Related papers: Fermionic eigenvector moment flow
We prove that the distribution of eigenvectors of generalized Wigner matrices is universal both in the bulk and at the edge. This includes a probabilistic version of local quantum unique ergodicity and asymptotic normality of the…
We prove eigenvalue processes from dynamical random matrix theory including Dyson Brownian motion, Wishart process, and Dynkin's Brownian motion of ellipsoids are results of projecting Brownian motion through Riemannian submersions induced…
We establish a correspondence between the evolution of the distribution of eigenvalues of a $N\times N$ matrix subject to a random Gaussian perturbing matrix, and a Fokker-Planck equation postulated by Dyson. Within this model, we prove the…
We study a mixture of one-dimensional bosons and spinless fermions at incommensurate filling using phenomenological bosonization and Green's functions techniques. We derive the relation between the parameters of the microscopic Hamiltonian…
We investigate collective behavior of a system of two-dimensional interacting Brownian particles in the hydrodynamic regime. By means of the Martin-Siggia-Rose-Jenssen-de Dominicis formalism, we built up a generating functional for…
We define a new diffusive matrix model converging towards the $\beta$-Dyson Brownian motion for all $\beta\in [0,2]$ that provides an explicit construction of $\beta$-ensembles of random matrices that is invariant under the…
It is well known that bosons and fermions exhibit opposite behaviors when experiencing interference, in the sense that bosons have a tendency to bunch whereas fermions have a tendency to antibunch. Recently, this complementarity was…
The dynamics of fermionic unparticles is developed from first principles. It is shown that any unparticle, whether fermionic or bosonic, can be recast in terms of a canonically quantized field, but with non-local interaction terms. We…
In this article, we calculate the friction between two counter-flowing bosonic and fermionic super-fluids. In the limit where the boson-boson and boson-fermion interactions can be treated within the mean-field approximation, we show that…
Motions of fluctuating Brownian particles in an incompressible viscous fluid have been studied by coupled simulations of Brownian particles and host fluid. We calculated the velocity autocorrelation functions of Brownian particles and…
We use the Whittaker vectors and the Drinfeld Casimir element to show that eigenfunctions of the difference Toda Hamiltonian can be expressed via fermionic formulas. Motivated by the combinatorics of the fermionic formulas we use the…
We present an interpolation between the bosonic and fermionic relations. This interpolation is given by an object which we call `generalized Brownian motion' and which is characterized by a generalization of the pairing rule for the…
Euler hydrodynamics of perfect fluids can be viewed as an effective bosonic field theory. In cases when the underlying microscopic system involves Dirac fermions, the quantum anomalies should be properly described. In 1+1 dimensions the…
In order to find reliable and efficient numerical approximation schemes, we suggest to identify the Functional Renormalization Group flow equations of one-particle irreducible two-point functions as Hamilton-Jacobi(-Bellman)-type partial…
We study joint eigenvector distributions for large symmetric matrices in the presence of weak noise. Our main result asserts that every submatrix in the orthogonal matrix of eigenvectors converges to a multidimensional Gaussian…
Bosonic and fermionic statistics are well known to give rise to antinomic behaviors, most notably boson bunching vs fermion antibunching. Here, we establish a fundamental relation that combines bosonic and fermionic multiparticle…
The Dirac Hamiltonian $H^{\left(D\right)}$ for relativistic charged fermions minimally coupled to (possibly time-dependent) electromagnetic fields is transformed with a purpose-built flow equation method, so that the result of that…
We have introduced a new transfer operator for chaotic flows whose leading eigenvalue yields the dynamo rate of the fast kinematic dynamo and applied cycle expansion of the Fredholm determinant of the new operator to evaluation of its…
After providing a general formulation of Fermion flows within the context of Hudson-Parthasarathy quantum stochastic calculus, we consider the problem of determining the noise coefficients of the Hamiltonian associated with a Fermion flow…
We introduce a `proper time' formalism to study the instability of the vacuum in a uniform external electric field due to particle production. This formalism allows us to reduce a quantum field theoretical problem to a quantum-mechanical…