arXiv research

In this paper, we consider the generalized lambda constant and the existence of ground states of the generalized Perelman's W-functional from a variational formulation. One result is concerned with the estimation of the generalized $λ$ constant. The other results are about the existence of ground states of generalized …

Study on ground states of semilinear elliptic equations with various potential wells.

The paper analyzes neural networks for solving high-dimensional Schrödinger eigenvalue problems.

The paper identifies magnetic ground states and their role in determining the conformal class of a surface.

We provide some new results of the ground state of quantum layers.

New method uses kernel methods to approximate ground states of quantum Hamiltonians efficiently.

New method uses adiabatic principles to improve ground-state preparation in quantum computing.

Classification of ground state solutions to critical Dirac equation on spheres.

Study uses supervised learning to classify quantum phases with limited measurements.

Study on existence of ground states for free energy on hyperbolic space.

CLuP achieves near optimal ground state energies for positive and negative Hopfield models.

Study on existence of ground states on curved spaces with conditions on potential growth.

Quantum annealing improves VB inference, avoiding local minima.

New pseudo-Hermitian models from non-semisimple TQFTs.

New algorithm nearly achieves ground state free energy of SK model.

We prove sharp pointwise decay estimates for critical Dirac equations on $\mathbb{R}^n$ with $n\geq 2$. They appear for instance in the study of critical Dirac equations on compact spin manifolds, describing blow-up profiles, and as effective equations in honeycomb structures. For the latter case, we find excited state…

Study heat profiles and eigenfunctions using Brownian motion.

Paper introduces untangling number to quantify 3-periodic tangle complexity.

Paper defines untangling number to measure entanglement complexity in 3-periodic networks.

Existence of Q-processes for Brownian motion on hyperbolic spaces with Poissonian potentials shown.

Statistical learning theory provides bounds of the generalization gap, using in particular the Vapnik-Chervonenkis dimension and the Rademacher complexity. An alternative approach, mainly studied in the statistical physics literature, is the study of generalization in simple synthetic-data models. Here we discuss the c…

Combining insights from machine learning and quantum Monte Carlo, the stochastic reconfiguration method with neural network Ansatz states is a promising new direction for high-precision ground state estimation of quantum many-body problems. Even though this method works well in practice, little is known about the learn…

Smooth solutions and classification of Dirac-Einstein equations on 3-manifolds.

Improves VQAs by balancing classical and quantum training resources.

An algorithmic limit of compressed sensing or related variable-selection problems is analytically evaluated when a design matrix is given by an overcomplete random matrix. The replica method from statistical mechanics is employed to derive the result. The analysis is conducted through evaluation of the entropy, an expo…

Solve Painleve VI to relate instanton bundles.

In this note we make an attempt to compare a cohomological theory of Hilbert spaces of ground states in the ${\cal N}=(2,2)$ 2d Landau-Ginzburg theory in models describing link embeddings in ${\mathbb{R}}^3$ to Khovanov and Khovanov-Rozansky homologies. To confirm the equivalence we exploit the invariance of Hilbert sp…

In this paper, we proved the quantum layer over a surface which is ruled outside a compact set, asymptotically flat but not totally geodesic admits ground states.

Study small perturbations on low energy Laplace eigenfunctions.

This note is devoted to Keller-Lieb-Thirring spectral estimates for Schrödinger operators on infinite cylinders: the absolute value of the ground state level is bounded by a function of a norm of the potential. Optimal potentials with small norms are shown to depend on a single variable. The proof is a perturbation arg…

Study of Dirac equation with non-local nonlinearity on spheres.

We consider a bounded domain $Ω$ of $\mathbb{R}^N$, $N\geq 3$, and $h$ a continuous function on $Ω$. Let $Γ$ be a closed curve contained in $Ω$. We study existence of positive solutions $u\in H^1_0(Ω)$ to the equation $-Δu+h u=ρ^{-σ}_Γu^{2^*_σ-1} \qquad \textrm{ in } Ω$ where $2^*_σ:=\frac{2(N-σ)}{N-2}$, $σ\in (0,2)…

Enhanced VMC methods improve neural wavefunction training.

Proves uniqueness of solutions for a nonlocal Liouville equation with finite Q-curvature.

In this paper, we prove the existence of the free boundary minimal hypersurface of least area in compact manifolds with boundary. Such hypersurface can be viewed as the ground state of the volume spectrum introduced by Gromov. Moreover, we characterize the orientation and Morse index of them.

Freedman proposes a family of Hamiltonians $H_{0,l}$ which define quantum loop gas models on any celluated compact surface. We study the simplest nontrivial cases: celluations of the torus. Our numerical data support Freedman's conjecture, but the conjectured space of ground states does not come out in full.

We present a theoretical analysis of Maximum a Posteriori (MAP) sequence estimation for binary symmetric hidden Markov processes. We reduce the MAP estimation to the energy minimization of an appropriately defined Ising spin model, and focus on the performance of MAP as characterized by its accuracy and the number of s…

New method uses quantum computing to process classical data efficiently.

In this paper, we study the spectrum of quantum tubes. Under certain intrinsic assumptions of the asymptotically flat submanifold of the Euclidean space, we prove the existence of the ground state of the quantum tube. The work is a generalization of Duclos, Exner and Krejcirik (CMP, 223(1), 13-28, 2001) and ourselves(m…

Study Berry connections for 2d GLSMs, linking to cohomology theories.

We give polynomial-time algorithms for the exact computation of lowest-energy (ground) states, worst margin violators, log partition functions, and marginal edge probabilities in certain binary undirected graphical models. Our approach provides an interesting alternative to the well-known graph cut paradigm in that it …

Researchers study fractional porous medium equation on hyperbolic space.

Existence of a complex structure on the $6$ dimensional sphere is proved in this paper. The proof is based on re-interpreting a hypothetical complex structure as a classical ground state of a Yang--Mills--Higgs-like theory on $S^6$. This classical vacuum solution is then constructed by Fourier expansion (dimensional re…

We prove that Nelson's massless scalar field model is infrared divergent in three dimensions. In particular, the Nelson Hamiltonian and the Hamiltonian obtained from Euclidean quantization are not unitarily equivalent. In contrast, for dimensions higher than three the Nelson Hamiltonian has a unique ground state in Foc…

In this article we use the Mean-Variance Model in order to measure the current market state. In our study we take the approach of detecting the overall alignment of portfolios in the spin picture. The projection to the ground-states enables us to use physical observables in order to describe the current state of the ex…

We present some applications of ideas from partial differential equations and differential geometry to the study of difference equations on infinite graphs. All operators that we consider are examples of "elliptic operators" as defined by Y. Colin de Verdiere. For such operators, we discuss analogs of inequalities of C…

We consider the problem of rational decision making in the presence of nonlinear constraints. By using tools borrowed from spin glass and random matrix theory, we focus on the portfolio optimisation problem. We show that the number of ``optimal'' solutions is generically exponentially large: rationality is thus de fact…

Study Dirac-Einstein equations on manifolds with boundary, focusing on constant volume and chiral conditions.