Related papers: Singularity resolution by lattice shifts in discre…
The density of states of a three dimensional Dirac equation with a random potential as well as in other problems of quantum motion in a random potential placed in sufficiently high spatial dimensionality appears to be singular at a certain…
We prove the approach to equilibrium of quenched isolated quantum systems for which the change in the Hamiltonian brought about by the quench satisfies a certain closed commutator algebra with all the extensive integrals of motion of the…
The one-dimensional hydrogen atom is an intriguing quantum mechanics problem that exhibits several properties which have been continually debated. In particular, there has been variance as to whether or not even-parity solutions exist, and…
Seminar held at JINR, Dubna, May 15, 2012. In General Relativity, spacetime singularities raise a number of problems, both mathematical and physical. One can identify a class of singularities - with smooth but degenerate metric - which,…
Future singularities arising in a family of models for the expanding Universe, characterized by sharing a convenient parametrization of the energy budget in terms of the deceleration parameter, are classified. Finite-time future…
The degree of freedom of the scalar field in scalar-tensor gravity is employed as "time" to deparametrize the Hamiltonian constraint of the theory. The deparametrized system is then nonperturbatively quantized by the approach of loop…
We demonstrate that the commonly known concept, which treats solitons as nonsingular solutions produced by the interplay of nonlinear self-attraction and linear dispersion, may be extended to include modes with a relatively weak singularity…
Using the Cartan formulation of General Relativity, we construct a well defined lattice-regularized theory capable to describe large non-perturbative quantum fluctuations of the frame field (or the metric) and of the spin connection. To…
In the present work we investigate the Newtonian limit of higher-derivative gravity theories with more than four derivatives in the action, including the non-analytic logarithmic terms resulting from one-loop quantum corrections. The first…
Motivated by generalized uncertainty principle, we derive a discrete picture of the space that respects Lorentz symmetry as well as gauge symmetry through setting an equivalency between linear GUP correction term and electromagnetic…
Various quasi-exact solvability conditions, involving the parameters of the periodic associated Lam{\'e} potential, are shown to emerge naturally in the quantum Hamilton-Jacobi approach. It is found that, the intrinsic nonlinearity of the…
Divergences that arise in the quantization of scalar quantum field models by means of a lattice-space functional integration may be attributed to a single integration variable, and this fact is demonstrated by showing that if the integrand…
Several quantum algorithms for linear algebra problems, and in particular quantum machine learning problems, have been "dequantized" in the past few years. These dequantization results typically hold when classical algorithms can access the…
Schr\"odinger operators often display singularities at the origin, the Coulomb problem in atomic physics or the various matter coupling terms in the Friedmann-Robertson-Walker problem being prominent examples. For various applications it…
Although the deformation of the Heisenberg algebra by a minimal length has become a central tool in quantum gravity phenomenology, it has never been rigorously obtained and is often derived using heuristic reasoning. In this study, we move…
Loop quantum gravity is believed to eliminate singularities such as the big bang and big crunch singularity. This belief is based on studies of so-called loop quantum cosmology which concerns symmetry-reduced models of quantum gravity. In…
We revisit the unified treatment of low-energy hadronic parity violation espoused by Desplanques, Donoghue, and Holstein to the end of an ab initio treatment of parity violation in low-energy nuclear processes within the Standard Model. We…
We discuss quantum many-body systems with lattice translation and discrete onsite symmetries. We point out that, under a boundary condition twisted by a symmetry operation, there is an exact degeneracy of ground states if the unit cell…
In many realizations of beyond the Standard Model theories, new massive particles are introduced, leading to a multi-scale system with widely separated energy scales. In this setting the Coleman-Weinberg effective potential, which describes…
Witten's supersymmetric quantum mechanics may incorporate potentials with strong singularities after their appropriate regularization. This was proposed by Das and Pernice [Nucl. Phys. B 561 (1999) 357 and arXiv: hep-th/0207112]. We suggest…