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Conformal prediction offers a practical framework for distribution-free uncertainty quantification, providing finite-sample coverage guarantees under relatively mild assumptions on data exchangeability. However, these assumptions cease to…
The paper presents a versatile framework for solids which undergo nonisothermal processes with irreversibly changing microstructure at large strains. It outlines rate-type and incremental variational principles for the full thermomechanical…
We derive a Debye-H\"uckel-like model of the electric ion-ion interaction for non-constant dielectric susceptibility, which does not depend on any kind of charging process due to its foundation in the general framework of non-equilibrium…
Conformal symmetry provides a systematic approximation to QCD in both its perturbative and nonperturbative domains. One can use the AdS/CFT correspondence between Anti-de Sitter space and conformal gauge theories to obtain an analytically…
A scattering model is developed for ultracold molecular collisions, which allows inelastic processes, chemical reactions, and complex formation to be treated in a unified way. All these scattering processes and various combinations of them…
This paper develops a unified analytical framework for determinant identities under finite-rank perturbations of square matrices that remains valid without invertibility assumptions. In contrast to classical inverse-based formulations, the…
Even though the Hubbard model is one of the most fundamental models of highly correlated electrons, analytical and numerical data describing its thermodynamics at nonzero magnetization are relatively scarce. We present a detailed…
By combining different ideas, a general and efficient protocol to deal with discontinuous phase transitions at low temperatures is proposed. For small $T$'s, it is possible to derive a generic analytic expression for appropriate order…
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
Models of complex dynamical systems like the Earth's climate often involve large numbers of uncertain parameters. Comprehensive exploration of the parameter space is typically prohibitive due to excessive computational costs. Systematic…
Inflation is an early period of accelerated cosmic expansion, thought to be sourced by high energy physics. A key task today is to use the influx of increasingly precise observational data to constrain the plethora of inflationary models…
The dynamical equations of an electromagnetic field coupled with a conducting material are studied. The properties of the interaction are described by a classical field theory with tensorial material laws in space-time geometry. We show…
A generalised form of time-translation-invariance permits to re-derive the known generic phenomenology of ageing, which arises in classical many-body systems after a quench from an initially disordered system to a temperature $T\leq T_c$,…
We rederive the finite size scaling formula for the apparent critical temperature by using Mean Field Theory for the Ising Model above the upper critical dimension. We have also performed numerical simulations in five dimensions and our…
In this work we analyze the universal scaling functions and the critical exponents at the upper critical dimension of a continuous phase transition. The consideration of the universal scaling behavior yields a decisive check of the value of…
It has previously been pointed out that the coexistence of infinite-range and short-range interactions causes a system to have a phase transition of the mean-field universality class, in which the cluster size is finite even at the critical…
Quantum phase transitions occur at zero temperature and involve the appearance of long-range correlations. These correlations are not due to thermal fluctuations but to the intricate structure of a strongly entangled ground state of the…
Conformal Prediction offers a powerful framework for quantifying uncertainty in machine learning models, enabling the construction of prediction sets with finite-sample validity guarantees. While easily adaptable to non-probabilistic…
A geometrically nonlinear continuum mechanical theory is formulated for deformation and failure behaviors of amorphous polymers. The model seeks to capture material response over a range of loading rates, temperatures, and stress states…
We apply the fidelity metric approach to analyze two recently introduced models that exhibit a quantum phase transition to a topologically ordered phase. These quantum models have a known connection to classical statistical mechanical…