arXiv subjects

Alireza Beygi

Publications and source records attributed to Alireza Beygi.

11 recordsLinked to original sources

arXiv2025

Emergence of kaonium as a sharp resonance in photon-photon to meson-meson cross-sections

We calculate the binding energies of the hypothetical mesonic atom, $K^+ K^-$ (kaonium), using the $K^+ K^- \to K^+ K^-$ elastic scattering amplitude. Our findings are in line with previously reported results, which involve solving an eigenvalue equation of the Kudryavtsev-Popov type. Using chiral perturbation theory, we show that kaonium manifests itself as a sharp resonance around 992 MeV accompanying $f_0 (980)$ or $a_0 (980)$ in cross-sections for processes $\gamma \gamma \to \pi^0 \pi^0$ or $\gamma \gamma \to \pi^0 \eta$. The latter process is particularly striking: the peak at the kaonium resonance energy is highly pronounced, with the ratio of the cross-sections $\sigma (\gamma \gamma \to \pi^0 \eta) / \sigma (\gamma \gamma \to \pi^0 \pi^0) \approx 9$. Due to the short lifetime of kaonium ($\sim 10^{-18}$ s) and its small decay width ($\sim 0.4$ keV), direct detection of this exotic atom poses a significant challenge and requires high experimental resolution. However, we show that once the formation of kaonium is considered in the cross-section, a better fit to the available experimental data is obtained.

hep-ph↗

arXiv2024

Three perspectives on entropy dynamics in a non-Hermitian two-state system

A comparative study of entropy dynamics as an indicator of physical behavior in an open two-state system with balanced gain and loss is presented. We distinguish the perspective taken in utilizing the conventional framework of Hermitian-adjoint states from an approach that is based on biorthogonal-adjoint states and a third case based on an isospectral mapping. In this it is demonstrated that their differences are rooted in the treatment of the environmental coupling mode. For unbroken $\mathcal{PT}$ symmetry of the system, a notable characteristic feature of the perspective taken is the presence or absence of purity oscillations, with an associated entropy revival. The description of the system is then continued from its $\mathcal{PT}$-symmetric pseudo-Hermitian phase into the regime of spontaneously broken symmetry, in the latter two approaches through a non-analytic operator-based continuation, yielding a Lindblad master equation based on the $\mathcal{PT}$ charge operator $\mathcal{C}$. This phase transition indicates a general connection between the pseudo-Hermitian closed-system and the Lindbladian open-system formalism through a spontaneous breakdown of the underlying physical reflection symmetry.

quant-ph↗

arXiv2022

Thermodynamic properties of non-Hermitian Nambu--Jona-Lasinio models

We investigate the impact of non-Hermiticity on the thermodynamic properties of interacting fermions by examining bilinear extensions to the $3+1$ dimensional $SU(2)$-symmetric Nambu--Jona-Lasinio (NJL) model of quantum chromodynamics at finite temperature and chemical potential. The system is modified through the anti-$PT$-symmetric pseudoscalar bilinear $\bar{\psi}\gamma_5 \psi$ and the $PT$-symmetric pseudovector bilinear $iB_\nu \,\bar{\psi}\gamma_5\gamma^\nu \psi$, introduced with a coupling $g$. Beyond the possibility of dynamical fermion mass generation at finite temperature and chemical potential, our findings establish model-dependent changes in the position of the chiral phase transition and the critical end-point. These are tunable with respect to $g$ in the former case, and both $g$ and $|B|/B_0$ in the latter case, for both lightlike and spacelike fields. Moreover, the behavior of the quark number, entropy, pressure, and energy densities signal a potential fermion or antifermion excess compared to the standard NJL model, due to the pseudoscalar and pseudovector extension respectively. In both cases regions with negative interaction measure $I = \epsilon-3p$ are found. Future indications of such behaviors in strongly interacting fermion systems, for example in the context of neutron star physics, may point toward the presence of non-Hermitian contributions. These trends provide a first indication of curious potential mechanisms for producing non-Hermitian baryon asymmetry. In addition, the formalism described in this study is expected to apply more generally to other Hamiltonians with four-fermion interactions and thus the effects of the non-Hermitian bilinears are likely to be generic.

hep-ph↗

arXiv2020

Non-Hermitian extension of the Nambu--Jona-Lasinio model in 3+1 and 1+1 dimensions

This paper presents a non-Hermitian PT-symmetric extension of the Nambu--Jona-Lasinio (NJL) model of quantum chromodynamics in 3+1 and 1+1 dimensions. In 3+1 dimensions, the SU(2)-symmetric NJL Hamiltonian $H_{\textrm{NJL}} = \barψ(-i γ^k \partial_k + m_0) ψ- G [ (\barψψ)^2 + (\barψi γ_5 \vecτ ψ)^2 ]$ is extended by the non-Hermitian, PT- and chiral-symmetric bilinear term $ig\barψγ_5 B_μ γ^μ ψ$; in 1+1 dimensions, where $H_{\textrm{NJL}}$ is a form of the Gross-Neveu model, it is extended by the non-Hermitian PT-symmetric but chiral symmetry breaking term $g \barψγ_5 ψ$. In each case, the gap equation is derived and the effects of the non-Hermitian terms on the generated mass are studied. We have several findings: in previous calculations for the free Dirac equation modified to include non-Hermitian bilinear terms, contrary to expectation, no real mass spectrum can be obtained in the chiral limit; in these cases a nonzero bare fermion mass is essential for the realization of PT symmetry in the unbroken regime. Here, in the NJL model, in which four-point interactions are present, we {\it do} find real values for the mass spectrum also in the limit of vanishing bare masses in both 3+1 and 1+1 dimensions, at least for certain specific values of the non-Hermitian couplings $g$. Thus, the four-point interaction overrides the effects leading to PT symmetry-breaking for these parameter values. Further, we find that in both cases, in 3+1 and in 1+1 dimensions, the inclusion of a non-Hermitian bilinear term can contribute to the generated mass. In both models, this contribution can be tuned to be small; we thus fix the fermion mass to its value when $m_0=0$ in the absence of the non-Hermitian term, and then determine the value of the coupling required so as to generate a bare fermion mass.

hep-ph↗

arXiv2019

Continuous quantum phase transition in the fermionic mass solutions of the Nambu-Jona-Lasinio model

Recently quantum simulators have been constructed to investigate experimentally the most prominent theoretical four-point many-body system described by the Hubbard model. By varying the coupling strength of the four-point interaction in relation to the kinetic term, one can analyze the phase structure of the model. This intriguing fact leads us to investigate whether similar Hamiltonians with four-point interactions can also be studied as a function of their four-point coupling strength. In this paper, we reexamine the Nambu-Jona-Lasinio model, regarding it generally beyond the context of quantum chromodynamics. Essentially, it is a model in which particle-antiparticle pairing leads to a BCS-like condensate, with the result that chiral symmetry is broken dynamically in the strong-coupling regime. To study the behavior of the system, it is necessary to move from this regime to a hypothetical regime of weak coupling, altering the coupling strength of the interaction arbitrarily. In order to do this, the gap equation must be regarded as complex and its Riemann surface structure must be known. We do this and obtain a continuous quantum phase transition characterized by the development of a complex order parameter (the dynamically generated mass) from the second sheet of the Riemann surface, as we move into the weak-coupling regime. The power-law behavior of the order parameter in the vicinity of the phase transition point is demonstrated to be independent of the choice of the regularization scheme with the critical exponent as $β\approx 0.55$. At the same time, the isovector pseudoscalar modes retain their feature as Goldstone modes and still have zero mass, while the isoscalar scalar meson follows the behavior of the order parameter and gains a width. Energetically, this mode is not favored over the normal, uncondensed mode but would have to be accessed through an excitation process.

hep-ph↗

arXiv2019

Relativistic PT-symmetric fermionic theories in 1+1 and 3+1 dimensions

Relativistic PT-symmetric fermionic interacting systems are studied in 1+1 and 3+1 dimensions. The objective is to include non-Hermitian PT-symmetric interaction terms that give {\it real} spectra. Such interacting systems could describe new physics. The simplest non-Hermitian Lagrangian density is $L=L_0+L_{int}=\barψ(i\not\partial-m)ψ-g\barψγ^5ψ$. The associated relativistic Dirac equation is PT invariant in 1+1 dimensions and the associated Hamiltonian commutes with PT. However, the dispersion relation $p^2=m^2-g^2$ shows that the PT symmetry is broken in the chiral limit $m\to0$. For interactions $L_{int}=-g(\barψγ^5ψ)^N$ with N=2,3, if the associated Dirac equation is PT invariant, the dispersion relation gives complex energies as $m\to0$. Other models are studied in which x-dependent PT-symmetric potentials such as $ix^3$, $-x^4$, $iκ/x$, Hulthén, or periodic potentials are coupled to $ψ$ and the classical trajectories plane are examined. Some combinations of these potentials give a real spectrum. In 3+1 dimensions, the simplest system $L=L_0+L_{int}=\barψ(i\not\partial-m)ψ-g\barψγ^5ψ$ resembles the 1+1-dimensional case but the Dirac equation is not PT invariant because $T^2=-1$. This explains the appearance of complex eigenvalues as $m\to0$. Other Lorentz-invariant 2-point and 4-point interactions give non-Hermitian PT-symmetric terms in the Dirac equation. Only the axial vector and tensor Lagrangian interactions $L_{int}=-i\barψ\tilde B_μγ^5γ^μψ$ and $L_{int}=-i\barψT_{μν}σ^{μν}ψ$ fulfil both requirements of PT invariance of the associated Dirac equation and non-Hermiticity. Both models give complex spectra as $m\to0$. The effect on the spectrum of the additional constraint of selfadjointness of the Hamiltonian with respect to the PT inner product is investigated.

math-ph↗

arXiv2018

No-signaling principle and quantum brachistochrone problem in $PT$-symmetric fermionic two- and four-dimensional models

Fermionic systems differ from bosonic ones in several ways, in particular that the time-reversal operator $T$ is odd, $T^2=-1$. For $PT$-symmetric bosonic systems, the no-signaling principle and the quantum brachistochrone problem have been studied to some degree, both of them controversially. In this paper, we apply the basic methods proposed for bosonic systems to {\it fermionic} two- and four-dimensional $PT$-symmetric Hamiltonians, and obtain several surprising results: We find - in contrast to the bosonic case - that the no-signaling principle is upheld for two-dimensional fermionic Hamiltonians, however, the $PT$ symmetry is broken. In addition, we find that the time required for the evolution from a given initial state, the spin-up, to a given final state, the spin-down, is a constant, independent of the parameters of the Hamiltonian, under the eigenvalue constraint. That is, it cannot - as in the bosonic case - be optimized. We do, however, also find a dimensional dependence: four-dimensional $PT$-symmetric fermionic Hamiltonians considered here again uphold the no-signaling principle, but it is not essential that the $PT$ symmetry be broken. The symmetry is, however, broken if the measure of entanglement is conserved. In the four-dimensional systems, the evolution time between orthogonal states is dependent on the parameters of the Hamiltonian, with the conclusion that it again can be optimized, and approach zero under certain circumstances. However, if we require the conservation of entanglement, the transformation time between these two states becomes the same constant as found in the two-dimensional case, which coincides with the minimum time for such a transformation to take place in the Hermitian case.

quant-ph↗

arXiv2018

Two- and four-dimensional representations of the PT- and CPT-symmetric fermionic algebras

Fermionic systems differ from their bosonic counterparts, the main difference with regard to symmetry considerations being that $T^2=-1$ for fermionic systems. In PT-symmetric quantum mechanics an operator has both PT and CPT adjoints. Fermionic operators $\eta$, which are quadratically nilpotent ($\eta^2=0$), and algebras with PT and CPT adjoints can be constructed. These algebras obey different anticommutation relations: $\eta\eta^{PT}+\eta^{PT}\eta=-1$, where $\eta^{PT}$ is the PT adjoint of $\eta$, and $\eta\eta^{CPT}+\eta^{CPT}\eta=1$, where $\eta^{CPT}$ is the CPT adjoint of $\eta$. This paper presents matrix representations for the operator $\eta$ and its PT and CPT adjoints in two and four dimensions. A PT-symmetric second-quantized Hamiltonian modeled on quantum electrodynamics that describes a system of interacting fermions and bosons is constructed within this framework and is solved exactly.

quant-ph↗

arXiv2017

Analytic structure of eigenvalues of coupled quantum systems

By analytically continuing the coupling constant $g$ of a coupled quantum theory, one can, at least in principle, arrive at a state whose energy is lower than the ground state of the theory. The idea is to begin with the uncoupled $g=0$ theory in its ground state, to analytically continue around an exceptional point (square-root singularity) in the complex-coupling-constant plane, and finally to return to the point $g=0$. In the course of this analytic continuation, the uncoupled theory ends up in an unconventional state whose energy is lower than the original ground state energy. However, it is unclear whether one can use this analytic continuation to extract energy from the conventional vacuum state; this process appears to be exothermic but one must do work to vary the coupling constant $g$.

math-ph↗

arXiv2016

Amplitude determination for $M M \to M M$, $M = \pi, K$ and cross-sections for $\gamma \gamma \to \pi^+ \pi^-, \pi^0 \pi^0, \pi^0 \eta$ in a chiral model

Dai and Pennington have performed a comprehensive analysis of essentially all pion and kaon pair production data from two-photon collisions below 1.5 GeV, including all high statistics results from Belle, as well as the older data from Mark II at SLAC, CELLO at DESY, and Crystal Ball at SLAC. Imposing the basic constraints required by analyticity, unitarity, and crossing symmetry and making use of Low's low-energy theorem for QED, they were able to extract the final-state, strong-interaction scattering amplitudes for the intermediate $\pi \pi \to \pi \pi$ and $\pi \pi \to K \overline{K}$ reactions in a model-independent fashion. In addition, they provided good fits to the respective $\gamma \gamma \to \pi \pi$ cross-sections that are known in the low-energy sector in the restricted angular range, $| \cos \theta | < 0.6 - 0.8$. Using the parameters obtained in this fashion, these authors constructed the $\gamma \gamma \to \pi \pi$ cross-sections integrated over the full angular range. In the present work, we use a version of chiral perturbation theory developed by Oller and Oset to evaluate the final-state, strong-interaction amplitudes theoretically, and we compare our low-energy QCD-based results with the amplitudes extracted by Dai and Pennington. We also calculate the $\gamma \gamma \to \pi \pi$ cross-sections (integrated over the full angular range) and compare them with those obtained by Dai and Pennington. These calculations give a more detailed insight into the fit of chiral perturbation theory, not just to the measured $\gamma \gamma \to \pi \pi$ cross-sections, as is usually presented, but rather to a higher level of detail through the available analysis of the experimental data for the underlying final-state, strong-interaction, meson-meson scattering amplitudes $\pi \pi \to \pi \pi$ and $\pi \pi \to K \overline{K}$ themselves. The fits appear to be sensible.

hep-ph↗

arXiv2015

Coupled Oscillator Systems Having Partial PT Symmetry

This paper examines chains of $N$ coupled harmonic oscillators. In isolation, the $j$th oscillator ($1\leq j\leq N$) has the natural frequency $ω_j$ and is described by the Hamiltonian $\frac{1}{2}p_j^2+\frac{1}{2}ω_j^2x_j^2$. The oscillators are coupled adjacently with coupling constants that are purely imaginary; the coupling of the $j$th oscillator to the $(j+1)$st oscillator has the bilinear form $iγx_jx_{j+1}$ ($γ$ real). The complex Hamiltonians for these systems exhibit {\it partial} $\mathcal{PT}$ symmetry; that is, they are invariant under $i\to-i$ (time reversal), $x_j\to-x_j$ ($j$ odd), and $x_j\to x_j$ ($j$ even). [They are also invariant under $i\to-i$, $x_j\to x_j$ ($j$ odd), and $x_j\to- x_j$ ($j$ even).] For all $N$ the quantum energy levels of these systems are calculated exactly and it is shown that the ground-state energy is real. When $ω_j=1$ for all $j$, the full spectrum consists of a real energy spectrum embedded in a complex one; the eigenfunctions corresponding to real energy levels exhibit partial $\mathcal{PT}$ symmetry. However, if the $ω_j$ are allowed to vary away from unity, one can induce a phase transition at which {\it all} energies become real. For the special case $N=2$, when the spectrum is real, the associated classical system has localized, almost-periodic orbits in phase space and the classical particle is confined in the complex-coordinate plane. However, when the spectrum of the quantum system is partially real, the corresponding classical system displays only open trajectories for which the classical particle spirals off to infinity. Similar behavior is observed when $N>2$.

quant-ph↗