相关论文: Quantum hamiltonians and prime numbers

We present a novel approach to the numerical computation of quasi-normal modes, based on the first-order (in radial derivative) formulation of the equations of motion and using a matrix version of the continued fraction method. This…

Motivated by applications of the discrete random Schr\"odinger operator, mathematical physicists and analysts, began studying more general Anderson-type Hamiltonians; that is, the family of self-adjoint operators $$H_\omega = H + V_\omega$$…

It has recently been suggested that black holes may be described as condensates of weakly interacting gravitons at a critical point, exhibiting strong quantum effects. In this paper, we study a model system of attractive bosons in one…

We present a detailed theoretical analysis of superradiant Rayleigh scattering from atomic Bose-Einstein condensates. A thorough investigation of the spatially resolved time-evolution of optical and matter-wave fields is performed in the…

Quasiparticle approach to dynamics of dark solitons is applied to the case of ring solitons. It is shown that the energy conservation law provides the effective equations of motion of ring dark solitons for general form of the nonlinear…

Some examples of branched Hamiltonians are explored both classically and in the context of quantum mechanics, as recently advocated by Shapere and Wilczek. These are in fact cases of switchback potentials, albeit in momentum space, as…

In this work, we propose a cohomological approach to studying perturbative anomalies in quantum mechanics. The Hamiltonian $\hat{H}$ together with the symmetry generator $\hat{S}$ forms a unitary representation of the two-dimensional…

Consider a particle sitting at a fixed position outside of a stable black hole. If the system is heated up, the black hole horizon grows and there should exist a critical temperature above which the particle enters the black hole interior.…

We discuss the analogy between a classical scalar field with a self-interacting potential, in a curved spacetime described by a quasi--bounded state, and a trapped Bose-Einstein condensate. In this context, we compare the Klein-Gordon…

We study Hamiltonians with point interactions in spaces of vector-valued functions. Using some information from the theory of quantum graphs we describe a class of the operators which can be reduced to the direct sum of several…

The common interpretation of the Hawking radiation as quantum tunneling has some ambiguity such as coordinate-dependence of tunneling rate and non-invariance of the action under canonical transformations. It is shown that the tunneling…

Analyzing some well established facts, we give a model-independent parameterization of black hole quantum computing in terms of a set of macro and micro quantities and their relations. These include the relations between the…

We show that supersymmetry and inflation, in a broad class of models, generically lead to formation of primordial black holes (PBHs) that can account for dark matter. Supersymmetry predicts a number of scalar fields that develop a coherent…

For long black holes have been considered as endowed with a definite temperature. Yet when the Schwarzschild black hole is treated as a canonical ensemble three problems arise: incompatibility with the Hawking radiation, divergence of the…

Certain models of cosmic inflation produce strong cosmological perturbations at short length scales, which may later collapse into primordial black holes. To find the statistics of these strong perturbations and the ensuing black holes, it…

We provide a joint numerical-analytical study of the physics of a flowing atomic Bose-Einstein condensate in the combined presence of an external trap and a step potential which accelerates the atoms out of the condensate creating a pair of…

We report a rigorous theory to show the origin of the unexpected periodic behavior seen in the consecutive differences between prime numbers. We also check numerically our findings to ensure that they hold for finite sequences of primes,…

I review the recent progress in providing a statistical foundation for black hole thermodynamics. In the context of string theory, one can now identify and count quantum states associated with black holes. One can also compute the analog of…

An exact and analytical solution, in four-dimensional general relativity coupled with Maxwell electromagnetism, is built by means of a Lie point symmetry of the Ernst equations, the Harrison transformation. The new spacetime describes a…

We describe a group theoretic analysis of Shor's algorithm and other related hidden subgroup problems in mathematics and relate these to symmetries of molecular and condensed phase assemblies. By recasting Shor's algorithm through the lens…