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.Comment: 39 pages, 15 figure

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.Comment: 8 pages, 1 figur

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. To begin with, we illustrate the phase portrait of this non-Hermitian model on the Bloch sphere, elucidating the changes in behavior as one moves across the phase transition boundary, as well as the emergent feature of unidirectional state evolution in the spontaneously broken PT-symmetry regime. This is followed by an examination of the purity and entropy dynamics. Here, 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 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 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 PT charge operator 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

Vibration analysis of a small diesel engine using diesel-biodiesel fuel blends

Biodiesel as an environmentally friendly fuel has the potential to provide comparable engine performance results.  Biodiesel is a renewable fuel produced from vegetable and seed oils, animal fats or waste edible oils.  Sound and vibration caused by the combustion process in the engine might have direct effects on users.   One of the important characteristics of diesel fuels is high noise and vibration.  The present study was carried out to examine the vibration of different diesel-biodiesel fuel blends in power tiller engine.  The main goal was to present fuels with the minimum vibration.  So, the time domain signals were analyzed in five levels of engine speed, three axes and six fuel blends on the engine.  The signal processing and statistical approach were applied for data analysis.  The results showed that in all engine speeds, the dominant frequency is matched to the piston stroke frequency of the engine, as well as the frequency of vibration with the increase of engine speed.  The experiments indicated that the magnitude of vibration in the power tiller engine depends on the axis of measurement, engine speed and the fuel blends.  Vibration acceleration is significantly affected by engine speed and the increase in forward speed due to the increase in vibration acceleration rms.  The results of the experiments revealed that vibration acceleration is significantly affected by the axis of measurement.  The magnitude of vibration acceleration in vertical axis was more than that in the other two axes and magnitude of vibration acceleration in the longitudinal axis was more than that in the lateral axis.  Fuel blends had significant effect on the vibration.  It demonstrated that B100, B5 and B20 have the lowest vibration.  On the contrary, B15 and B10 have the highest vibration.   Keywords: vibration analysis, power tiller, time domain, frequency domain, diesel-biodiesel fuel blend

The Foot That Broke Both Hips: A Case Report and Literature Review of Tumor-Induced Osteomalacia

Tumor-induced osteomalacia (TIO) is a rare paraneoplastic syndrome characterized by hypophosphatemia and clinical symptoms of osteomalacia. Only discussed as case reports, there is still limited knowledge of this condition as a potentially curable cause of osteomalacia among clinicians and pathologists. In this article, we present a case of tumor-induced osteomalacia in a 59-year-old gentleman followed by an up-to-date review of the existing literature on TIO