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Exceptional points (EPs), arising in non-Hermitian systems, have garnered significant attention in recent years, enabling advancements in sensing, wave manipulation, and mode selectivity. However, their role in quantum systems, particularly…
A deformed Bianchi type I metric in noncommutative gauge gravity is obtained. The gauge potential (tetrad fields) and scalar curvature are determined up to the second order in the noncommutativity parameters. The noncommutativity correction…
Exotic spinors arise in non-simply connected base manifolds due to the nonequivalent spinor structure. The dynamics of exotic spinors are endowed with an additional differential factor. In this work, we merge the exotic spinor scenario with…
Topological phase transitions are typically characterized by abrupt changes in a quantized invariant. Here we report a contrasting paradigm in non-Hermitian parity-time symmetric systems, where the topological invariant remains conserved,…
Severe thunderstorms cause substantial economic and human losses in the United States. Simultaneous high values of convective available potential energy (CAPE) and storm relative helicity (SRH) are favorable to severe weather, and both they…
Noncommutative version of D-dimensional relativistic particle is proposed. We consider the particle interacting with the configuration space variable $\theta^{\mu\nu}(\tau)$ instead of the numerical matrix. The corresponding Poincare…
A supersymmetric spin-1/2 particle in the noncommutative plane, subject to an arbitrary magnetic field, is considered, with particular attention paid to the homogeneous case. The system has three different phases, depending on the magnetic…
Non-Hermitian systems exhibit a variety of unique features rooted in the presence of exceptional points (EP). The distinct topological structure in the proximity of an EP gives rise to counterintuitive behaviors absent in Hermitian systems,…
In this thesis I study various aspects of theories in the two most studied examples of noncommutative spacetimes: canonical spacetime ($[x_{\mu},x_{\nu}]=\theta_{\mu\nu}$) and $\kappa$-Minkowski spacetime ($[x_{i},t]=\kappa^{-1} x_{i}$). In…
Time-independent scattering methods are widely employed to analyze transport in non-Hermitian systems. Their application, however, rests on a critical yet often overlooked assumption: that an incident wave is a pure superposition of…
Quantum group Fourier transform methods are applied to the study of processes on noncommutative Minkowski spacetime $[x^i,t]=\imath\lambda x^i$. A natural wave equation is derived and the associated phenomena of {\it in vacuo} dispersion…
Simple few-body systems often serve as theoretical laboratories across various branches of theoretical physics. A prominent example is the two-electron Harmonium model, which has been widely studied over the past three decades to gain…
Phase transitions in non-Hermitian systems are at the focus of cutting edge theoretical and experimental research. On the one hand, parity-time- ($\cal PT$-) and anti-$\cal PT$-symmetric physics have gained ever-growing interest, due to the…
Exceptional points (EPs) in non-Hermitian photonic systems have attracted considerable research interest due to their singular eigenvalue topology and associated anomalous physical phenomena. These properties enable diverse applications…
There ought to exist a description of quantum field theory which does not depend on an external classical time. To achieve this goal, in a recent paper we have proposed a non-commutative special relativity in which space-time and matter…
We develop a semiclassical framework for studying quantum particles constrained to curved surfaces using the momentous quantum mechanics formalism, which extends classical phase-space to include quantum fluctuation variables (moments). In a…
We obtain the ANNNI model from a Heisenberg model with large single--ion anisotropy energy, $D$, as might be relevant for helical spin systems. We treat quantum fluctuations to lowest order in $1/S$ at zero temperature within an expansion…
A phenomenological Hamiltonian of a closed (i.e., unitary) quantum system is assumed to have an $N$ by $N$ real-matrix form composed of a unperturbed diagonal-matrix part $H^{(N)}_0$ and of a tridiagonal-matrix perturbation…
Parity-time ($\mathcal{PT}$) symmetry plays an important role both in non-Hermitian and topological systems. In non-Hermitian systems $\mathcal{PT}$ symmetry can lead to an entirely real energy spectrum, while in topological systems…
Non-Hermitian systems have attracted significant interest because of their intriguing and useful properties, including exceptional points (EPs), where eigenvalues and the corresponding eigenstates of non-Hermitian operators become…