Related papers: Complex-Dynamical Solution to the Many-Body Intera…
The quenched unitary Bose gas is a paradigmatic example of a strongly interacting out-of-equilibrium quantum system, whose dynamics become difficult to describe theoretically due to the growth of non-Gaussian quantum correlations. We…
Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi--particle dynamical system by finding polynomial solutions of a partial differential equations is…
We present a comprehensive quantum many body theory for kq deformed particles, offering a novel framework that relates particle statistics directly to effective interaction strength. Deformed by the parameters k and q, these particles…
We review recent results which clarify the role of the integrable many-body problems in the quantum field theory framework.They describe the dynamics of the topological degrees of freedom in the theories which are obtained by perturbing the…
At long times residual couplings to the environment become relevant even in the most isolated experiments, creating a crucial difficulty for the study of fundamental aspects of many-body dynamics. A particular example is many-body…
The theory of real-time quantum many-body dynamics as put forward in Ref. [arXiv:0710.4627] is evaluated in detail. The formulation is based on a generating functional of correlation functions where the Keldysh contour is closed at a given…
The relativistic 2-body problem, much like the non-relativistic one, is reduced to describing the motion of an effective particle in an external field. The concept of a relativistic reduced mass and effective particle energy introduced some…
Obtaining dynamics of an interacting quantum many-body system connected to multiple baths initially at different, finite, temperatures and chemical potentials is a challenging problem. This is due to a combination of the prevalence of…
One of the oldest problems in physics is that of calculating the motion of $N$ particles under a specified mutual force: the $N$-body problem. Much is known about this problem if the specified force is non-relativistic gravity, and…
Quantum information theory has considerably helped in the understanding of quantum many-body systems. The role of quantum correlations and in particular, bipartite entanglement, has become crucial to characterise, classify and simulate…
The two-body problem with a central interaction on simply connected constant curvature spaces of an arbitrary dimension is considered. The explicit expression for the quantum two-body Hamiltonian via a radial differential operator and…
It is argued that the world is a dissipative dynamic system, a phase flow of which is formed by conformally-symplectic mapping. The key assumption is that the concept of energy in microcosm makes sense only for the steady motions…
Non-equilibrium quantum dynamics represents an emerging paradigm for condensed matter physics, quantum information science, and statistical mechanics. Strongly interacting Rydberg atoms offer an attractive platform to study…
We study the quantum mechanical many-body problem of $N$ nonrelativistic electrons interacting with their self-generated classical electromagnetic field and $K$ static nuclei. The system of coupled equations governing the dynamics of the…
Computationally intractable tasks are often encountered in physics and optimization. Such tasks often comprise a cost function to be optimized over a so-called feasible set, which is specified by a set of constraints. This may yield, in…
We study the static and dynamical properties of isolated many-body quantum systems and compare them with the results for full random matrices. In doing so, we link concepts from quantum information theory with those from quantum chaos. In…
We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…
During recent years the interest to dynamics of quantum systems has grown considerably. Quantum many body systems out of equilibrium often manifest behavior, different from the one predicted by standard statistical mechanics and…
The emergence of macroscopic coherence in a many-body quantum system is a ubiquitous phenomenon across different physical systems and scales. This Chapter reviews key concepts characterizing such systems (correlation functions,…
The quantum mechanical many-body problem is rarely analytically solvable. One notable exception is the case of two electrons interacting via a Coulomb potential in a uniform magnetic field. The motion is confined to a two-dimensional plane,…