Related papers: Quadratic bosonic and free white noises
In order to test theoretical predictions, we have studied the phenomenon of stochastic resonance in an electronic experimental system driven by white non Gaussian noise. In agreement with the theoretical predictions our main findings are:…
We study the renormalization of a bosonic quadratic Hamiltonian with an ultraviolet divergence. The Hamiltonian is composed of the sum of a free part and the square of the smeared field operator. We explicitly diagonalize the Hamiltonian…
A brief presentation of the basic concepts in quantum probability theory is given in comparison to the classical one. The notion of quantum white noise, its explicit representation in Fock space, and necessary results of noncommutative…
We study nonchiral wave functions for systems with continuous spins obtained from the conformal field theory (CFT) of a free, massless boson. In contrast to the case of discrete spins, these can be treated as bosonic Gaussian states, which…
Trajectories in the space of the unitarily inequivalent representations of the canonical commutation relations are shown to be classical trajectories. Under convenient conditions, they may exhibit properties typical of chaotic behavior in…
Well-defined nonlinear deformations of free quantum fields are introduced as manifestly Poincar\'e invariant scaling and resonance properties of non-dynamical scale models in Minkowski space, instead of introducing nonlinear dynamical…
We develop a general framework for the open dynamics of an ensemble of quantum particles subject to spacetime fluctuations about the flat background. An arbitrary number of interacting bosonic and fermionic particles are considered. A…
We introduce the Random Quadratic Form (RQF): a stochastic differential equation which formally corresponds to the gradient flow of a random quadratic functional on a sphere. While the one-point dynamics of the system is a Brownian motion…
We use computational linear algebra and commutative algebra to study spaces of relations satisfied by quadrilinear operations. The relations are analogues of associativity in the sense that they are quadratic (every term involves two…
We apply the Dirac factorization method to the nonrelativistic harmonic oscillator and, more in general, to Hamiltonians with a generic potential. It is shown that this procedure naturally leads to a supersymmetric formulation of the…
We study the parabolic defocusing stochastic quantization equation with both mutliplicative spatial white noise and an independant space-time white noise forcing, on compact surfaces, with polynomial nonlinearity. After renormalizing the…
The wave equation (free boson) problem is studied from the viewpoint of the relations on the symplectic manifolds associated to the boundary induced by solutions. Unexpectedly there is still something to say on this simple, well-studied…
The concept of electron holes plays a significant role in condensed matter physics. Here we develop the concept of bosonic holes, which exhibit negative particle excitations, in quadratic bosonic systems. Unlike electron holes, the Fock…
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…
We consider the relativistic electron-positron field interacting with itself via the Coulomb potential defined with the physically motivated, positive, density-density quartic interaction. The more usual normal-ordered Hamiltonian differs…
The concept of stochastic resonance in nonlinear dynamics is applied to interpret the capacity of noisy quantum channels. The two-Pauli channel is used to illustrate the idea. The fidelity of the channel is also considered. Noise…
In this work, we investigate the semiclassical limit of a simple bosonic quantum many-body system exhibiting both integrable and chaotic behavior. A classical Hamiltonian is derived using coherent states. The transition from regularity to…
We develop a bosonization formalism that captures non-perturbatively the interaction effects on the $\mathbf{Q}=0$ continuum of excitations of nodal fermions above one dimension. Our approach is a natural extension of the classic…
In this paper, we attempt to shed light on a new class of nonstationary random fields which exhibit, what we call, local invariant nonstationarity. We argue that the local invariant property has a special interaction with a new generalized…
We consider a model of bosonic memory channel, which induces correlations among the transmitted signals. The application of suitable unitary transformations at encoding and decoding stages allows the complete removal of correlations,…