Mathematical Physics Papers of the Week

This study presents a novel hybrid framework that integrates Physics-Informed Neural Networks (PINNs) with boosting methods to enhance the accuracy and robustness of solutions for Lane-Emden type differential equations.

Here we use the topology of the space of complex Hadamard matrices, which describe transitions between MUBs, to characterize all sets in dimension six.

We develop a common framework for classical simulation of boson and fermion sampling under thermal loss, including pure loss.

In this paper, a compact high-order gas-kinetic scheme (HGKS) is developed for compressible arbitrary Lagrangian-Eulerian (ALE) computations on three-dimensional unstructured meshes.

We study polynuclear growth (PNG) on the half-line with Poisson nucleations in the bulk and at the boundary.

We show that the vacuum partition function of the $q$-deformed oscillator \[ L_q(z):= \langle0|e^{zT_q}|0\rangle, \qquad T_q := \mathsf{a}_q + \mathsf{a}_q^* \] satisfies the Lee-Yang property, i.e., all zeros of $L_q$ lie on the imaginary line for all $q\in[-1, 1)$, proving the conjectures of Okuyama'23.

We develop a numerical conformal bootstrap for two-dimensional CFTs with $c>1$ based on Virasoro conformal blocks, computed with Zamolodchikov's recursion and optimal polynomial interpolation.

We construct an exact map between continuum fermion fields and lattice fields in 1+1 dimensions.

We provide an explicit scheme to realize a quantum memory in any 2D non-chiral topological order.

In this work, we introduce the structured pseudospectrum into black hole perturbation theory.

We introduce spectral symmetry fingerprints (SymFP), which enable discrete point-group identification through rank-template matching and continuous symmetry analysis by quantifying spectral energy beyond target rank constraints.

In this paper, we study anomalies of $d$-dimensional topological quantum field theories (TQFTs) coupled to parameter spaces and their implications for ground-state degeneracies.

We characterize the exact error-exponent trade-off in binary quantum hypothesis testing with a rejection option for faithful states on a finite-dimensional Hilbert space.

In this paper, we study Egorov's theorem for Laplacian eigenfunctions on compact hyperbolic surfaces in Zelditch's quantization.

We derive a trajectory-level decomposition of total entropy production that cleanly separates transient state relaxation, housekeeping heat, and external protocol driving.

For $m\otimes n$ systems with $n\ge m\ge3$, we determine the exact maximum purity of absolutely positive partial transpose (APPT) states and the unique maximizing ordered spectrum when $n\ge2m^2-4$ for even $m$ or $n\ge2m^2-m-4$ for odd $m$.

For every qutrit--qudit system $\mathbb{C}^3\otimes\mathbb{C}^n$, $n\ge3$, we prove that the maximum purity is the same for absolutely separable and APPT states and equals $\max\{(3n+8)/(3n+2)^2,\,3/(8n)\}$.

We present a systematic framework for gauging continuous symmetries, and show that the Schur-Weyl duality arises naturally as a realization of this construction with open boundary conditions.

We provide a counterexample to the weak Gibbs and regularity conjectures.

Another approach, using symmetry spans, which specify two embeddings of a common symmetry into two larger symmetries, was proposed by the authors. In this work, we show that a symmetry span can enforce gaplessness even when both larger symmetries are invertible and non-anomalous: each alone admits a trivially gapped phase, but because the embeddings differ by a twist associated with a symmetry-protected topological phase, the symmetry they generate admits no gapped phase with finitely many ground states.