, which exhibit fractonic behavior. In particular, we present three dual field theory descriptions of the…
In recent work we developed a description of cosmic large scale structure formation in terms of non-equilibrium ensembles of classical particles, with time evolution obtained in the framework of a statistical field theory. In these works,…
Fluctuations from a hydrodynamic limit of a one-dimensional asymmetric system come at two levels. On the central limit scale n^{1/2} one sees initial fluctuations transported along characteristics and no dynamical noise. The second order of…
We apply kinetic field theory to non-linear cosmic structure formation. Kinetic field theory decomposes the cosmic density field into particles and follows their trajectories through phase space. We assume that initial particle momenta are…
The (2+1)-dimensional Thirring model is studied by using the Gaussian approximation method in the functional Schr\"odinger picture. Although the dynamical symmetry breaking does not occur in the large N limit, it does occur in the Gaussian…
Continuum spacetime is expected to emerge via phase transition in discrete approaches to quantum gravity. A promising example is tensorial group field theory but its phase diagram remains an open issue. The results of recent attempts in…