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Entanglement is the crucial ingredient of quantum many-body physics, and characterizing and quantifying entanglement in closed system dynamics of quantum simulators is an outstanding challenge in today's era of intermediate scale quantum…
It is shown that the Hamilton equations in supersymmetric quantum mechanics can be presented in nonassociative form, where the Hamiltonian is decomposed into two nonassociative factors.
The multiphoton algebras for one-dimensional Hamiltonians with infinite discrete spectrum, and for their associated kth-order SUSY partners are studied. In both cases, such an algebra is generated by the multiphoton annihilation and…
Unitary principal series representations of the conformal group appear in the dS/CFT correspondence. These are infinite dimensional irreducible representations, without highest weights. In earlier work of Guijosa and the author it was shown…
A novel analytically solvable deformed Woods-Saxon potential is investigated by means of the Supersymmetric Quantum Mechanics. Hamiltonian hierarchy method and the shape invariance property are used in the calculations. The energy levels…
Entanglement is central to our understanding of many-body quantum matter. In particular, the entanglement spectrum, as eigenvalues of the reduced density matrix of a subsystem, provides a unique footprint of properties of strongly…
Cylindrically symmetric quantum mechanical systems with position dependent masses (PDM) admitting at least one second order integral of motion are classified. It is proved that there exist 68 such systems which are inequivalent. Among them…
We demonstrate that for general conformal field theories (CFTs), the entanglement for small perturbations of the vacuum is organized in a novel holographic way. For spherical entangling regions in a constant time slice, perturbations in the…
We analyze the problem of spin decomposition for an interacting system from a natural perspective of constructing angular momentum eigenstates. We split, from the total angular momentum operator, a proper part which can be separately…
We study the general form of M"obius covariant local commutation relations in conformal chiral quantum field theories and show that they are intrinsically determined up to structure constants, which are subject to an infinite system of…
We split the generic conformal mechanical system into a "radial" and an "angular" part, where the latter is defined as the Hamiltonian system on the orbit of the conformal group, with the Casimir function in the role of the Hamiltonian. We…
For a two-spin model which is (classically) integrable on a five-dimensional hypersurface in six-dimensional parameter space and for which level degeneracies occur exclusively (with one known exception) on four-dimensional manifolds…
We consider classical and quantum mechanics related to an additional noncommutativity, symmetric in position and momentum coordinates. We show that such mechanical system can be transformed to the corresponding one which allows employment…
Algebraic approach to the integrability condition called shape invariance is briefly reviewed. Various applications of shape-invariance available in the literature are listed. A class of shape-invariant bound-state problems which represent…
Hidden symmetries in a covariant Hamiltonian formulation are investigated involving gauge covariant equations of motion. The special role of the Stackel-Killing tensors is pointed out. A reduction procedure is used to reduce the original…
The thermodynamics and the entanglement properties of two-dimensional conformal field theories ($2$d CFTs) on curved backgrounds are studied. By means of conformal mapping we study the equivalent system on flat space governed by the…
We present a unified approach to representations of quantum mechanics on noncommutative spaces with general constant commutators of phase-space variables. We find two phases and duality relations among them in arbitrary dimensions.…
A certain notion of canonical equivalence in quantum mechanics is proposed. It is used to relate quantal systems with discrete ones. Discrete systems canonically equivalent to the celebrated harmonic oscillator as well as the quartic and…
The confluent second-order supersymmetric quantum mechanics, in which the factorization energies tend to a common value, is used to generate Hamiltonians with known spectra departing from the hyperbolic Rosen-Morse and Eckart potentials.…
The SL(2,R) invariant Hamiltonian systems are discussed within the frame- work of the orbit method. It is shown that both dynamics and symmetry trans- formations are globally well-defined on phase space. The flexibility in the choice of…