## Search

Now showing items 1-10 of 12

#### On discrete Wigner transforms

In this work, we derive a discrete analog of the Wigner transform over the
space $(\mathbb{C}^p)^{\otimes N}$ for any prime $p$ and any positive integer
$N$. We show that the Wigner transform over this space can be constructed ...

#### Frozen Gaussian approximation with surface hopping for mixed quantum-classical dynamics: A mathematical justification of fewest switches surface hopping algorithms

(2017-04-23)

We develop a surface hopping algorithm based on frozen Gaussian approximation for
semiclassical matrix Schr\"odinger equations, in the spirit of Tully's fewest switches
surface hopping method. The algorithm is asymptotically ...

#### Detecting localized eigenstates of linear operators

(2017-11-30)

We describe a way of detecting the location of localized eigenvectors of a linear
system $Ax = \lambda x$ for eigenvalues $\lambda$ with $|\lambda|$ comparatively large.
We define the family of functions $f_{\alpha}: \left\{1.2. ...

#### Riesz Energy on the Torus: Regularity of Minimizers

(2017-11-30)

We study sets of $N$ points on the $d-$dimensional torus $\mathbb{T}^d$ minimizing
interaction functionals of the type \[ \sum_{i, j =1 \atop i \neq j}^{N}{ f(x_i -
x_j)}. \] The main result states that for a class of functions ...

#### A Quantum Kinetic Monte Carlo Method for Quantum Many-body Spin Dynamics

(2017-11-30)

We propose a general framework of quantum kinetic Monte Carlo algorithm, based on
a stochastic representation of a series expansion of the quantum evolution. Two approaches
have been developed in the context of quantum many-body ...

#### Fractional stochastic differential equations satisfying fluctuation-dissipation theorem

(2017-04-23)

We consider in this work stochastic differential equation (SDE) model for particles
in contact with a heat bath when the memory effects are non-negligible. As a result
of the fluctuation-dissipation theorem, the differential ...

#### Thermodynamic Limit of Crystal Defects with Finite Temperature Tight Binding

(2017-04-23)

We consider a tight binding model for localised crystalline defects with electrons
in the canonical ensemble (finite electronic temperature) and nuclei positions relaxed
according to the Born--Oppenheimer approximation. ...

#### A Mathematical Theory of Optimal Milestoning (with a Detour via Exact Milestoning)

(2017-04-23)

Milestoning is a computational procedure that reduces the dynamics of complex systems
to memoryless jumps between intermediates, or milestones, and only retains some information
about the probability of these jumps and the ...

#### A Variation on the Donsker-Varadhan Inequality for the Principial Eigenvalue

(2017-04-23)

The purpose of this short note is to give a variation on the classical Donsker-Varadhan
inequality, which bounds the first eigenvalue of a second-order elliptic operator
on a bounded domain $\Omega$ by the largest mean first ...

#### Lindblad equation and its semi-classical limit of the Anderson-Holstein model

(2017-04-23)

For multi-level open quantum system, the interaction between different levels could
pose challenge to understand the quantum system both analytically and numerically.
In this work, we study the approximation of the dynamics ...