We consider a simple quantum system subjected to a classical random force. Under certain conditio... more We consider a simple quantum system subjected to a classical random force. Under certain conditions it is shown that the noise-averaged Wigner function of the system follows an integro-differential stochastic Liouville equation. In the simple case of polynomial noise-couplings this equation reduces to a generalized Fokker-Planck form. With nonlinear noise injection new ``quantum diffusion'' terms arise that have no counterpart in the classical case. Two special examples that are not of a Fokker-Planck form are discussed: the first with a localized noise source and the other with a spatially modulated noise source.
Low Energy Accelerator Beam Dynamics Halos of Intense Proton Beams
Supercomputing Sheds Light on the Dark Universe
At Argonne National Laboratory, scientists are using supercomputers to shed light on one of the g... more At Argonne National Laboratory, scientists are using supercomputers to shed light on one of the great mysteries in science today, the Dark Universe. With Mira, a petascale supercomputer at the Argonne Leadership Computing Facility, a team led by physicists Salman Habib and Katrin Heitmann will run the largest, most complex simulation of the universe ever attempted. By contrasting the results from Mira with state-of-the-art telescope surveys, the scientists hope to gain new insights into the distribution of matter in the universe, advancing future investigations of dark energy and dark matter into a new realm. The team's research was named a finalist for the 2012 Gordon Bell Prize, an award recognizing outstanding achievement in high-performance computing.
Faced with a backlog of nuclear waste and weapons plutonium, as well as an everincreasing public ... more Faced with a backlog of nuclear waste and weapons plutonium, as well as an everincreasing public concern about safety and environmental issues associated with conventional nuclear reactors, many countries are studying new, accelerator-driven technologies that hold the promise of providing safe and e ective solutions to these problems. Proposed projects include accelerator transmutation of waste (ATW), accelerator-based conversion of plutonium (ABC), accelerator-driven energy production (ADEP), and accelerator production of tritium (APT). Also, next-generation spallation neutron sources based on similar technology will play a major role in materials science and biological science research. The design of accelerators for these projects will require a major advance in numerical modeling capability. For example, beam dynamics simulations with approximately 100 million particles will be needed to ensure that extremely stringent beam loss requirements (less than a nanoampere per meter) can be met. Compared with typical presentday modeling using 10,000-100,000 particles, this represents an increase of 3-4 orders of magnitude. High performance computing (HPC) platforms make it possible to perform such large scale simulations, which require 10's of GBytes of memory. They also make it possible to perform smaller simulations in a matter of hours that would require months to run on a single processor workstation. This paper will describe how HPC platforms can be used to perform the numerically intensive beam dynamics simulations required for development of these new accelerator-driven technologies.
Some recent investigations of the thermal equilibrium properties of kinks in a 1+1-dimensional, c... more Some recent investigations of the thermal equilibrium properties of kinks in a 1+1-dimensional, classical {phi}{sup 4} field theory are reviewed. The distribution function, kink density, correlation function, and certain thermodynamic quantities were studied both theoretically and via large scale simulations. A simple double Gaussian variational approach within the transfer operator formalism was shown to give good results in the intermediate temperature range where the dilute gas theory is known to fail.
Thermal Vortex Motion in a Two-Dimensional Condensate
We carry out an analytical and numerical study of the motion of an isolated vortex, defined as a ... more We carry out an analytical and numerical study of the motion of an isolated vortex, defined as a point singularity of a complex scalar field $\psi(\r,t)$ obeying a nonlinear stochastic Schrödinger equation. The vortex does not execute a simple random walk and the probability distribution of vortex flights has non-Gaussian (exponential) tails. We quantify these effects and explain their origin as due to the convective transport of the vortex by the random flow field of thermal excitations. These results present a dynamical picture of the vortex both as a passive scalar advected to random background superflow and as a heavy Brownian particle.
Advanced Scientific Computing Research Exascale Requirements Review. An Office of Science review sponsored by Advanced Scientific Computing Research, September 27-29, 2016, Rockville, Maryland
We consider quantum fields in an external potential and show how, by using the Fourier trans- for... more We consider quantum fields in an external potential and show how, by using the Fourier trans- form on propagators, one can obtain the mass-shell constraint conditions and the Liouville-Vlasov equation for the Wigner distribution function. We then consider the Hadamard function G&(x&,x2) of a real, free, scalar field in curved space. We postulate a form for the Fourier transform F'~'(X, k) of the propagator with respect to the difference variable x =x& -x2 on a Riemann normal coordi- nate centered at g. We show that F''z' is the result of applying a certain Q-dependent operator on a covariant Wigner function F. We derive from the wave equations for 6& a covariant equation for the distribution function and show its consistency. We seek solutions to the set of Liouville-Vlasov equations for the vacuum and nonvacuum cases up to the third adiabatic order. Finally we apply this method to calculate the Hadamard function in the Einstein universe. We show that the covari- ant Wigner function can incorporate certain relevant global properties of the background spacetime. Covariant Wigner functions and Liouville-Vlasov equations are also derived for free fermions in curved spacetime. The method presented here can serve as a basis for constructing quantum ki- netic theories in curved spacetime or for near-uniform systems under quasiequilibrium conditions. It can also be useful to the development of a transport theory of quantum fields for the investigation of grand unification and post-Planckian quantum processes in the early Universe. variable. This means that dynamical systems can have nonlocal (or history-dependent) behavior. This also
Langevin simulation provides an effective way to study collisional effects in beams by reducing t... more Langevin simulation provides an effective way to study collisional effects in beams by reducing the six-dimensional Fokker-Planck equation to a group of stochastic ordinary differential equations. These resulting equations usually have multiplicative noise since the diffusion coefficients in these equations are functions of position and time. Conventional algorithms, e.g. Euler and Heun, give only first order convergence of moments in a finite time interval. In this paper, a stochastic leap-frog algorithm for the numerical integration of Langevin stochastic differential equations with multiplicative noise is proposed and tested. The algorithm has a second-order convergence of moments in a finite time interval and requires the sampling of only one uniformly distributed random variable per time step. As an example, we apply the new algorithm to the study of a mechanical oscillator with multiplicative noise.
Nano-electro-mechanical devices are now rapidly approaching the point where it will be possible t... more Nano-electro-mechanical devices are now rapidly approaching the point where it will be possible to observe quantum mechanical behavior. However, for such behavior to be visible it is necessary to reduce the thermal motion of these devices down to temperatures in the millikelvin range. Here we consider the use of feedback control for this purpose. We analyze an experimentally realizable situation in which the position of the resonator is continuously monitored by a Single-Electron Transistor. Because the resonator is harmonic, it is possible to use a classical description of the measurement process, and we discuss both the quantum and classical descriptions. Because of this the optimal feedback algorithm can be calculated using classical control theory. We examine the quantum state of the controlled oscillator, and the achievable effective temperature. Our estimates indicate that with current experimental technology, feedback cooling is likely to bring the required milliKelvin temperatures within reach.
A subset of QuantISED Sensor PIs met virtually on May 26, 2020 to discuss a response to a charge ... more A subset of QuantISED Sensor PIs met virtually on May 26, 2020 to discuss a response to a charge by the DOE Office of High Energy Physics. In this document, we summarize the QuantISED sensor community discussion, including a consideration of HEP science enabled by quantum sensors, describing the distinction between Quantum 1.0 and Quantum 2.0, and discussing synergies/complementarity with the new DOE NQI centers and with research supported by other SC offices. Quantum 2.0 advances in sensor technology offer many opportunities and new approaches for HEP experiments. The DOE HEP QuantISED program could support a portfolio of small experiments based on these advances. QuantISED experiments could use sensor technologies that exemplify Quantum 2.0 breakthroughs. They would strive to achieve new HEP science results, while possibly spinning off other domain science applications or serving as pathfinders for future HEP science targets. QuantISED experiments should be led by a DOE laboratory...
Langevin simulation provides an effective way to study collisional effects in beams by reducing t... more Langevin simulation provides an effective way to study collisional effects in beams by reducing the six-dimensional Fokker-Planck equation to a group of stochastic ordinary differential equations. These resulting equations usually have multiplicative noise since the diffusion coefficients in these equations are functions of position and time. Conventional algorithms, e.g. Euler and Heun, give only first order convergence of moments in a finite time interval. In this paper, a stochastic leap-frog algorithm for the numerical integration of Langevin stochastic differential equations with multiplicative noise is proposed and tested. The algorithm has a second-order convergence of moments in a finite time interval and requires the sampling of only one uniformly distributed random variable per time step. As an example, we apply the new algorithm to the study of a mechanical oscillator with multiplicative noise.
Conference title not supplied, Conference location not supplied, Conference dates not supplied, Aug 1, 2000
Langevin simulation provides an effective way to study col-Iisional effects in beams by reducing ... more Langevin simulation provides an effective way to study col-Iisional effects in beams by reducing the six-dimensional Fokker-Planck equation to a group of stochastic ordinary differential equations. These resulting equations usually have multiplicative noise since the diffusion coeftlcients in these equations are functions of position and time. Conventional algorithms, e.g. Euler and Heun, give only first order convergence of moments in a finite time interval. In this paper, a stochastic leap-frog algorithm for the numerical integration of Langevin stochastic differential equations with multiplicative noise is proposed and tested. The algorithm has a second-order convergence of momenta in a finite time interval and requires the sampling of only one uniformly distributed random variable per time step. As an example, we apply the new algorithm to the study of a mechanic oscillator with multiplicative noise.
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Papers by Salman Habib