Related papers: Superintegrability, symmetry and point particle T-…
Plasma physics give an example of physical system of particles with the long range interaction. At small velocity of particles we can consider the plasma approximately as a system of particles with the Coulomb interaction. The Coulomb…
We discuss dualities of the integrable dynamics behind the exact solution to the N=2 SUSY YM theory. It is shown that T duality in the string theory is related to the separation of variables procedure in dynamical system. We argue that…
Spontaneous symmetry breaking has revolutionized the understanding in numerous fields of modern physics. Here, we theoretically demonstrate the spontaneous time-reversal symmetry breaking in a cavity quantum electrodynamics system in which…
Superintegrable systems with monopole interactions in flat and curved spaces have attracted much attention. For example, models in spaces with a Taub-NUT metric are well-known to admit the Kepler-type symmetries and provide non-trivial…
Possibility of electronic charge and spin separation leading to charge density wave and spin density wave is well established in one dimensional systems in presence and absence of Coulomb interaction. We start from quasi one dimension and…
This thesis is divided in two parts. The first part contains the study of some properties of the electromagnetic duality in 4 dimensions. An extended double potential formalism for linearized gravity is introduced which allows to write an…
We study the dynamics of charged, spherically symmetric dust shells in the presence of a positive cosmological constant. We find generalizations of the well-known solutions in asymptotically flat spacetime, in particular orbits into…
Topological quantum phase transitions intrinsically intertwine self-similarity and topology of many-electron wave-functions, and divining them is one of the most significant ways to advance understanding in condensed matter physics. Our…
The concept of supersymmetry in a quantum mechanical system is extended, permitting the recognition of many more supersymmetric systems, including very familiar ones such as the free particle. Its spectrum is shown to be supersymmetric,…
This paper investigates the significance of T-duality in string theory: the indistinguishability with respect to all observables, of models attributing radically different radii to space -- larger than the observable universe, or far…
As a generalization and extension of our previous paper [Escobar-Ruiz and Azuaje, J. Phys. A: Math. Theor. 57, 105202 (2024)], in this work, the notions of particular integral and particular integrability in classical mechanics are extended…
Dualities and duality transformations form a well established methodology in various aspects of quantum many body physics and quantum field theories, allowing one to exploit equivalence between models which may naively seem completely…
We study the scattering dynamics of an $n$-component spinor wavefunction in a random environment on a two-dimensional lattice. In the presence of particle-hole symmetry we find diffusion on large scales. The latter is described by a…
We study various temporal correlation functions of a tagged particle in one-dimensional systems of interacting point particles evolving with Hamiltonian dynamics. Initial conditions of the particles are chosen from the canonical thermal…
It is proposed that the paradox of wave-particle duality in quantum mechanics may be resolved using a physical picture analogous to magnetic domains. Within this picture, a quantum particle represents a coherent region of a quantum wave…
The two-dimensional extension of the one-dimensional PDM-Lagrangians and their nonlocal point transformation mappings into constant unit-mass exactly solvable Lagrangians is introduced. The conditions on the related two-dimensional…
The $t$-model represents the Hubbard model in the limit $U \to \infty$ and is one of the basic models of strongly correlated electrons. On a one-dimensional chain, the model is integrable, and the charge dynamics corresponds to that of free…
We describe the interplay between electric-magnetic duality and higher symmetry in Maxwell theory. When the fine-structure constant is rational, the theory admits non-invertible symmetries which can be realized as composites of…
One-dimensional scattering mediated by non-Hermitian Hamiltonians is studied. A schematic set of models is used which simulate two point interactions at a variable strength and distance. The feasibility of the exact construction of the…
T-Duality is a poorly understood symmetry of the space-time fields of string theory that interchanges long and short distances. It is best understood in the context of toroidal compactification where, loosely speaking, radii of the torus…