Related papers: Self-Consistent Projection Operator Theory for Qua…
Estimating the steady-state properties of open many-body quantum systems is a fundamental challenge in quantum science and technologies. In this work, we present a scalable approach based on semi-definite programming to derive certified…
Driven-dissipative quantum many-body systems have attracted increasing interest in recent years as they lead to novel classes of quantum many-body phenomena. In particular, mean-field calculations predict limit cycle phases, slow…
A new quantum mechanical notion -- Conditional Density Matrix -- is discussed and is applied to describe some physical processes. This notion is a natural generalization of von Neumann density matrix for such processes as divisions of…
This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and…
We show that the set of projections in an operator system can be detected using only the abstract data of the operator system. Specifically, we show that if $p$ is a positive contraction in an operator system $V$ which satisfies certain…
Experimental studies of synthetic quantum matter are necessarily restricted to approximate ground states prepared on finite-size quantum simulators. In general, this limits their reliability for strongly correlated systems, for instance, in…
Recent experiments have demonstrated single-site resolved observation of cold atoms in optical lattices. Thus, in the future it may be possible to take repeated snapshots of an interacting quantum many-body system during the course of its…
A general class of discrete unitary models are described whose behavior in the continuum limit corresponds to a many-body Schrodinger equation. On a quantum computer, these models could be used to simulate quantum many-body systems with an…
In this thesis the variational optimisation of the density matrix is discussed as a method in many-body quantum mechanics. This is a relatively unknown technique in which one tries to obtain the two-particle reduced density matrix directly…
The methods of quantum chemistry and solid state theory to solve the many-body problem are reviewed. We start with the definitions of reduced density matrices, their properties (contraction sum rules, spectral resolutions, cumulant…
Dynamical maps are the principal subject of the open system theory. Formally, the dynamical map of a given open quantum system is a density matrix transformation that takes any initial state and sends it to the state at a later time.…
We consider the time evolution of quantum states by many-body Schr\"odinger dynamics and study the rate of convergence of their reduced density matrices in the mean field limit. If the prepared state at initial time is of coherent or…
We introduce a general formalism, based on the stochastic formulation of quantum mechanics, to obtain localized quasi-classical wave packets as dynamically controlled systems, for arbitrary anharmonic potentials. The control is in general…
Computing the exact dynamics of many-body quantum systems becomes intractable as system size grows. Here, we present a symmetry-based method that provides an exponential reduction in the complexity of a broad class of such problems…
In this paper we present a new quantum-trajectory based treatment of quantum dynamics suitable for dissipative systems. Starting from a de Broglie/Bohm-like representation of the quantum density matrix, we derive and define quantum…
We present a systematic approach for constructing steady state density operators of Markovian dissipative evolution for open quantum chain models with integrable bulk interaction and boundary incoherent driving. The construction is based on…
Recent experimental developments in diverse areas - ranging from cold atomic gases over light-driven semiconductors to microcavity arrays - move systems into the focus, which are located on the interface of quantum optics, many-body physics…
The mean-field approximation based on effective interactions or density functionals plays a pivotal role in the description of finite quantum many-body systems that are too large to be treated by ab initio methods. Some examples are…
We propose an energy-driven stochastic master equation for the density matrix as a dynamical model for quantum state reduction. In contrast, most previous studies of state reduction have considered stochastic extensions of the Schr\"odinger…
Using the supersymmetry approach, we study spectral statistical properties of a two-dimensional quantum particle subject to a non-uniform magnetic field. We focus mainly on the problem of regularisation of the field theory. Our analysis…