Currently Funded Research
Recent Research
Planned Future Research

Currently Funded Research

Theoretical studies of Quantum and classical coherent states
A three-year research grant awarded to Prof. Jorge V. Jose by the NSF

The goal of this research program was to unravel specific hallmarks of quantum phenomena of model systems that are chaotic or have unpredictable behavior in the classical limit. Quantum chaos---the study of quantized classical non-integrable Hamiltonian systems---is by now a developed and sophisticated field, mostly for single particle systems. This area of research has turned up beautiful connections between classical chaotic behavior and their quantum counterparts. The areas of research considered in this proposal had four parts:

(i) Very little has been done to look at quantum many-particle systems which exhibit classical chaotic behavior. Classical many-particle chaos is qualitatively very different from single particle Hamiltonian chaos. One would expect that their quantum equivalents must reflect this difference, but this has not been widely investigated. There are a number of reasons for this. The first is that interacting many particle systems are very difficult to study both classically and quantum mechanically. We have started to consider this question in terms of a gas of non-interacting electrons subjected to time-periodic magnetic fields. the motivation for this work also comes from experiments done in quantum dot structures. We asked the following question: what is the relevance of the Pauli exclusion principle for a gas of noninteracting electron gas that can be classically chaotic. Our initial results do indicate that the Pauli exclusion "force" significantly modifies the behavior of the magnetic properties of this gas. We will next make this problem more realistic and include the all important Coulomb interaction, both classically and quantum mechanically. Since the many particle problem is very hard we propose to start considering a system with few interacting charges that have mixed phase space dynamics, this time both in the boson and fermion cases.

(ii) Billiard dynamics has played a very important role in the study of quantum chaos. Here we proposed to study billiards that have broken rotational invariance that have "fractional" angular momentum with or without constant external magnetic fields. Specifically, we proposed to consider "pacman" and "sector" "wedge" geometries, that have been, in fact, partially studied experimentally. These modification in geometry must play an important role in the classical dynamics and the quantum spectral properties as well as in the experimentally measured magnetic response of these type of billiards.

(iii) Study chaotic scattering of single particles in time-dependent potential billiards. We considered the classical and quantum dynamics of a particle constrained by an infinite external billiard boundary and a finite internal oscillatory boundary potential. There is significant interest in problems where the billiards are deformed from circular in semiconductor laser physics, since the deformations lead to an increase in the radiated intensity and to a selection in the orientation of the radiation in nanoscale quantum dot lasers. Furthermore, since the internal potential is finite we expect to have "ray splitting" phenomena in a time-dependent oscillatory potential. We also proposed to study the effects of chaotic scattering in the Ahoronov-Bohm affect.

(iv) A connections between friction and chaos, in the context of simple time-dependent classical and quantum models. This is an important problem since it addresses the basic physical and conceptual question of energy dissipation that can allow us to explore the connections between classical chaos, dissipation, and decoherence. This work may have important technical consequences. Related to this problem are issues of importance in quantum computation.

Ventricular Fibrillation

A three-year research grant awarded to Alain Karma by the American Heart Association .

Samll Heart

Professor Karma received this grant for his expected contribution to cardiac fibrillation (VF) studies. He studied the onset of VF, when the electrical activity of the heart suddenly becomes disorganized, both in time and in space, across the ventricular muscle. Prof. Karma's research attempts to develop an understanding of cardiac arrythmias, which include ventricular tachycardia and ventricular fibrillation, through which he hopes to create realistic and reliable models for cardiologists to use in predicting the induction of these fibrillations. To accomplish this, Prof. Karma has combined his expertise in large scale computer simulations, nonlinear dynamics and chaos, with an understanding of cell electrophysiology and clinical cardiology.

A Study of the Theoretical Atomic Level Mechanisms for Sliding Friction

A three-year research grant awarded to Jeffrey B. Sokoloff by the Department of Energy.

Professor Sokoloff received this grant to explore the fundamental mechanisms for dissipation in sliding friction. He plans to study how organized translational motion of a system is converted into internal excitations by using a combination of analytic and computer techniques on simplified models, which will help to uncover the basic physical principles involved. The investigation itself will be separated into three areas: a study of the effects of defects on the energy dissipated when two crystalline solids slide with respect to each other; a determination of the differences in behavior expected for friction due to the generation of lattice vibrations created by electronic excitations; and lastly, whether the normal mechanism for the conversion of organized mechanical energy into internal energy will still hold for very small solids, for which results obtained in the thermodynamic limit would be inexact.



Recent Research
Modeling the Neural Control of Zebra fish Locomotive Behaviors
S.A. Hill, M.A. Borla*, J.V. Jose and D.M. O'Malley
Soc. Neurosci. Abs., 29:278.10 (2003)

ABSTRACT: The 7-day old larval zebrafish has a complex locomotive repertoire, including a sophisticated prey capture behavior. The underlying neural controls are being examined using a variety of optical techniques (reviewed in O Malley et al., 2003). We are interested in how descending control signals from brainstem shape neural activity patterns in spinal cord. For example, during capture swim bouts, larvae are able to modulate the bending of the trunk (which is used to propel larvae towards their prey) in a precise and rapid manner (Borla et al., 2002). Specifically, larvae are able to adjust bend location, amplitude and frequency on a bend-to-bend basis. To investigate how such modulation might occur, we have constructed a model of spinal neural circuitry. Descending control signals are input into this spinal CPG model so as to alter motoneuron firing patterns in a manner that mimics the observed locomotive behaviors. Because the zebrafish spinal cord CPG is not yet understood (see e.g. Hale et al., 2001), our model is based on spinal cord rhythm generation models derived from experiments on Xenopus and lamprey (Dale et al., 1995; Wolf and Roberts, 1995; Buchanan, 1999). This model is being constructed using the Neuron modeling program, which offers the flexibility to incorporate numerous computationally-efficient artificial neurons into functional networks (Hines and Carnevale, 2001). Initial single-segment models are being used to examine how local variables such as frequency and burst-amplitude can be dynamically modulated via descending signals. By coupling a series of such oscillators together (building on extant models of intersegmental coordination: Williams et al., 1990; Skinner and Mulloney, 1998), we hope to generate longitudinally propagating rhythms. This would constitute a kind of artificial spinal cord that could help us explore the neural basis of the fine axial motor control exhibited during larval capture swims.
How different Fermi surface maps emerge in photoemission from Bi2212
M.C. Asensio, J. Avila, L. Roca, A. Tejeda, G.D. Gu, M. Lindroos, R.S. Markiewicz, A. Bansil
Phys. Rev. B67, 014519 (2003)

ABSTRACT: We report angle-resolved photoemission spectra (ARPES) from the Fermi energy ($E_F$) over a large area of the ($k_x,k_y$) plane using 21.2 eV and 32 eV photons in two distinct polarizations from an optimally doped single crystal of Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi2212), together with extensive first-principles simulations of the ARPES intensities. The results display a wide-ranging level of accord between theory and experiment and clarify how myriad Fermi surface (FS) maps emerge in ARPES under various experimental conditions. The energy and polarization dependences of the ARPES matrix element help disentangle primary contributions to the spectrum due to the pristine lattice from those arising from modulations of the underlying tetragonal symmetry and provide a route for separating closely placed FS sheets in low dimensional materials.
Resonance Raman investigations of Escherichia coli-expressed Pseudomonas putida cytochrome P450 and P420
Wells AV, Li P, Champion PM, Martinis SA, Sligar SG.
Biochemistry 42, 6149 (2003)

ABSTRACT: High-resolution resonance Raman spectra of the ferric, ferrous, and carbonmonoxy (CO)-bound forms of wild-type Escherichia coli-expressed Pseudomonas putida cytochrome P450cam and its P420 form are reported. The ferric and ferrous species of P450 and P420 have been studied in both the presence and absence of excess camphor substrate. In ferric, camphor-bound, P450 (mos), the E. coli-expressed P450 is found to be spectroscopically indistinguishable from the native material. Although substrate binding to P450 is known to displace water molecules from the heme pocket, altering the coordination and spin state of the heme iron, the presence of camphor substrate in P420 samples is found to have essentially no effect on the Raman spectra of the heme in either the oxidized or reduced state. A detailed study of the Raman and absorption spectra of P450 and P420 reveals that the P420 heme is in equilibrium between a high-spin, five-coordinate (HS,5C) form and low-spin six-coordinate (LS,6C) form in both the ferric and ferrous oxidation states. In the ferric P420 state, H2O evidently remains as a heme ligand, while alterations of the protein tertiary structure lead to a significant reduction in affinity for Cys(357) thiolate binding to the heme iron. Ferrous P420 also consists of an equilibrium between HS,5C and LS,6C states, with the spectroscopic evidence indicating that H2O and histidine are the most likely axial ligands. The spectral characteristics of the CO complex of P420 are found to be almost identical to those of a low pH of Mb. Moreover, we find that the 10-ns transient Raman spectrum of the photolyzed P420 CO complex possesses a band at 220 cm-1, which is strong evidence in favor of histidine ligation in the CO-bound state. The equilibrium structure of ferrous P420 does not show this band, indicating that Fe-His bond formation is favored when the iron becomes more acidic upon CO binding. Raman spectra of stationary samples of the CO complex of P450 reveal VFe-CO peaks corresponding to both substrate-bound and substrate-free species and demonstrate that substrate dissociation is coupled to CO photolysis. Analysis of the relative band intensities as a function of photolysis indicates that the CO photolysis and rebinding rates are faster than camphor rebinding and that CO binds to the heme faster when camphor is not in the distal pocket.
Two-phase microstructure selection in peritectic solidification: from island banding to coupled growth
T.S. Lo, S. Dobler, M. Plapp, A. Karma, and W. Kurz,
Acta Materiala 51, 599-611 (2003).

ABSTRACT: We report the first experimental observation in directionally solidified peritectic Fe-Ni alloys of two-phase island banding microstructures that consist of rows of islands of one solid phase (either peritectic or primary) inside the continuous matrix of the other phase. These microstructures form under predominantly diffusion-limited growth conditions and when both phases are morphologically stable, as recently predicted by numerical simulations of a phase-field model. They are observed either as transients that seed the formation of coupled growth structures, or as the final microstructure. Phase-field simulations are reported that shed light on the relationship of island banding and coupled growth as well as on the growth conditions and nucleation parameters that control the dynamical selection of these two basic microstructures in peritectic alloys.
Multiplicativity of Accessible Fidelity and Quantumness for Sets of Quantum States
K.M.R. Audenaert, C.A. Fuchs, C. King, A. Winter
Quantum Information and Computation 4, No. 1, 1-11, (2004)

ABSTRACT: Two measures of sensitivity to eavesdropping for alphabets of quantum states were recently introduced by Fuchs and Sasaki in quant-ph/0302092. These are the accessible fidelity and quantumness. In this paper we prove an important property of both measures: They are multiplicative under tensor products. The proof in the case of accessible fidelity shows a connection between the measure and characteristics of entanglement-breaking quantum channels.
Direct determination of the complete set of iron normal modes in a porphyrin-imidazole model for carbonmonoxy-heme proteins: [Fe(TPP)(CO)(1-MeIm)].
Rai BK, Durbin SM, Prohofsky EW, Sage JT, Ellison MK, Roth A, Scheidt WR, Sturhahn W, Alp EE.
J.Phys.Chem.B107,11170-11177(2003)

ABSTRACT: Detailed Fe vibrational spectra have been obtained for the heme model complex [Fe(TPP)(CO)(1-MeIm)] using a new, highly selective and quantitative technique, Nuclear Resonance Vibrational Spectroscopy (NRVS). This spectroscopy measures the complete vibrational density of states for iron atoms, from which normal modes can be calculated via refinement of the force constants. These data and mode assignments can reveal previously undetected vibrations and are useful for validating predictions based on optical spectroscopies and density functional theory, for example. Vibrational modes of the iron porphyrin-imidazole compound [Fe(TPP)(CO)(1-MeIm)] have been determined by refining normal mode calculations to NRVS data obtained at an X-ray synchrotron source. Iron dynamics of this compound, which serves as a useful model for the active site in the six-coordinate heme protein, carbonmonoxy-myoglobin, are discussed in relation to recently determined dynamics of a five-coordinate deoxy-myoglobin model, [Fe(TPP)(2-MeHIm)]. For the first time in a six-coordinate heme system, the iron-imidazole stretch mode has been observed, at 226 cm(-)(1). The heme in-plane modes with large contributions from the nu(42), nu(49), nu(50), and nu(53) modes of the core porphyrin are identified. In general, the iron modes can be attributed to coupling with the porphyrin core, the CO ligand, the imidazole ring, and/or the phenyl rings. Other significant findings are the observation that the porphyrin ring peripheral substituents are strongly coupled to the iron doming mode and that the Fe-C-O tilting and bending modes are related by a negative interaction force constant.
Friction in the Zero Sliding Velocity Limit
C. Daly, J. Zhang and J. B. Sokoloff
Physical Review E68, 066118(2003).

ABSTRACE: Using an adiabatic approximation method, which searches for Tomlinson model-like instabilities for a simple but still realistic model for two crystalline surfaces, with mobile molecules present at the interface, sliding relative to each other, we are able to account for the virtually universal occurrence of "dry friction" at zero temperature. A modified version of this method allows us to calculate the kinetic friction at non-zero temperature as well. We have also considered the static friction, and have demonstrated that the model is able to account for static friction being larger than kinetic friction.
Imaging by flat lens using negative refraction.
Parimi PV, Lu WT, Vodo P, Sridhar S.
Nature, 426, 404 (2003)

ABSTRACT: The positive refractive index of conventional optical lenses means that they need curved surfaces to form an image, whereas a negative index of refraction allows a flat slab of a material to behave as a lens and focus electromagnetic waves to produce a real image. Here we demonstrate this unique feature of imaging by a flat lens, using the phenomenon of negative refraction in a photonic crystalline material. The key advance that enabled us to make this observation lies in the design of a photonic crystal with suitable dispersion characteristics to achieve negative refraction over a wide range of angles.
Kinetic Regulation of Single DNA Molecule Denaturation by T4 Gene 32 Protein Structural Domains.
Kiran Pant, Richard L. Karpel, and Mark C. Williams.
Journal of Molecular Biology 327: 571-578. 2003.

ABSTRACT: Bacteriophage T4 gene 32 protein (gp32) is a single-stranded DNA (ssDNA) binding protein, and is essential for DNA replication, recombination and repair. While gp32 binds preferentially and cooperatively to ssDNA, it has not been observed to lower the thermal melting temperature of natural double-stranded DNA (dsDNA). However, in single molecule stretching experiments, gp32 significantly destabilizes lambda DNA. In this study, we develop a theory of the effect of the protein on single dsDNA stretching curves, and apply it to the measured dependence of the DNA overstretching force on pulling rate in the presence of the full-length and two truncated forms of the protein. This allows us to calculate the ate of cooperative growth of single clusters of protein along ssDNA that are formed as the dsDNA molecule is stretched, as well as determine the site size of the protein binding to ssDNA. The rate of cooperative binding (ka) of both gp32 and of its roteolytic fragment *I (which lacks 48-residues from C-terminus) varies non-linearly with protein concentration, and appears to exceed the diffusion limit. We develop a model of protein association with the ends of growing clusters of cooperatively bound protein enhanced by 1-D diffusion along dsDNA, under the condition of protein excess. Upon globally fitting ka vs. protein concentration, we determine the binding site size and the noncooperative binding constants to double-stranded DNA for gp32 and I. Our experiment mimics the growth of clusters of gp32 that likely exist at the DNA replication fork in vivo, and explains the origin of the "kinetic block" to dsDNA melting by gene 32 protein observed in thermal melting experiments.
For for information about recent research,
please go to 2003 Year End Report.


Planned Future Research
There are two basic areas of research pursued at CIRCS. One of relates to the dynamical properties of proteins and the electric signalling in cardiac tissue. The other involves the properties of mesoscopic material science systems. Mesoscopic systems are entities defined at an intermediate scale between microscopic and macroscopic. They include systems artificially fabricated by modern photolithographic techniques as well as biological macromolecules such as proteins.

Although these systems may appear to be unrelated, they carry the uniform theme of involving entities coupled to a large set of freedoms which lead to dissipation and complex behavior. For example, these couplings appear to be responsible for the fundamental properties seen in protein folding and molecular recognition. Many of these functions can be represented by a large set of nonlinear coupled oscillators, and thus are capable of exhibiting the important phenomena of complex pattern formation. For example, patterns of electrical and chemical signaling that underlie the biological function of cellular networks have also become the subject of intense research that involves biologists, mathematicians, and physicists.

A general characteristic of these problems is that they involve systems not found in isolation, but surrounded by a larger system--the environment. The interaction between the small and large system leads to the phenomena of dissipation. This is a very important problem that up to now has not been tackled in any systematic way. For example, in molecular biology the aqueous environment (the large system) appears to play crucial roles in defining the different protein functions (the small system).

Many theoretical studies which ignore the large system have been carried out, even though experimental evidence is mounting that one cannot explain basic protein functions (like folding, for example) without including water. The same can be said of mesoscopic quantum electronics, where the environment also plays a crucial role.

Biophysical Problems

Protein Hydration Proteins are compact molecular machines whose structure, dynamics, and function depend on a shell of several hundred water molecules associated with the protein surface. In biotechnological applications, however, the practical use of proteins as biocatalytic materials often involves immersion in solutions with low water content or incorporation into a solid phase. It is important to understand the mechanism by which hydration enables protein function and the quantity of water required.

Profs. Champion, Sage, and Sridhar have already shown that hydration water can be detected at the molecular level using both high frequency dielectric spectroscopy (1) and microbalance techniques (2). We at CIRCS propose to expand these investigations to include biological systems involved in molecular recognition: if the energies of constrained water structures are as high as recently calculated (3), unusual dynamics must accompany the "docking" of biological molecules in solution. Furthermore, we will determine the level of hydration needed to establish functional protein dynamics in "dry" environments such as organic solvents or dehydrated films adsorbed on solid surfaces (2).

Together, Profs. Champion, Sage, and Sridhar possess established experimental capability to study condensed phases in the sub-optical (dc to mm-wave) and FIR spectral range that provides a unique experimental setup to probe dynamics over 14 decades of frequency.

[1] "Direct determination of the complete set of iron normal modes in a porphyrin-imidazole model for carbonmonoxy-heme proteins: [Fe(TPP)(CO)(1-MeIm)]." Rai BK, Durbin SM, Prohofsky EW, Sage JT, Ellison MK, Roth A, Scheidt WR, Sturhahn W, Alp EE. J.Phys.Chem.B107,11170-11177(2003)
[2] "Quantitative Vibrational Dynamics of Iron in Nitrosyl Porphyrins" Bogdan M. Leu, Marek Z. Zgierski, Graeme R. A. Wyllie, W. Robert Scheidt, Wolfgang Sturhahn, E. Ercan Alp, Stephen M. Durbin, and J. Timothy Sage J. AM. CHEM. SOC. 9 VOL. 126, NO. 13, 2003
[3] "Resonance Raman investigations of Escherichia coli-expressed Pseudomonas putida cytochrome P450 and P420" Wells AV, Li P, Champion PM, Martinis SA, Sligar SG. Biochemistry 42, 6149 (2003)

Glassy Behavior and Noise in Proteins

Profs. Israeloff and Sage use micro-lithography to optically isolate and study single heme protein molecules labeled with fluorescent dye molecules. Prof. Mabrouk in the Chemistry Department at NU is an expert in selectively attaching biomolecules with varying strength to substrates, allowing a variety of patterned geometrys and environments to be probed. With these single-molecule techniques a number of longstanding biophysical questions can be addressed which are fundamentally unanswerable from studies of molecular ensembles.

The project will makes of in-house microlithography facilities as well as the Cornell National Nanofabrication Facility for fabrication of smaller structures. By monitoring the evolution of the fluorescence wavelength or intensity, they will observe the spontaneous fluctuations of the protein conformation. By analyzing this protein "noise," a number of effects can be studied for the first time. The extent to which protein dynamics is hierarchically constrained as some glasses are believed to be, and whether proteins undergo a glass transition as suggested by Fraunfelder will be studied. On the theoretical side, Prof. José will try to model the hierarchical nature of this complex dynamical system.

Birth and Decay of Coherent States in Biomolecules

Photon driven electronic or vibrational excitation of biomolecules followed by elementary processes such as photolysis or charge transport will be studied using ultrafast laser techniques (1,2). The protein reaction dynamics and the dissipation of excess energy will be monitored by Profs. Champion and Sage in biological systems such as cytochrome c, myoglobin, and the more complex photosynthetic "reaction center." They aim to probe locally hot vibrational modes (immediately after photoexcitation) and study their influence on the quantum yield and irreversibility of biological electron transport processes. Profs. José and Karma aim to develop quantitative theoretical models describing how the surrounding protein material "dresses" an active site biological chromophore and how the Brownian dynamics of the protein, as well as the quantum mechanical excitations of the embedded chromophore, affect the fundamental reactions.

[1] "Real Time Observation of Heme Protein Vibrations Using Femtosecond Coherence Spectroscopy" 1. L. Zhu, P. Li, M. Huang, J.T. Sage and P.M. Champion Phys. Rev. Lett. 72, 301 (1994).
[2] "Observation of Coherent Reaction Dynamics in Heme Proteins" L. Zhu, J.T. Sage and P.M. Champion Science 266, 629 (1994).

Macromolecular Crystallization

Solidification involves a large number of individual units, but a better understanding of the physics underlying this complex process would have many practical ramifications. For example, production of advanced technological materials such as semiconductor wafers and nonlinear optical materials could be greatly improved.

Sage, Karma, and Champion propose to investigate the crystallization of biological macromolecules, which is the principal technical bottleneck to determining the structures of these molecules. Experimental input, either from optical techniques or AFM measurements, will guide theoretical calculations of step motion. This project would merge the expertise of Prof. Karma, who is a leader in the theoretical understanding of solidification processes, and Prof. Sage, who has extensive experience in the growth and spectroscopic characterization of protein crystals.

Significant experimental input for the calculations would come from the work of Prof. George Phillips (Rice University), who is systematically generating crystal structures of myoglobin proteins having a specific surface mutation that induces crystallization in a different space group and has agreed to supply Prof. Sage with such crystals for spectroscopic measurements.

Modelling of Complex Patterns of Electrical Signalling in Cardiac Arrhythmias

The normal function of the heart muscle is marked by the simplicity of the pathway of electrical signalling that connects its different tissue regions. In contrast, fibrillation and sudden cardiac death is marked by the spontaneous formation of complex spatio-temporal patterns of electrical signalling produced by the cooperative behavior of a large network of myocardial cells that destroy the coherent contraction of the ventricular muscle.

It is presently recognized that the onset of this electrical activity, which is associated with other life threatening arrhythmias, remains poorly understood despite years of extensive clinical research and the investment of large resources.

A well targeted interdisciplinary effort that combines on the one hand expertise in pattern formation, large scale computer simulations, nonlinear dynamics and chaos, and, on the other, expertise in cell electrophysiology and clinical cardiology, seems presently almost indispensable to arrive at a understanding of these arrhythmias which is sufficiently reliable to be useful in terms of human health.

Profs. Karma, Alan Garfinkel, and James Weiss from the Department of Medicine (Cardiology) at UCLA plan to extend and consolidate a collaborative effort that has been initiated during the last year between them. The UCLA researchers have agreed to act as consultants to the CIRCS. The primary initial focus of this research will be on studying the onset of ventricular fribrillation. Large scale computer simulations of two and three dimensional tissues (including up to 10 x 7 excitable elements), which may reproduce the correct muscle architecture and fiber orientation will be needed to properly simulate the mechanism by which complex pathways of electrical signalling are formed in bulk ventricular tissue.

In direct application, clinical observations will be corroborated with the results of both model simulations and tissue observations to devise new diagnostic means to detect and prevent cardiac fibrillation.

[1] "Model of intracellular calcium cycling in ventricular myocytes" Shiferaw Y, Watanabe MA, Garfinkel A, Weiss JN, Karma A. Biophys.J.85,3666-86(2003)

Materials Science

Computer Modelling of Combined Flow and Solidification

Understanding the interaction of hydrodynamic flows with the crystal-melt interface has remained a major theoretical challenge in the area of solidification and materials processing. The set of nonlinear partial differential equations with complex boundaries which describe the interaction of flow and solidification are far too difficult to be tackled analytically in most interesting situations. Thus, they need to be approached by large scale computer simulations in conjunction with well-controlled experiments. Profs. Karma and Williams envision setting up a major computational effort aimed at understanding the fundamental aspects of this problem.

[1] "Two-phase microstructure selection in peritectic solidification: from island banding to coupled growth" T.S. Lo, S. Dobler, M. Plapp, A. Karma, and W. Kurz Acta Materiala 51, 599-611 (2003)
[2] "Phase-Field Approach for Faceted Solidification" Jean-Marc Debierre, Alain Karma, Franck Celestini, Rahma Guerin Phys. Rev. E 68, 041604 (2003)
[3] "Pattern Stability and Trijunction Motion in Eutectic Solidification" S. Akamatsu, M.Plapp, G. Faivre, A. Karma Materials Science 2002, 4, 535-539

Quantum Chaos and the Theory of Friction

One of the least understood, yet most important phenomena in physics, biology, and engineering is dissipation. It is usually assumed to be a result of the coupling of a perturbing force which acts on the system with a large number of excited states, either internal to the system being studied or in a heat bath to which the system in question is coupled. Profs. Champion, José, Krim, Sokoloff, and Sridhar propose to study dissipation in classical and quantum systems. To date, most theories of dissipation require the existence of a continuous energy distribution of such states.

However, if the system being studied is of mesoscopic size, excitations have a discrete energy spectrum. Such excitations will not in general dissipate energy. Recent findings appear to indicate that dissipation effects appear differently in a classical than in a quantum system, depending if the classical system is integrable or not.

The goal will be to understand and estimate when the "large system" produces dissipation in the small system, and proceed to apply this knowledge to specific mesoscopic biological and material science systems.

Furthermore, they plan to propose definitive experiments designed to study the role of coupling to the "large system" that produces friction, hopefully to find ways to reduce it.

Large Sets of Coupled Nonlinear Oscillators

Our basic understanding of nonequilibrium phenomena and the patterns they produce remains extremely limited. Inherently, they involve a large number of degrees of freedom interacting nonlinearly over many different lengths and time scales.

So far, dynamical systems and chaos theory have only been successful in coping with situations where this number is small, which is more often the exception than the rule. Profs. José and Karma plan to develop an understanding and eventually a means to control the behavior of complex nonequilibrium systems when this number is large. They have already done work together exploring some of these issues.

[1] D. Dominguez, J. V. José, A. Karma and C. Wiecko, Phys. Rev. Lett. 67, 2367, (1991)