Related papers: Time evolution formalism in the complex scaling me…
Over the past decade, Finite Element Method (FEM) has served as a foundational numerical framework for approximating the terms of Time Series Expansion (TSE) as solutions to transient Partial Differential Equation (PDE). However, the…
Many astrophysical simulations involve extreme dynamic range of timescales around 'special points' in the domain (e.g. black holes, stars, planets, disks, galaxies, shocks, mixing interfaces), where processes on small scales couple strongly…
Earth introduces strong attenuation and dispersion to propagating waves. The time-fractional wave equation with very small fractional exponent, based on Kjartansson's constant-Q theory, is widely recognized in the field of geophysics as a…
Crystallization, a fundamental phase transition process governing material formation in natural and industrial contexts, involves the spontaneous emergence of long-range structural order from disordered phases. This long-range periodicity…
We have developed a universal method to form the reference signal for the stabilization of arbitrary atomic clocks based on Ramsey spectroscopy. Our approach uses an interrogation scheme of the atomic system with two different Ramsey…
The field of deep-learning-based ECG analysis has been largely dominated by convolutional architectures. This work explores the prospects of applying the recently introduced structured state space models (SSMs) as a particularly promising…
A method is presented that, when used in conjunction with single molecule experimental techniques, allows for the extraction of rates and mechanical properties of a biomolecule undergoing transitions between mechanically distinct states.…
In this work, motivated by the sine-square deformation (SSD) for (1+1)-dimensional quantum critical systems, we study the non-equilibrium quantum dynamics of a conformal field theory (CFT) with SSD, which was recently proposed to have…
We present a quantum algorithm for the dynamical simulation of time-dependent Hamiltonians. Our method involves expanding the interaction-picture Hamiltonian as a sum of generalized permutations, which leads to an integral-free Dyson series…
An established strategy for material modeling is provided by energy-based principles such that evolution equations in terms of ordinary differential equations can be derived. However, there exist a variety of material models that also need…
In this paper, we present a proof-of-concept quantum algorithm for simulating time-dependent Hamiltonian evolution by reducing the problem to simulating a time-independent Hamiltonian in a larger space using a discrete clock Hamiltonian…
The interplay between interactions and quenched disorder can result in rich dynamical quantum phenomena far from equilibrium, particularly when many-body localization prevents the system from full thermalization. With the aim of tackling…
Decoherence of a center spin or qubit in a spin bath is essentially determined by the many-body bath evolution. We develop a cluster-correlation expansion (CCE) theory for the spin bath dynamics relevant to the qubit decoherence problem. A…
We describe an algorithm to simulate time evolution using the Multi-scale Entanglement Renormalization Ansatz (MERA) and test it by studying a critical Ising chain with periodic boundary conditions and with up to L ~ 10^6 quantum spins. The…
A common approach to studying high-dimensional systems with emergent low-dimensional behavior is based on lift-evolve-restrict maps (called equation-free methods): first, a user-defined lifting operator maps a set of low-dimensional…
We consider a class of space-time coupled evolution equations (CEEs), obtained by a subordination of the heat operator. Our CEEs reformulate and extend known governing equations of non-Markovian processes arising as scaling limits of…
A new theoretical method is proposed to describe the ground and excited cluster states of atomic nuclei. The method utilizes the equation-of-motion of the Gaussian wave packets to generate the basis wave functions having various cluster…
A continuum theory is used to predict scaling laws for the morphological relaxation of crystal surfaces in two independent space dimensions. The goal is to unify previously disconnected experimental observations of decaying surface…
We analize the relational quantum evolution of generally covariant systems in terms of Rovelli's evolving constants of motion and the generalized Heisenberg picture. In order to have a well defined evolution, and a consistent quantum…
A method for numerical approximation of a new class of fractional parabolic stochastic evolution equations is introduced and analysed. This class of equations has recently been proposed as a space-time extension of the SPDE-method in…