Difference between revisions of "Applied/ACMS/absF11"
(→George Hagedorn, Virginia Tech) 
(→Omar Morandi, TU Graz) 

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{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"  { style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"  
    
−   bgcolor="#DDDDDD" align="center" '''  +   bgcolor="#DDDDDD" align="center" '''Modeling quantum transport with the phasespace formalism''' 
    
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−  +  Quantum modeling is becoming a crucial aspect in nanoelectronics research in perspective of analog and digital applications. Devices like interband tunneling diodes or graphene sheets are examples of solid state structures that are receiving a great importance in the modern nanotechnology for highspeed and miniaturized systems. Differing from the usual transport where the electronic current flows within a single band, the remarkable feature of such solid state structures is the possibility to achieve a sharp coupling among states belonging to different bands. As a consequence, the single band transport or the classical phasespace description of the charge motion based on the Boltzmann equation are not longer accurate. Moreover, in a crystal where the effective Hamiltonian is expressed by a partially diagonalized basis (e. g. in graphene or in semiconductors), the usual definitions of the macroscopic quantities, as for example the mean velocity or the particle density, no longer apply. The theory of Berry phases offers an elegant explanation of this effect in terms of the intrinsic curvature of the perturbed band.  
+  
+  Different approaches have been proposed to achieve a full quantum description of electron transport where the interaction among the different bands can be included. Among them, the phasespace formulation of quantum mechanics based on the concept of “WignerWeyl quantization”, offers a framework in which the quantum phenomena can be described with a classical language and the question of the quantumclassical correspondence can be directly investigated. In this contribution, an extension of the original WignerWeyl theory based on a suitable projection procedure, is presented. The applications of this formalism span among different subjects: the multiband transport and applications to nanodevices, the infinite order approximations of the motion and the characterization of a system in terms of Berry phases or, more generally, the representation of a quantum system as a Riemann manifold with a suitable connection. Furthermore, some asymptotic procedures devised for the approx imation of the quantum WignerWeyl solution have shown a very attractive connection with the DysonFeynmann theory of the particle interaction, which allows us to describe quantum transition by means of an effective Boltzmann process.  
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Revision as of 17:08, 21 September 2011
Contents
 1 Sigurd Angenent, UWMadison
 2 John Finn, Los Alamos
 3 Jay Bardhan, Rush Univ
 4 Omar Morandi, TU Graz
 5 George Hagedorn, Virginia Tech
 6 Qiang Deng, UWMadison
 7 Ray Pierrehumbert, U of Chicago
 8 Jianfeng Lu, Courant Institute
 9 Anne Shiu, U of Chicago
 10 Organizer contact information
 11 Archived semesters
Sigurd Angenent, UWMadison
Deterministic and random models for polarization in yeast cells 
I'll present one of the existing models for "polarization in yeast cells." The heuristic description of the model allows at least two mathematical formulations, one using pdes (a reaction diffusion equation) and one using stochastic particle processes, which give different predictions for what will happen. The model is simple enough to understand and explain why this is so. 
John Finn, Los Alamos
Symplectic integrators with adaptive time steps 
TBA 
Jay Bardhan, Rush Univ
Understanding Protein Electrostatics using BoundaryIntegral Equations 
The electrostatic interactions between biological molecules play important roles determining their structure and function, but are challenging to model because they depend on the collective response of thousands of surrounding water molecules. Continuum electrostatic theory  e.g., the Poisson equation  offers a successful and simple theory for biomolecule science and engineering, and boundaryintegral equation formulations of the problem offer several theoretical and computational advantages. In this talk, I will highlight some recent modeling advances derived from the boundaryintegral perspective, which have important applications in biophysics and whose mathematical foundations may be useful in other domains as well. First, one may derive a fast electrostatic model that resembles Generalized Born theory, but is based on a rigorous operator approximation for rapid, accurate estimation of a Green's function. In addition, we have been exploring a boundaryintegral approach to nonlocal continuum theory as a means to model the influence of water structure, an important piece of molecular physics left out of the standard continuum theory. 
Omar Morandi, TU Graz
Modeling quantum transport with the phasespace formalism 
Quantum modeling is becoming a crucial aspect in nanoelectronics research in perspective of analog and digital applications. Devices like interband tunneling diodes or graphene sheets are examples of solid state structures that are receiving a great importance in the modern nanotechnology for highspeed and miniaturized systems. Differing from the usual transport where the electronic current flows within a single band, the remarkable feature of such solid state structures is the possibility to achieve a sharp coupling among states belonging to different bands. As a consequence, the single band transport or the classical phasespace description of the charge motion based on the Boltzmann equation are not longer accurate. Moreover, in a crystal where the effective Hamiltonian is expressed by a partially diagonalized basis (e. g. in graphene or in semiconductors), the usual definitions of the macroscopic quantities, as for example the mean velocity or the particle density, no longer apply. The theory of Berry phases offers an elegant explanation of this effect in terms of the intrinsic curvature of the perturbed band. Different approaches have been proposed to achieve a full quantum description of electron transport where the interaction among the different bands can be included. Among them, the phasespace formulation of quantum mechanics based on the concept of “WignerWeyl quantization”, offers a framework in which the quantum phenomena can be described with a classical language and the question of the quantumclassical correspondence can be directly investigated. In this contribution, an extension of the original WignerWeyl theory based on a suitable projection procedure, is presented. The applications of this formalism span among different subjects: the multiband transport and applications to nanodevices, the infinite order approximations of the motion and the characterization of a system in terms of Berry phases or, more generally, the representation of a quantum system as a Riemann manifold with a suitable connection. Furthermore, some asymptotic procedures devised for the approx imation of the quantum WignerWeyl solution have shown a very attractive connection with the DysonFeynmann theory of the particle interaction, which allows us to describe quantum transition by means of an effective Boltzmann process. 
George Hagedorn, Virginia Tech
Time Dependent Semiclassical Quantum Dynamics: Analysis and Numerical Algorithms

We begin with some elementary comments about timedependent quantum mechanics and the role of Planck's constant. We then describe several mathematical results about approximate solutions to the Schr\"odinger equation for small values of the Planck constant. Finally, we discuss numerical difficulties of semiclassical quantum dynamics and algorithms that have recently been developed, including some work in progress. 
Qiang Deng, UWMadison
TBA

TBA 
Ray Pierrehumbert, U of Chicago
TBA

TBA 
Jianfeng Lu, Courant Institute
TBA

TBA 
Anne Shiu, U of Chicago
TBA

TBA 
Organizer contact information
Archived semesters
 Spring 2011
 Fall 2010
 Spring 2010
 Fall 2009
 Spring 2009
 Fall 2008
 Spring 2008
 Fall 2007
 Spring 2007
 Fall 2006
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