Related papers: Smooth Boundary Conditions For Quantum Lattice Sys…
Rarely noted paradoxes and their resolution lead to non-Hermitian behaviors due to boundary terms, even for closed systems and with real potentials. The role played by these non-Hermiticities on quantum mechanical uncertainty relations is…
In this letter, we report our systematic construction of the lattice Hamiltonian model of topological orders on open surfaces, with explicit boundary terms. We do this mainly for the Levin-Wen stringnet model. The full Hamiltonian in our…
We use classes of Hilbert lattice equations for an alternative representation of Hilbert lattices and Hilbert spaces of arbitrary quantum systems that might enable a direct introduction of the states of the systems into quantum computers.…
Smoothed analysis of complexity bounds and condition numbers has been done, so far, on a case by case basis. In this paper we consider a reasonably large class of condition numbers for problems over the complex numbers and we obtain…
Continuum solvation methods can provide an accurate and inexpensive embedding of quantum simulations in liquid or complex dielectric environments. Notwithstanding a long history and manifold applications to isolated systems in open boundary…
This article investigates an energy balance model coupled to the primitive equations by a dynamic boundary condition with and without noise on the boundary. It is shown that this system is globally strongly well-posed both in the…
In quantum control, quantum speed limits provide fundamental lower bounds on the time that is needed to implement certain unitary transformations. Using Lie algebraic methods, we link these speed limits to symmetries of the control…
We propose a new way to implement Dirichlet boundary conditions for complex shapes using data from a single node only, in the context of the lattice Boltzmann method. The resulting novel method exhibits second-order convergence for the…
A Hamiltonian lattice formulation of lattice gauge theories opens the possibility for quantum simulations of the non-perturbative dynamics of QCD. By parametrizing the gauge invariant Hilbert space in terms of plaquette degrees of freedom,…
The stochastic limit for the system of spins interacting with a boson field is investigated. In the finite volume an application of the stochastic golden rule shows that in the limit the dynamics of a quantum system is described by a…
Systems with non-Hermitian skin effects are very sensitive to the imposed boundary conditions and lattice size, and thus an important question is whether non-Hermitian skin effects can survive when deviating from the open boundary…
This paper considers the problem of robust stability for a class of uncertain quantum systems subject to unknown perturbations in the system Hamiltonian. Some general stability results are given for different classes of perturbations to the…
Several proposals for quantum computation utilize a lattice type architecture with qubits trapped by a periodic potential. For systems undergoing many body interactions described by the Bose-Hubbard Hamiltonian, the ground state of the…
Hamilton's equations of motion are local differential equations and boundary conditions are required to determine the solution uniquely. Depending on the choice of boundary conditions, a Hamiltonian may thereby describe several different…
This dissertation presents and prove the viability of a non-standard method for controlling the state of a quantum system by modifying its boundary conditions instead of relying on the action of external fields. The standard approach to…
In geometry processing, smoothness energies are commonly used to model scattered data interpolation, dense data denoising, and regularization during shape optimization. The squared Laplacian energy is a popular choice of energy and has a…
Quantum systems can show qualitatively new forms of behavior when they are driven by fast time-periodic modulations. In the limit of large driving frequency, the long-time dynamics of such systems can often be described by a…
We consider the initial-boundary value problem for systems of quasilinear wave equations on domains of the form $[0,T] \times \Sigma$, where $\Sigma$ is a compact manifold with smooth boundaries $\partial\Sigma$. By using an appropriate…
This paper proposes a new method, in the frequency domain, to define absorbing boundary conditions for general two-dimensional problems. The main feature of the method is that it can obtain boundary conditions from the discretized equations…
Leveraging the techniques found in the literature on Quantum Equilibration for finite dimensional systems, we develop the theory of Quantum Equilibration for the case of infinite-dimensional systems, particularly the cases where the…