We present a gauge-theoretic formulation of Nambu non-equilibrium thermodynamics (NNET) within a common gauge-fixed worldline framework. In this formulation, the generalized thermodynamic force is described by an Abelian thermodynamic connection, and ordinary Onsager dynamics is recovered by fixing its temporal component through the dissipation function.

Japan

So Katagiri

A gauge-theoretic formulation of Nambu non-equilibrium thermodynamics

Klein–Gordon and Dirac oscillators are formulated on the constant-curvature spacetime <math altimg='si22.svg'><mrow><msub><mi>g</mi><mrow><mi>&#956;</mi><mi>&#957;</mi></mrow></msub><mo linebreak='goodbreak'>=</mo><msup><mi>s</mi><mrow><mo>&#8722;</mo><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><msub><mi>&#951;</mi><mrow><mi>&#956;</mi><mi>&#957;</mi></mrow></msub></mrow></math> generated by the Fock&#8211;Lorentz conformal factor <math altimg='si1.svg'><mrow><mi>s</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo linebreak='goodbreak'>+</mo><mi>c</mi><mi>t</mi><mo linebreak='goodbreak'>/</mo><mi>R</mi></mrow></math>, a conformal Poincar&#233; patch of de Sitter spacetime. This metric is a geometric postulate rather than a consequence of the Fock&#8211;Lorentz transformations, whose projective map pulls Minkowski space back to a flat metric. In the ordinary cotangent-bundle phase space, <math altimg='si23.svg'><mrow><mrow><mo>(</mo><msup><mi>E</mi><mn>2</mn></msup><mo linebreak='badbreak'>&#8722;</mo><msup><mi mathvariant='bold'>p</mi><mn>2</mn></msup><msup><mi>c</mi><mn>2</mn></msup><mo>)</mo></mrow><msup><mi>s</mi><mn>2</mn></msup><mo linebreak='goodbreak'>=</mo><msubsup><mi>m</mi><mrow><mn>0</mn></mrow><mn>2</mn></msubsup><msup><mi>c</mi><mn>4</mn></msup></mrow></math> is the conformal-coordinate representation of the covariant mass shell, not a deformed dispersion relation. Covariant actions yield the canonically rescaled scalar equation, including its order- <math altimg='si21.svg'><msup><mi>R</mi><mrow><mo>&#8722;</mo><mn>2</mn></mrow></msup></math> term, and the Dirac equation with <math altimg='si24.svg'><mrow><msub><mi>m</mi><mtext>app</mtext></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><msub><mi>m</mi><mn>0</mn></msub><mo linebreak='goodbreak'>/</mo><mi>s</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math>. The oscillator couplings are coordinate-defined simplified models. Two Klein&#8211;Gordon factor orderings give <italic>alternative</italic> oscillator models, not independent physical sectors of one scalar field; their conditional fixed-time spectra and the Dirac-oscillator spectrum are obtained analytically. In the stable domain <math altimg='si25.svg'><mrow><msubsup><mi>&#954;</mi><mrow><mi>&#958;</mi></mrow><mn>2</mn></msubsup><mo linebreak='goodbreak'>&gt;</mo><mn>0</mn></mrow></math> with positive squared instantaneous eigenvalues, the Klein&#8211;Gordon modes are treated as a second-order adiabatic system with both level and particle&#8211;antiparticle gaps. Changing the trap-frequency prescription removes the leading coordinate spectral drift after eigenvalue rescaling, but the rescaled eigenvalue is not a locally measured energy.

Algeria

A. Boumali

Kazakhstan

N. Jafari

Türkiye

Manizheh Botshekananfard

Klein–Gordon and Dirac oscillators in a constant-curvature Fock–Lorentz background

We investigate the composite system of a <math altimg='si1.svg'><mrow><mn>2</mn><mo linebreak='goodbreak'>+</mo><mn>1</mn></mrow></math>-dimensional electric charge placed in the background field of a Nielsen&#8211;Olesen flux tube. The explicit analytic results are obtained in the static probe approximation and in the controlled large-separation regime <italic>&#945;x</italic> <inf>0</inf>&#8239;&#8811;&#8239;1, where <math altimg='si2.svg'><mrow><mi>&#945;</mi><mo linebreak='goodbreak'>=</mo><msqrt><mn>2</mn></msqrt><mi>e</mi><mi>a</mi></mrow></math>. We show that the combined configuration carries a non-vanishing field angular momentum, closely analogous to the familiar charge&#8211;monopole systems in <math altimg='si3.svg'><mrow><mn>3</mn><mo linebreak='goodbreak'>+</mo><mn>1</mn></mrow></math> dimensions. We also find that the system possesses a finite field momentum, which appears to violate the center-of-energy theorem. A detailed analysis reveals that this field momentum is compensated by a hidden mechanical momentum carried by the flux tube&#8217;s currents, thereby preserving the center-of-energy theorem.

United States

Anajak Phonchantuek

Douglas Singleton

Nielsen–Olesen flux tube plus electric charge

Tree-level open-string disk integrals obey finite-difference equations in the kinematic invariants, but these equations do not by themselves select a unique solution: they leave an arbitrary periodic matrix factor. We show that finitely many fixed-angle high-energy boundary conditions remove this functional ambiguity at any fixed multiplicity. On generic continuous kinematic rays, the periodic quotient is sampled densely, so exponentially suppressed branch mixing must vanish identically. In split-positive kinematics, the scattering equations identify the relevant high-energy branches. In one fixed, branch-labeled column frame, calibration on one ray and exponential growth bounds on finitely many permuted rays remove the nonconstant periodic ambiguity. The period matrix is then fixed up to a constant right factor, with the remaining freedom removed by any nonsingular normalization, such as the field-theory limit. Thus finite high-energy data complete the kinematic difference equations into a global uniqueness criterion for the Koba–Nielsen period matrix.

China

Ye Zhou (周烨)

High-energy uniqueness of open-string disk integrals

We study the canonical thermodynamics of a one-particle model in which a relativistic oscillator in <italic>d</italic> spatial dimensions is coupled to the finite Laplacian spectrum of a fuzzy two-sphere with angular-momentum cutoff <italic>J<inf>F</inf></italic>; the fuzzy eigenvalues shift the squared mass. In the nonrelativistic window, where the partition function factorises, the internal heat capacity follows the known positive <math altimg='si19.svg'><msup><mi>T</mi><mrow><mo>&#8722;</mo><mn>2</mn></mrow></msup></math> finite-spectrum law. For the full Klein&#8211;Gordon trace at fixed finite <italic>J<inf>F</inf></italic> and fixed model parameters, the fuzzy contribution to the heat capacity is instead negative and decays as <math altimg='si19.svg'><msup><mi>T</mi><mrow><mo>&#8722;</mo><mn>2</mn></mrow></msup></math>, with a mass- and dimension-dependent coefficient; its leading term and, for <italic>d</italic>&#8239;&#8805;&#8239;3, its next-to-leading term are derived and confirmed by exact canonical sums. The two <math altimg='si19.svg'><msup><mi>T</mi><mrow><mo>&#8722;</mo><mn>2</mn></mrow></msup></math> laws hold in disjoint regimes, because the corresponding limits do not commute. For the three-dimensional Dirac oscillator, the unrestricted canonical trace diverges; spinor results are therefore defined only in a conditional ensemble with fixed conserved total angular momentum, which does not regularise or replace the unrestricted trace. No large- <italic>J<inf>F</inf></italic> or commutative limit is considered.

Abdelmalek Boumali

Thermodynamics of relativistic oscillators coupled to a fuzzy-sphere internal spectrum

We study vacuum electron-positron pair production in a spatially uniform bichromatic electric field within the quantum-kinetic framework for fermions. The external background models the superposition of two counterpropagating circularly polarized laser pulses and combines a strong slowly varying component with a weak rapidly oscillating one. We analyze the weak-field multiphoton regime, the strong-field tunneling regime, and their combination corresponding to the dynamically assisted Schwinger effect. Our main focus is on helicity-resolved observables. The main result is that, within the parameter range considered here, the ratio of the momentum distributions for opposite helicities is governed predominantly by the polar angle with respect to the propagation axis and depends only weakly on the momentum magnitude and azimuthal angle. Dynamical assistance enhances not only the total yield but also the helicity asymmetry: right- and left-handed electrons preferentially populate opposite momentum half-spaces. The corresponding asymmetry becomes more pronounced as the weak-field frequency is increased. These results identify a distinct helicity feature of the dynamically assisted Schwinger effect in rotating strong-field backgrounds and provide a compact characterization of the associated helicity-resolved spectra.

Russia

A.I. Baksheev

V.A. Bokhan

Iceland

A. Kudlis

I.A. Aleksandrov

Helicity effects in the dynamically assisted Schwinger mechanism

We prove a no-go theorem for observing a Majorana phase through open two-flavor neutrino oscillations: every completely positive trace-preserving evolution covariant under rotations of the mass-coherence plane is exactly phase blind. This statement applies beyond unital decoherence and includes the standard nonunital phase-covariant qubit semigroups. Within the unital Pauli-GKSL class, covariance is equivalent, in a transverse principal-axis frame, to equality of the two transverse rates. A rate anisotropy supplies an environmental phase reference. If its principal axis has azimuth <italic>&#945;</italic>, the exact finite-time dependence is <math altimg='si31.svg'><mrow><mi>A</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>+</mo><mi>B</mi><mo>(</mo><mi>t</mi><mo>)</mo><mi>cos</mi><mn>2</mn><mo>(</mo><mi>&#981;</mi><mo linebreak='goodbreak'>&#8722;</mo><mi>&#945;</mi><mo>)</mo></mrow></math>; no other phase harmonic occurs in the declared class, and both functions are obtained in closed form. More generally, within the declared two-flavor preparation&#8211;channel&#8211;measurement setting, no fixed completely positive trace-preserving evolution can produce a phase harmonic above the second, and we identify the environmental structure responsible for each admissible harmonic. A rephasing of the mass basis shifts <italic>&#981;</italic> and <italic>&#945;</italic> by the same amount, so only the relative angle <math altimg='si32.svg'><mrow><mi>&#981;</mi><mo linebreak='goodbreak'>&#8722;</mo><mi>&#945;</mi></mrow></math> is convention independent, and the surviving degeneracy is <math altimg='si33.svg'><mrow><mi>&#981;</mi><mo linebreak='goodbreak'>&#8722;</mo><mi>&#945;</mi><mo>&#8764;</mo><mi>&#945;</mi><mo linebreak='goodbreak'>&#8722;</mo><mi>&#981;</mi><mo>&#8764;</mo><mi>&#981;</mi><mo linebreak='goodbreak'>&#8722;</mo><mi>&#945;</mi><mo linebreak='goodbreak'>+</mo><mi>&#960;</mi></mrow></math>. Viewed as a function of baseline and energy, the phase-dependent term is in quadrature with the vacuum oscillation: its exact nodes occur at <math altimg='si34.svg'><mrow><mstyle mathvariant='normal'><mi>&#937;</mi></mstyle><mi>L</mi><mo linebreak='goodbreak'>=</mo><mi>k</mi><mi>&#960;</mi></mrow></math>, while at fixed energy and rates its first maximum obeys <math altimg='si35.svg'><mrow><mi>tan</mi><mstyle mathvariant='normal'><mi>&#937;</mi></mstyle><mi>L</mi><mo linebreak='goodbreak'>=</mo><mstyle mathvariant='normal'><mi>&#937;</mi></mstyle><mo linebreak='goodbreak'>/</mo><mstyle mathvariant='normal'><mi>&#915;</mi></mstyle></mrow></math>. In the weak-decoherence limit, the first node approaches the conventional vacuum first-oscillation maximum and the first maximum approaches half that baseline-to-energy ratio. The result replaces basis-dependent statements about diagonal or off-diagonal dissipators with a sharp physical boundary: open dynamics can render the oscillation probability sensitive to the Majorana phase only relative to an environmental axis defined independently of the mixing convention, and even then cannot determine that phase uniquely.

Atsushi Otsuka

When can decoherence reveal a Majorana phase? A phase-covariance no-go theorem for two-flavor neutrino oscillations

We study neutral massive test particles in a four-dimensional, static black-hole spacetime sourced by an anisotropic fluid with <math altimg='si9.svg'><mrow><msub><mi>p</mi><mi>r</mi></msub><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mi>&#961;</mi><mo linebreak='goodbreak'>/</mo><mrow><mo>(</mo><mn>2</mn><mi>q</mi><mo linebreak='badbreak'>&#8722;</mo><mn>1</mn><mo>)</mo></mrow></mrow></math> and <math altimg='si10.svg'><mrow><msub><mi>p</mi><mi>t</mi></msub><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><msub><mi>p</mi><mi>r</mi></msub></mrow></math>, where <italic>q</italic> is a positive integer. Starting from the metric, we derive the radial effective potential, the energy and angular momentum of circular timelike geodesics, and a dimensionless master equation for marginal stability. Explicit horizon and far-field expansions establish the relevant endpoint signs. We prove that the physically admissible circular-orbit branch has exactly one marginally stable radius, separating unstable from stable circular motion. The master equation is written explicitly for <math altimg='si11.svg'><mrow><mi>q</mi><mo linebreak='goodbreak'>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></mrow></math>, and its Schwarzschild and fixed-radius large- <italic>q</italic> limits are obtained. Numerical solutions illustrate the effective potential and characteristic radii. Radii are expressed in units of the horizon parameter &#966;, and the ADM mass is <math altimg='si12.svg'><mrow><mi>M</mi><mo linebreak='goodbreak'>=</mo><mi>&#966;</mi><mo>(</mo><mn>1</mn><mo linebreak='goodbreak'>+</mo><mn>2</mn><mi>p</mi><mo>)</mo></mrow></math>, where <italic>p</italic> measures the fluid contribution to the metric.

Pakistan

R. Nazer

Z. Yousaf

Massive particles and ISCO with anisotropic model in black hole spacetimes

The Bell-CHSH inequality provides a powerful probe of quantum correlations in relativistic quantum field theory. We study its violation in the vacuum of the free massless Majorana field in 1+1 dimensions using modular wedge localization. By introducing a rapidity variable, we obtain a particularly simple representation of the one-particle Hilbert space as a direct sum of two scalar components, in which the spinor mixing present in previous formulations is eliminated. This allows us to give an explicit algorithm for constructing four bounded, Hermitian, dichotomic operators whose Bell-CHSH expectation value can be made arbitrarily close to the Tsirelson bound ( <math altimg='si1.svg'><mrow><mn>2</mn><msqrt><mn>2</mn></msqrt></mrow></math>). We derive the resulting Bell-CHSH functional in terms of the modular spectral weight and provide a semi-analytic family of test functions that realizes this near-saturation explicitly.

Brazil

J.R. Apfata

J.G.A. Caribé

S.P. Sorella

More on Majorana fields, modular localization and near-saturation of the Tsirelson bound

<list id='lst0001'><list-item id='lstitem0001'><label>&#8226;</label><para id='p0001'>The thermodynamics of the spin-<italic>s</italic> XXZ Weiss model is solved via SU(2) multiplicities.</para></list-item><list-item id='lstitem0002'><label>&#8226;</label><para id='p0002'>The level degeneracies are closed-form order-<math altimg='si18.svg'><mrow><mo>(</mo><mn>2</mn><mi>s</mi><mo linebreak='goodbreak'>+</mo><mn>1</mn><mo>)</mo></mrow></math> generalized binomials.</para></list-item><list-item id='lstitem0003'><label>&#8226;</label><para id='p0003'>Critical <math altimg='si19.svg'><mrow><msub><mi>T</mi><mi>c</mi></msub><mo linebreak='goodbreak'>=</mo><mi>J</mi><mi>s</mi><mrow><mo>(</mo><mi>s</mi><mo linebreak='badbreak'>+</mo><mn>1</mn><mo>)</mo></mrow><mo linebreak='goodbreak'>/</mo><mn>3</mn></mrow></math> is &#916;-independent; the transition is second order.</para></list-item><list-item id='lstitem0004'><label>&#8226;</label><para id='p0004'>For &#916;&#8239;&lt;&#8239;1, an easy-plane dome replaces the isotropic first-order line.</para></list-item><list-item id='lstitem0005'><label>&#8226;</label><para id='p0005'>Exact finite-size sums up to 10<sup>4</sup> spins validate the asymptotics.</para></list-item></list>