Related papers: Special integrals of motion in quantum integrable …
We investigate a quantum non-relativistic system describing the interaction of two particles with spin 1/2 and spin 0, respectively. Assuming that the Hamiltonian is rotationally invariant and parity conserving we identify all such systems…
This thesis offers novel strategies for the measurement of quantum correlations present in controllable quantum systems, as well as for a full-fledged implementation of the models of light-matter interaction through which these correlations…
A notion of a particular integrability is introduced when two operators commute on a subspace of the space where they act. Particular integrals for one-dimensional (quasi)-exactly-solvable Schroedinger operators and Calogero-Sutherland…
A systematic search for superintegrable quantum Hamiltonians describing the interaction between two particles with spin 0 and 1/2, is performed. We restrict to integrals of motion that are first-order (matrix) polynomials in the components…
A homological construction of integrals of motion of the classical and quantum Toda field theories is given. Using this construction, we identify the integrals of motion with cohomology classes of certain complexes, which are modeled on the…
Strongly correlated electron systems require the development of new theoretical schemes in order to describe their unusual and unexpected properties. The usual perturbation schemes are inadequate and new concepts must be introduced. In our…
We present a theory characterizing the phases emerging as a consequence of continuous symmetry-breaking in quantum and classical systems. In symmetry-breaking phases, dynamics is restricted due to the existence of a set of conserved charges…
The quantum dynamical systems of identical particles admitting an additional integral quadratic in momenta are considered. It is found that an appropriate ordering procedure exists which allows to convert the classical integrals into their…
The applications of spin-based quantum sensors to measurements probing fundamental physics are surveyed. Experimental methods and technologies developed for quantum information science have rapidly advanced in recent years, and these tools…
A superintegrable system is, roughly speaking, a system that allows more integrals of motion than degrees of freedom. This review is devoted to finite dimensional classical and quantum superintegrable systems with scalar potentials and…
Coherent state functional integrals for the minisuperspace models of quantum cosmology are studied. By the well-established canonical theories, the transition amplitudes in the path-integral representations of Wheeler-DeWitt quantum…
We consider here the coexistence of first- and third-order integrals of motion in two dimensional classical and quantum mechanics. We find explicitly all potentials that admit such integrals, and all their integrals. Quantum superintegrable…
We give an elementary introduction to the notion of quantum entanglement between distinguishable parties and review a recent proposal about solid state quantum computation with spin-qubits in quantum dots. The indistinguishable character of…
Quantum systems inside high-Q cavities offer an excellent testbed for the control of emergent symmetries induced by light and their interplay with quantum matter. Recently several developments in cavity experiments with neutral atoms and…
The dynamical behavior of interacting systems plays a fundamental role for determining quantum correlations, such as entanglement. In this Letter, we describe temporal quantum effects of the inseparable evolution of composite quantum states…
We extend recent work by Tremblay, Turbiner, and Winternitz which analyzes an infinite family of solvable and integrable quantum systems in the plane, indexed by the positive parameter k. Key components of their analysis were to demonstrate…
Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner…
A classical (or quantum) superintegrable system on an n-dimensional Riemannian manifold is an integrable Hamiltonian system with potential that admits 2n-1 functionally independent constants of the motion that are polynomial in the momenta,…
The density matrix of a non-relativistic quantum system, divided into $N$ sub-systems, is rewritten in terms of the set of all partitioned density matrices for the system. For the case where the different sub-systems are distinguishable, we…
We determine approximate numerical integrals of motion of 2D symmetric Hamiltonian systems. We detail for a few gravitational potentials the conditions under which quasi-integrals are obtained as polynomial series. We show that each of…