Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.18980

Transmission representation of the Josephson free energy beyond the short-junction limit

Anton R. Akhmerov
View original source ↗Read source document ↗Export metadata ↓

Abstract

Beenakker's formula, $U(φ)-U(0)=Δ\sum_n\bigl(1-\sqrt{1-τ_n\sin^2(φ/2)}\bigr)$, expresses the zero-temperature energy-phase relation of a short Josephson junction through its normal-state transmission eigenvalues. We generalize this transmission representation beyond the short-junction limit and express the phase-dependent free energy of a time-reversal-symmetric $s$-wave junction as a Matsubara sum over channels with frequency-dependent transmissions. The representation constrains the small-phase expansion of the free energy. In particular, we prove that the normalized ratio of its quartic and quadratic coefficients satisfies $-1\leα_r\le7/80$ at finite temperature. We also construct a four-site junction with $α_r>0$, which disproves the conjectured upper bound $α_r\le0$. So that these results can be trusted without repeating the derivations, every numbered equation is formally verified in the Lean proof assistant.

Explore related subjects

cond-mat.mes-hallcond-mat.supr-con

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Anton R. Akhmerov. 2026-10-13. Transmission representation of the Josephson free energy beyond the short-junction limit. https://arxiv.org/abs/2610.18980

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Theory of phonon angular momentum transport across a smooth crystal interface

We theoretically elucidate the transfer of phonon angular momentum by acoustic modes across a smooth interface between crystals. We analyze this process, which is difficult to describe with the conventional acoustic mismatch model, using a reformulated boundary condition and the Boltzmann theory. For an interface between a chiral and an achiral crystal, our analysis reveals that thermal gradients in the chiral crystal induce angular momentum, which diffuses into the achiral crystal even without heat flow. Notably, within an approximation retaining the chirality-induced population imbalance, the density of angular momentum can be enhanced near the interface. These findings advance our understanding of phonon transport and its interplay with electron spins.

cond-mat.mes-hall↗
arXiv2026

Boundary condition for phonon distribution functions at a smooth crystal interface and interfacial angular momentum transfer

We theoretically elucidate the boundary conditions for phonon distribution functions of long-wavelength acoustic phonons at smooth crystal interfaces. We first derive boundary conditions that fully incorporate reflection, transmission, and mode conversion. We obtain these conditions for phonons from those for classical lattice vibrations, using the correspondence between the quantum and classical descriptions. This formulation provides a theoretical foundation for the acoustic mismatch model, widely used to analyze Kapitza resistance. We then refine the boundary conditions to include spatial dependence parallel to the interface. The refined form captures transverse shifts of elastic wave packets, analogous to the optical Imbert--Fedorov shift, and ensures conservation of total angular momentum. Consequently, circularly polarized phonons carrying spin angular momentum (SAM) generate phonon orbital angular momentum (OAM) at the interface. We analytically determine the spatial profile of this OAM and demonstrate that SAM and OAM are both involved in the interfacial diffusion of chiral phonons. Our theory provides concise boundary conditions for phonons, with applications ranging from heat transport to phonon angular momentum transport.

cond-mat.mes-hall↗
arXiv2026

Cooperative Boundary Switching of Mesoscopic Real Spectra in a Non-Hermitian Chain Family

At fixed bulk criticality, every fixed nonsingular real single-end potential preserves a growing local population of real eigenvalues in an open analytic family of non-Hermitian chains. An open region of two-end real potentials removes this population. A boundary-amplitude criterion fixes the minimum number of controlled ends. The population grows as $\sqrt N$, where $N$ is chain length, although its normalized spectral weight vanishes and the local limiting bands remain unchanged. For a representative chain's four zero-detuning settings, an independent passive Hermitian double chain converts this distinction into separated resonances at one fixed local port under a common coupling scan at fixed probe carrier. Its absolute reflection contrast and stability margin both scale as $N^{-1}$, with explicit sufficient resource budgets. Boundary amplitudes thus fix a minimum control requirement that limiting bands and thermodynamic spectral density do not specify.

cond-mat.mes-hall↗