Monday, April 22 |
07:00 - 08:45 |
Breakfast ↓ Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building. (Vistas Dining Room) |
08:45 - 09:00 |
Introduction and Welcome by BIRS Staff ↓ A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions. (TCPL 201) |
09:00 - 10:00 |
Graham Worth: Solving the time-dependent Schroedinger equations using variational Gaussian Wavepackets: Advantages and problems (TCPL 201) |
10:00 - 10:30 |
Coffee Break (TCPL Foyer) |
10:30 - 11:05 |
Jiri Vanicek: Family of Gaussian wavepacket dynamics methods from the perspective of a nonlinear Schrödinger equation ↓ Many approximate solutions of the time-dependent Schrödinger equation can be formulated as exact solutions of a nonlinear Schrödinger equation with an effective Hamiltonian operator depending on the state of the system. We show that Heller's thawed Gaussian approximation, Coalson and Karplus's variational Gaussian approximation, and other Gaussian wavepacket dynamics methods fit into this framework if the effective potential is a quadratic polynomial with state-dependent coefficients. We study such a nonlinear Schrödinger equation in full generality: we derive general equations of motion for the Gaussian's parameters, demonstrate the time reversibility and norm conservation, and analyze conservation of the energy, effective energy, and symplectic structure. We also describe efficient, high-order geometric integrators for the numerical solution of this nonlinear Schrödinger equation. The general theory is illustrated by examples of this family of Gaussian wavepacket dynamics, including the variational and nonvariational thawed and frozen Gaussian approximations, and their special limits based on the global harmonic, local harmonic, single-Hessian, local cubic, and local quartic approximations for the potential energy. We also propose a new method by augmenting the local cubic approximation with a single fourth derivative. Without substantially increasing the cost, the proposed "single-quartic" variational Gaussian approximation improves the accuracy over the local cubic approximation and, at the same time, conserves both the effective energy and symplectic structure, unlike the much more expensive local quartic approximation. Most results are presented in both Heller's and Hagedorn's parametrizations of the Gaussian wavepacket. In my talk, I will accompany the theory with applications of the different versions of Gaussian wavepacket dynamics to the calculation of vibrationally resolved electronic spectra as well as with numerical examples demonstrating the geometric properties and fast convergence of the integrators.
[1] J. Chem. Phys. 159, 014114 (2023) (TCPL 201) |
11:05 - 11:40 |
Chao Yang: Numerical Methods for Simulating Non-equilibrium Quantum Dynamics ↓ A practical way to compute time-dependent observables of a non-equilibrium quantum many-body system is to focus on the single-particle Green's function defined on the Keldysh contour. The equation of motion satisfied by such a Green's function is a set of nonlinear integro-differential equations called the Kadanoff-Baym equations. We will describe numerical methods for solving this type of equations and show how to use dynamic mode decomposition and recurrent neural networks to reduce computational complexity. (TCPL 201) |
11:30 - 13:00 |
Lunch ↓ Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building. (Vistas Dining Room) |
11:40 - 12:15 |
Buyang Li: Numerical approximation of discontinuous solutions of the semilinear wave equation ↓ A high-frequency recovered fully discrete low-regularity integrator is constructed to approximate rough and possibly discontinuous solutions of the semilinear wave equation. The proposed method, with high-frequency recovery techniques, can capture the discontinuities of the solutions correctly without spurious oscillations and approximate rough and discontinuous solutions with a higher convergence rate than pre-existing methods. Rigorous analysis is presented for the convergence rates of the proposed method in approximating solutions such that (u,∂tu)∈C([0,T];Hγ×Hγ−1) for γ∈(0,1]. For discontinuous solutions of bounded variation in one dimension (which allow jump discontinuities), the proposed method is proved to have almost first-order convergence under the step size condition τ∼N−1, where τ and N denote the time step size and the number of Fourier terms in the space discretization, respectively. Numerical examples are presented in both one and two dimensions to illustrate the advantages of the proposed method in improving the accuracy in approximating rough and discontinuous solutions of the semilinear wave equation. The numerical results are consistent with the theoretical results and show the efficiency of the proposed method. (TCPL 201) |
14:00 - 14:35 |
Daniel Peterseim: Quantum Solver for Partial Differential Equations ↓ This talk presents a quantum algorithm for the solution of prototypical second-order linear elliptic partial differential equations discretized by d-linear finite elements on Cartesian grids of a bounded d-dimensional domain. The core of the construction is a multilevel BPX preconditioner, which transforms the linear system into a well-conditioned one, essential for the use of quantum computers. We show that suitable functionals of the solution can be computed on a quantum computer up to tolerance tol with complexity proportional to 1/tol, neglecting logarithmic terms. For a fixed physical dimension d, this complexity is comparable to the optimal complexity of the one-dimensional problem and improves existing results. We also present a quantum circuit that implements the algorithm and report some basic numerical results. (TCPL 201) |
14:45 - 15:05 |
Group Photo ↓ Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo! (TCPL Foyer) |
15:00 - 15:30 |
Coffee Break (TCPL Foyer) |
15:30 - 15:40 |
Sergio Blanes: Shortly about my reasearch interests ↓ The main idea of this meeting is, of course, to share our research interests, latest achievements and learn from our colleagues about their latest discoveries. All we are looking forward to listening to the interesting talks and to having chats during our free time.
This short, "5-10-minute" introductory talk is intended to help us in establishing new research connections or maybe even collaborations! (TCPL 201) |
15:40 - 15:50 |
Silvia Cardenas Lopez: Shortly about my research interests ↓ The main idea of this meeting is, of course, to share our research interests, latest achievements and learn from our colleagues about their latest discoveries. All we are looking forward to listening to the interesting talks and to having chats during our free time.
This short, "5-10-minute" introductory talk is intended to help us in establishing new research connections or maybe even collaborations! (TCPL 201) |
15:50 - 16:00 |
Antonia Freibert: Shortly about my research interests ↓ The main idea of this meeting is, of course, to share our research interests, latest achievements and learn from our colleagues about their latest discoveries. All we are looking forward to listening to the interesting talks and to having chats during our free time.
This short, "5-10-minute" introductory talk is intended to help us in establishing new research connections or maybe even collaborations! (TCPL 201) |
16:00 - 16:10 |
Niccolò Geracitano: Shortly about my research interests ↓ The main idea of this meeting is, of course, to share our research interests, latest achievements and learn from our colleagues about their latest discoveries. All we are looking forward to listening to the interesting talks and to having chats during our free time.
This short, "5-10-minute" introductory talk is intended to help us in establishing new research connections or maybe even collaborations! (TCPL 201) |
16:10 - 16:20 |
Ilya Kuprov: Shortly about my research interests ↓ The main idea of this meeting is, of course, to share our research interests, latest achievements and learn from our colleagues about their latest discoveries. All we are looking forward to listening to the interesting talks and to having chats during our free time.
This short, "5-10-minute" introductory talk is intended to help us in establishing new research connections or maybe even collaborations! (TCPL 201) |
16:20 - 16:30 |
Simen Kvaal: Shortly about my research interests ↓ The main idea of this meeting is, of course, to share our research interests, latest achievements and learn from our colleagues about their latest discoveries. All we are looking forward to listening to the interesting talks and to having chats during our free time.
This short, "5-10-minute" introductory talk is intended to help us in establishing new research connections or maybe even collaborations! (TCPL 201) |
16:30 - 16:40 |
Caroline Lasser: Shortly about my research interests ↓ The main idea of this meeting is, of course, to share our research interests, latest achievements and learn from our colleagues about their latest discoveries. All we are looking forward to listening to the interesting talks and to having chats during our free time.
This short, "5-10-minute" introductory talk is intended to help us in establishing new research connections or maybe even collaborations! (TCPL 201) |
16:40 - 16:50 |
Marcin Marciniak: Shortly about my research interests ↓ The main idea of this meeting is, of course, to share our research interests, latest achievements and learn from our colleagues about their latest discoveries. All we are looking forward to listening to the interesting talks and to having chats during our free time.
This short, "5-10-minute" introductory talk is intended to help us in establishing new research connections or maybe even collaborations! (TCPL 201) |
16:50 - 17:00 |
Łukasz Płociniczak: Shortly about my research interests ↓ The main idea of this meeting is, of course, to share our research interests, latest achievements and learn from our colleagues about their latest discoveries. All we are looking forward to listening to the interesting talks and to having chats during our free time.
This short, "5-10-minute" introductory talk is intended to help us in establishing new research connections or maybe even collaborations! (TCPL 201) |
17:00 - 17:10 |
Jesús María Sanz-Serna: Shortly about my research interests ↓ The main idea of this meeting is, of course, to share our research interests, latest achievements and learn from our colleagues about their latest discoveries. All we are looking forward to listening to the interesting talks and to having chats during our free time.
This short, "5-10-minute" introductory talk is intended to help us in establishing new research connections or maybe even collaborations! (TCPL 201) |
17:10 - 17:20 |
Oliver Schwarze: Shortly about my research interests ↓ The main idea of this meeting is, of course, to share our research interests, latest achievements and learn from our colleagues about their latest discoveries. All we are looking forward to listening to the interesting talks and to having chats during our free time.
This short, "5-10-minute" introductory talk is intended to help us in establishing new research connections or maybe even collaborations! (TCPL 201) |
17:20 - 17:30 |
Karolina Kropielnicka: Shortly about my research interests ↓ The main idea of this meeting is, of course, to share our research interests, latest achievements and learn from our colleagues about their latest discoveries. All we are looking forward to listening to the interesting talks and to having chats during our free time.
This short, "5-10-minute" introductory talk is intended to help us in establishing new research connections or maybe even collaborations! (TCPL 201) |
17:30 - 19:30 |
Dinner ↓ A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building. (Vistas Dining Room) |