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We present a new variational method for investigating the ground state and out of equilibrium dynamics of quantum many-body bosonic and fermionic systems. Our approach is based on constructing variational wavefunctions which extend Gaussian…
We study time evolution of a subsystem's density matrix under unitary evolution, generated by a sufficiently complex, say quantum chaotic, Hamiltonian, modeled by a random matrix. We exactly calculate all coherences, purity and…
The dynamical evolution of an open quantum system can be governed by the Lindblad equation of the density matrix. In this paper, we propose to characterize the density matrix topology by the topological invariant of its modular Hamiltonian.…
The Gaussian state description of continuous variables is adapted to describe the quantum interaction between macroscopic atomic samples and continuous-wave light beams. The formalism is very efficient: a non-linear differential equation…
Gaussian states are the backbone of quantum information protocols with continuous variable systems, whose power relies fundamentally on the entanglement between the different modes. In the case of global pure states, knowledge of the…
We develop a master equation formalism to describe the evolution of the average density matrix of a closed quantum system driven by a stochastic Hamiltonian. The average over random processes generally results in decoherence effects in…
The time evolution of a Gaussian density matrix of a one dimensional particle, generated by a quadratic, ${\cal O}(\partial_t^2)$ effective Lagrangian, describing a harmonic potential, a friction force and decoherence, is studied within the…
Quantum dynamical semigroups are applied to the study of the time evolution of harmonic oscillators, both bosonic and fermionic. Explicit expressions for the density matrices describing the states of these systems are derived using the…
We consider a classically chaotic system that is described by a Hamiltonian H(Q,P;x), where (Q,P) describes a particle moving inside a cavity, and x controls a deformation of the boundary. The quantum-eigenstates of the system are |n(x)>.…
Weyl's formulation of quantum mechanics opened the possibility of studying the dynamics of quantum systems both in infinite-dimensional and finite-dimensional systems. Based on Weyl's approach, generalized by Schwinger, a self-consistent…
State space models are well-known for their versatility in modeling dynamic systems that arise in various scientific disciplines. Although parametric state space models are well studied, nonparametric approaches are much less explored in…
We consider physical Hamiltonians that can be represented by the multiparametric Gaussian ensembles, theoretically derive the state ensembles for its eigenstates and analyze the effect of varying system conditions on its bipartite…
By using a simple observation that the density processes appearing in Ito's martingale representation theorem are invariant under the change of measures, we establish a non-linear version of the Cameron-Martin formula for solutions of a…
A simple and efficient method for characterization of multidimensional Gaussian states is suggested and experimentally demonstrated. Our scheme shows analogies with tomography of finite dimensional quantum states, with the covariance matrix…
In a recent work we presented a recursive algorithm to compute the matrix elements of a generic Gaussian transformation in the photon-number basis. Its purpose was to evolve a quantum state by building the transformation matrix and…
In the spirit of the generalized one-particle density matrix for fermions, we introduce generalized one- and two-particle density matrices to state representability conditions up to second order for boson systems without assuming particle…
We study the quantum dynamics generated by a non-Hermitian Hamiltonian subject to stochastic perturbations in its anti-Hermitian part, describing fluctuating gains and losses. The dynamics averaged over the noise is described by an…
The description of states and dynamics in non-Hermitian systems is fundamentally linked to the choice of an appropriate theoretical framework -- a point of ongoing debate in the field. This work addresses this issue by proposing a…
We investigate permutation-invariant continuous variable quantum states and their covariance matrices. We provide a complete characterization of the latter with respect to permutation-invariance, exchangeability and representing convex…
The usual position-momentum commutation relation plays a fundamental role in the mathematical description of continuous-variable quantum systems. In the case of a qudit described by a Hilbert space of a high enough dimension, there exists a…