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I give an introductory review of recent, fascinating developments in supersymmetric gauge theories. I explain pedagogically the miraculous properties of supersymmetric gauge dynamics allowing one to obtain exact solutions in many instances.…
In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg…
We study the classical and quantum oscillator in the context of a non-additive (deformed) displacement operator, associated with a position-dependent effective mass, by means of the supersymmetric formalism. From the supersymmetric partner…
Quantum computing promises the possibility of studying the real-time dynamics of nonperturbative quantum field theories while avoiding the sign problem that obstructs conventional lattice approaches. Current and near-future quantum devices…
An exact superpotential is derived for the N=1 theories which arise as massive deformations of N=4 supersymmetric Yang-Mills (SYM) theory. The superpotential of the SU(N) theory formulated on R^{3}\times S^{1} is shown to coincide with the…
Open quantum systems play a central role in contemporary nanoscale technologies, including molecular electronics, quantum heat engines, quantum computation and information processing. A major theoretical challenge is to construct dynamical…
Semiclassical methods are essential in analyzing quantum mechanical systems. Although they generally produce approximate results, relatively rare potentials exist for which these methods are exact. Such intriguing potentials serve as…
In supersymmetric extensions of the Standard Model, the observed particles come in fermion-boson pairs necessary for the realization of supersymmetry (SUSY). In spite of the expected abundance of super-partners for all the known particles,…
We describe a scheme for constructing quantum mechanics in which a quantum system is considered as a collection of open classical subsystems. This allows using the formal classical logic and classical probability theory in quantum…
A supersymmetric generalization of the Lieb-Liniger-Yang dynamics governing $N$ massive bosons moving on a line with delta interactions among them at coinciding points is developed. The analysis of the delicate balance between integrability…
The true dynamical randomness is obtained as a natural fundamental property of deterministic quantum systems. It provides quantum chaos passing to the classical dynamical chaos under the ordinary semiclassical transition, which extends the…
The hyperconfluent third-order supersymmetric quantum mechanics, in which all the factorization energies tend to a common value, is analyzed. It will be shown that the final potential as well can be achieved by applying consecutively a…
Stochastic quantisation normally involves the introduction of a fictitious extra time parameter, which is taken to infinity so that the system evolves to an equilibrium state.In the case of a locally supersymmetric theory, an interesting…
The Feynman quantum-classical isomorphism between classical statistical mechanics in 3+1 dimensions and quantum statistical mechanics in 3 dimensions is used to connect classical polymer self-consistent field theory with quantum…
We investigate the transition from quantum to classical mechanics using a one-dimensional free particle model. In the classical analysis, we consider the initial positions and velocities of the particle drawn from Gaussian distributions.…
Links between supersymmetric classical and quantum mechanics are explored. Diagrammatic representations for \hbar-expansions of norms of ground states are provided. The WKB spectra of supersymmetric non harmonic oscillators are found.
We discuss a set of novel discrete symmetries of a free N = 2 supersymmetric (SUSY) quantum mechanical system which is the limiting case of a widely-studied interacting SUSY model of a charged particle constrained to move on a sphere in the…
Different ways to incorporate two-dimensional systems, which are not amenable to separation of variables, into the framework of Supersymmetrical Quantum Mechanics (SUSY QM) are analyzed. In particular, the direct generalization of…
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…
Quantum Hamilton-Jacobi Theory and supersymmetric quantum mechanics (SUSYQM) are two parallel methods to determine the spectra of a quantum mechanical systems without solving the Schr\"odinger equation. It was recently shown that the shape…