arXiv subjects

Samuel Kováčik

Publications and source records attributed to Samuel Kováčik.

28 records · Page 2Linked to original sources

arXiv2018

Triple Point of a Scalar Field Theory on a Fuzzy Sphere

The model of a scalar field with quartic self-interaction on the fuzzy sphere has three known phases: a uniformly ordered phase, a disordered phase and a non-uniformly ordered phase, the last of which has no classical counterpart. These three phases are expected to meet at a triple point. By studying the infinite matrix size limit, we locate the position of this triple point to within a small triangle in terms of the parameters of the model. We find the triple point is closer to the coordinate origin of the phase diagram than previous estimates but broadly consistent with recent analytic predictions.

hep-th↗

arXiv2018

Magnetic Monopoles in (Noncommutative) Quantum Mechanics

We utilize the close relation between the complex space $\textbf{C}^2$ and the real space $\textbf{R}^3$ to reformulate quantum mechanics in a manner which allows to, either or both, describe magnetic monopoles and quantize the underlying space, obtaining (noncommutative) quantum mechanics (with magnetic monopoles).

quant-ph↗

arXiv2018

Alternative Description of Magnetic Monopoles in Quantum Mechanics

We present an alternative description of magnetic monopoles by lifting quantum mechanics from 3-dimensional space into a one with 2 complex dimensions. Magnetic monopoles are realized as a generalization of the considered states. Usual algebraic relations and magnetic fields describing monopoles are reproduced, with the Dirac quantization condition satisfied naturally.

quant-ph↗

arXiv2018

Magnetic monopoles in noncommutative quantum mechanics 2

In this paper we extend the analysis of magnetic monopoles in quantum mechanics in three dimensional rotationally invariant noncommutative space $\textbf{R}^3_λ$. We construct the model step-by-step and observe that physical objects known from previous studies appear in a very natural way. Nonassociativity became a topic of great interest lately, often in a connection with magnetic monopoles. We show that this model does not possess this property.

math-ph↗

arXiv2017

Magnetic monopoles and symmetries in noncommutative space

In this paper, we review the progress in the analysis of magnetic monopoles as generalized states in quantum mechanics. We show that the considered model contains rich algebraic structure that generates symmetries which have been utilized in different physical contexts. Even though are we focused on quantum mechanics in noncommutative space $\textbf{R}_λ^3$, the results can be reconstructed in ordinary quantum mechanics in $\textbf{R}^3$ as well.

hep-th↗

arXiv2017

$R^3_λ$ inspired black holes

We study a black hole with a blurred mass density instead of a singular one, which is caused by the noncommutativity of 3-space. Depending on its mass, such object has either none, one or two event horizons. It possesses properties, which become important on a microscopic scale, in particular, the Hawking temperature does not increase indefinitely as the mass goes to zero, but vanishes instead. Such frozen and extremely dense pieces of matter are good dark matter candidates.

gr-qc↗

arXiv2017

The Flavoured BFSS Model at High Temperature

We study the high temperature series expansion of the Berkooz-Douglas matrix model which describes the D0/D4--brane system. At high temperature the model is weakly coupled and we develop the series to second order. We check our results against the high temperature regime of the bosonic model (without fermions) and find excellent agreement. We track the temperature dependence of the bosonic model and find backreaction of the fundamental fields lifts the zero temperature adjoint mass degeneracy. In the low temperature phase the system is well described by a gaussian model with three masses $m^t_A=1.964 \pm 0.003$, $m^l_A=2.001 \pm 0.003$ and $m_f=1.463 \pm 0.001$, the adjoint longitudional and transverse masses and the mass of the fundamental fields respectively.

hep-th↗

arXiv2016

Magnetic monopoles in noncommutative quantum mechanics

We discuss certain generalization of the Hilbert space of states in noncommutaive quantum mechanics that, as we show, introduces magnetic monopoles into the theory. Such generalization arises very naturally in the considered model, but can be easily reproduced in ordinary quantum mechanics as well. This approach offers a different viewpoint on the Dirac quantization condition and other important relations for magnetic monopoles. We focus mostly on the kinematic structure of the theory, but investigate also a dynamical problem (with the Coulomb potential).

physics.gen-ph↗

arXiv2016

NC plane waves, Casimir effect and flux tube potential with Lüscher terms

We analyze plane waves in a model of quantum mechanics in a three dimensional noncommutative (NC) space $R^3_λ$. Signature features of NC models are impossibility of probing distances smaller than a certain length scale λ and a presence of natural energetic cut-off at energy scale of order $1/λ^2$ (in convenient units). We analyze consequences of such restrictions on a 1 dimensional Casimir effect. The result shows resemblance to flux tube potential for quark-antiquark pairs and to effective bosonic string theories with Lüscher terms. Such behavior might effect the radius of possible compact (fuzzy) dimensions.

quant-ph↗

arXiv2015

Quantum Mechanics in Noncommutative space

This paper provides an examination of how are prediction of standard quantum mechanic (QM) affected by introducing a noncommutative (NC) structure into the configuration space of the considered system (electron in the Coulomb potential in the present case). The parameter controlling the extent of modification is denoted as λ. The coordinates in the NC space are realized via creation and annihilation operators acting in an auxiliary Fock space, this one being chosen in such a way that the rotational invariance of the system remains intact also in NCQM. Analog of Schrödinger equation for hydrogen atom is found and analytically solved, both for bound states and scattering. The exact formulas for NC corrections are given. None of the NC predictions contradicts experimentally verified QM results, since in the correspondence limit λ -> 0 both QM and NCQM coincide. Highly surprising feature of the NC version is the existence of bound states for repulsive potential at ultra-high energies. However, these disappear from the Hilbert space in the mentioned limit. The whole problem is solved also using a method analogous to that of Pauli. Besides rotational invariance, the dynamical symmetry related to the conservation of NC analog of Laplace-Runge-Lenz vector is being used and the results obtained this way are in the full agreement with those given by "Schrödinger-like" approach. The presented NC deformation of QM preserves all those mysterious properties of the Coulomb system that made it a distinguished key-stone of the modern physics.

math-ph↗