Related papers: Phase transition for loop representations of Quant…
We show that the number of copies of a given rooted tree in a conditioned Galton-Watson tree satisfies a law of large numbers under a minimal moment condition on the offspring distribution.
We present a systematic analysis of quantum Heisenberg-, XY- and interchange models on the complete graph. These models exhibit phase transitions accompanied by spontaneous symmetry breaking, which we study by calculating the generating…
We consider a branching random walk on a multi($Q$)-type, supercritical Galton-Watson tree which satisfies Kesten-Stigum condition. We assume that the displacements associated with the particles of type $Q$ have regularly varying tails of…
We are interested in the structure of multitype Bienaym\'e-Galton-Watson (BGW) trees conditioned on integer linear combinations of the numbers of vertices of given types. We show that, under regularity assumptions on the offspring…
We prove a law of large numbers for the range of rotor walks with random initial configuration on regular trees and on Galton-Watson trees. More precisely, we show that on the classes of trees under consideration, even in the case when the…
We provide a complete picture of the local convergence of critical or subcritical Galton-Watson tree conditioned on having a large number of individuals with out-degree in a given set. The generic case, where the limit is a random tree with…
Using the group structure of the state space of $q-$state models, a new definition of contour for long-range spin-systems in $\Z^d$ ($d\geq 2$), and a multidimensional version of Fr\"{o}hlich-Spencer contours, we prove phase transition for…
We study the totally asymmetric simple exclusion process (TASEP) on trees where particles are generated at the root. Particles can only jump away from the root, and they jump from $x$ to $y$ at rate $r_{x,y}$ provided $y$ is empty. Starting…
We calculate the single-particle momentum distribution of a quantum many-particle system in the presence of the Coulomb interaction and a confining potential. The region of intermediate momenta, where the confining potential dominates,…
We consider a special class of Galton-Watson theta-processes in a varying environment fully defined by four parameters, with two of them $(\theta,r)$ being fixed over time $n$, and the other two $(a_n,c_n)$ characterizing the altering…
Matrix product states, a key ingredient of numerical algorithms widely employed in the simulation of quantum spin chains, provide an intriguing tool for quantum phase transition engineering. At critical values of the control parameters on…
In a scalar field theory, when the tree level potential admits broken symmetry ground states, the quantum corrections to the static effective potential are complex. (The imaginary part is a consequence of an instability towards phase…
We study the decay of survival probability at quantum phase transitions (QPT). The semiclassical theory is found applicable in the vicinities of critical points with infinite degeneracy. The theory predicts a power law decay of the survival…
A quantum finite multi-barrier system, with a periodic potential, is considered and exact expressions for its plane wave amplitudes are obtained using the Transfer Matrix method [10]. This quantum model is then associated with a stochastic…
We establish an intriguing connection between quantum phase transitions and bifurcations in the reduced fidelity between two different reduced density matrices for quantum lattice many-body systems with symmetry-breaking orders. Our finding…
Consider a branching random walk, where the branching mechanism is governed by a Galton-Watson process, and the migration by a finite range symmetric irreducible random walk on the integer lattice $\mathbb{Z}^d$. Let $Z_n(z)$ be the number…
Continuous-time quantum walk is one of the alternative approaches to quantum computation, where a universal set of quantum gates can be achieved by scattering a quantum walker on some specially-designed structures embedded in a sparse graph…
We study the typical behavior of the harmonic measure of balls in large critical Galton-Watson trees whose offspring distribution has finite variance. The harmonic measure considered here refers to the hitting distribution of height $n$ by…
Under minimal condition, we prove the local convergence of a critical multi-type Galton-Watson tree conditioned on having a large total progeny by types towards a multi-type Kesten's tree. We obtain the result by generalizing Neveu's strong…
We are interested in the genealogical structure of alleles for a Bienaym\'e-Galton-Watson branching process with neutral mutations (infinite alleles model), in the situation where the initial population is large and the mutation rate small.…