arXiv subjects

J. M. Deutsch

Publications and source records attributed to J. M. Deutsch.

At least 37 records · Page 2Linked to original sources

arXiv2010

Density fluctuations of polymers in disordered media

We study self avoiding random walks in an environment where sites are excluded randomly, in two and three dimensions. For a single polymer chain, we study the statistics of the time averaged monomer density and show that these are well described by multifractal statistics. This is true even far from the percolation transition of the disordered medium. We investigate solutions of chains in a disordered environment and show that the statistics cease to be multifractal beyond the screening length of the solution.

cond-mat.soft↗

arXiv2010

Ideal Linear Chain Polymers with Fixed Angular Momentum

The statistical mechanics of a linear non-interacting polymer chain with a large number of monomers is considered with fixed angular momentum. The radius of gyration for a linear polymer is derived exactly by functional integration. This result is then compared to simulations done with a large number of non-interacting rigid links at fixed angular momentum. The simulation agrees with the theory up to finite size corrections. The simulations are also used to investigate the anisotropic nature of a spinning polymer. We find universal scaling of the polymer size along the direction of the angular momentum, as a function of rescaled angular momentum.

cond-mat.soft↗

arXiv2010

Internal dissipation of a polymer

The dynamics of flexible polymer molecules are often assumed to be governed by hydrodynamics of the solvent. However there is considerable evidence that internal dissipation of a polymer contributes as well. Here we investigate the dynamics of a single chain in the absence of solvent to characterize the nature of this internal friction. We model the chains as freely hinged but with localized bond angles and 3-fold symmetric dihedral angles. We show that the damping is close but not identical to Kelvin damping, which depends on the first temporal and second spatial derivative of monomer position. With no internal potential between monomers, the magnitude of the damping is small for long wavelengths and weakly damped oscillatory time dependent behavior is seen for a large range of spatial modes. When the size of the internal potential is increased, such oscillations persist, but the damping becomes larger. However underdamped motion is present even with quite strong dihedral barriers for long enough wavelengths.

cond-mat.soft↗

arXiv2009

Thermodynamic entropy of a many body energy eigenstate

It is argued that a typical many body energy eigenstate has a well defined thermodynamic entropy and that individual eigenstates possess thermodynamic characteristics analogous to those of generic isolated systems. We examine large systems with eigenstate energies equivalent to finite temperatures. When quasi-static evolution of a system is adiabatic (in the quantum mechanical sense), two coupled subsystems can transfer heat from one subsystem to another yet remain in an energy eigenstate. To explicitly construct the entropy from the wave function, degrees of freedom are divided into two unequal parts. It is argued that the entanglement entropy between these two subsystems is the thermodynamic entropy per degree of freedom for the smaller subsystem. This is done by tracing over the larger subsystem to obtain a density matrix, and calculating the diagonal and off-diagonal contributions to the entanglement entropy.

cond-mat.stat-mech↗

arXiv2009

Induced Orientational Effects in Relaxation of Polymer Melts

We study stress relaxation in bi-disperse entangled polymer solutions. Shorter chains embedded in a majority of longer ones are known to be oriented by coupling to them. We analyze the mechanism for this both by computer simulation and theoretically. We show that the results can be understood in terms of stress fluctuations in a polymer melt and chain screening. Stress fluctuations are frozen on the relaxation time of the longer chains, and these will induce strong orientational couplings in the shorter chains.

cond-mat.soft↗

arXiv2008

Exact Solution to Ideal Chain with Fixed Angular Momentum

The statistical mechanics of a non-interacting polymer chain in the limit of a large number of monomers is considered when the total angular momentum, L, is fixed. The radius of gyration for a ring polymer in this situation is derived exactly in closed form by functional integration techniques. Even when L = 0 the radius of gyration differs from that of a random walk by a prefactor of order unity. The dependence on L is discussed qualitatively and the large L limit can be understood by physical arguments.

cond-mat.stat-mech↗

arXiv2007

Ising Dynamics with Damping

We show for the Ising model that is possible construct a discrete time stochastic model analogous to the Langevin equation that incorporates an arbitrary amount of damping. It is shown to give the correct equilibrium statistics and is then used to investigate nonequilibrium phenomena, in particular, magnetic avalanches. The value of damping can greatly alter the shape of hysteresis loops, and for small damping and high disorder, the morphology of large avalanches can be drastically effected. Small damping also alters the size distribution of avalanches at criticality.

cond-mat.mtrl-sci↗

arXiv2007

Polymers in a vacuum

In a variety of situations, isolated polymer molecules are found in a vacuum and here we examine their properties. Angular momentum conservation is shown to significantly alter the average size of a chain and its conservation is only broken slowly by thermal radiation. The time autocorrelation for monomer position oscillates with a characteristic time proportional to chain length. The oscillations and damping are analyzed in detail. Short range repulsive interactions suppress oscillations and speed up relaxation but stretched chains still show damped oscillatory time correlations.

cond-mat.soft↗

arXiv2007

Disorder-induced magnetic memory: Experiments and theories

Beautiful theories of magnetic hysteresis based on random microscopic disorder have been developed over the past ten years. Our goal was to directly compare these theories with precise experiments. We first developed and then applied coherent x-ray speckle metrology to a series of thin multilayer perpendicular magnetic materials. To directly observe the effects of disorder, we deliberately introduced increasing degrees of disorder into our films. We used coherent x-rays to generate highly speckled magnetic scattering patterns. The apparently random arrangement of the speckles is due to the exact configuration of the magnetic domains in the sample. In effect, each speckle pattern acts as a unique fingerprint for the magnetic domain configuration. Small changes in the domain structure change the speckles, and comparison of the different speckle patterns provides a quantitative determination of how much the domain structure has changed. How is the magnetic domain configuration at one point on the major hysteresis loop related to the configurations at the same point on the loop during subsequent cycles? The microscopic return-point memory(RPM) is partial and imperfect in the disordered samples, and completely absent when the disorder was not present. We found the complementary-point memory(CPM) is also partial and imperfect in the disordered samples and completely absent when the disorder was not present. We found that the RPM is always a little larger than the CPM. We also studied the correlations between the domains within a single ascending or descending loop. We developed new theoretical models that do fit our experiments.

cond-mat.mtrl-sci↗

arXiv2006

Spin Precession and Avalanches

In many magnetic materials, spin dynamics at short times are dominated by precessional motion as damping is relatively small. In the limit of no damping and no thermal noise, we show that for a large enough initial instability, an avalanche can transition to an ergodic phase where the state is equivalent to one at finite temperature, often above that for ferromagnetic ordering. This dynamical nucleation phenomenon is analyzed theoretically. For small finite damping the high temperature growth front becomes spread out over a large region. The implications for real materials are discussed.

cond-mat.mtrl-sci↗

arXiv2005

Mechanism for nonequilibrium symmetry breaking and pattern formation in magnetic films

Magnetic thin films exhibit a strong variation in properties depending on their degree of disorder. Recent coherent x-ray speckle experiments on magnetic films have measured the loss of correlation between configurations at opposite fields and at the same field, upon repeated field cycling. We perform finite temperature numerical simulations on these systems that provide a comprehensive explanation for the experimental results. The simulations demonstrate, in accordance with experiments, that the memory of configurations increases with film disorder. We find that non-trivial microscopic differences exist between the zero field spin configuration obtained by starting from a large positive field and the zero field configuration starting at a large negative field. This seemingly paradoxical beahvior is due to the nature of the vector spin dynamics and is also seen in the experiments. For low disorder, there is an instability which causes the spontaneous growth of line-like domains at a critical field, also in accord with experiments. It is this unstable growth, which is highly sensitive to thermal noise, that is responsible for the small correlation between patterns under repeated cycling. The domain patterns, hysteresis loops, and memory properties of our simulated systems match remarkably well with the real experimental systems.

cond-mat.other↗

arXiv2004

Disorder-induced microscopic magnetic memory

Using coherent x-ray speckle metrology, we have measured the influence of disorder on major loop return point memory (RPM) and complementary point memory (CPM) for a series of perpendicular anisotropy Co/Pt multilayer films. In the low disorder limit, the domain structures show no memory with field cycling--no RPM and no CPM. With increasing disorder, we observe the onset and the saturation of both the RPM and the CPM. These results provide the first direct ensemble-sensitive experimental study of the effects of varying disorder on microscopic magnetic memory and are compared against the predictions of existing theories.

cond-mat.mtrl-sci↗

arXiv2004

Scaling of polymers in aligned rods

We study the behavior of self avoiding polymers in a background of vertically aligned rods that are either frozen into random positions or free to move horizontally. We find that in both cases the polymer chains are highly elongated, with vertical and horizontal size exponents that differ by a factor of 3. Though these results are different than previous predictions, our results are confirmed by detailed computer simulations.

cond-mat.soft↗

arXiv2004

Hysteresis multicycles in nanomagnet arrays

We predict two new physical effects in arrays of single-domain nanomagnets by performing simulations using a realistic model Hamiltonian and physical parameters. First, we find hysteretic multicycles for such nanomagnets. The simulation uses continuous spin dynamics through the Landau-Lifshitz-Gilbert (LLG) equation. In some regions of parameter space, the probability of finding a multicycle is as high as ~0.6. We find that systems with larger and more anisotropic nanomagnets tend to display more multicycles. This result demonstrates the importance of disorder and frustration for multicycle behavior. We also show that there is a fundamental difference between the more realistic vector LLG equation and scalar models of hysteresis, such as Ising models. In the latter case, spin and external field inversion symmetry is obeyed but in the former it is destroyed by the dynamics, with important experimental implications.

cond-mat.mtrl-sci↗

arXiv2004

Modeling of microarray data with zippering

The ability of oligonucleotide microarrays to measure gene expression has been hindered by an imperfect understanding of the relationship between input RNA concentrations and output signals. We argue that this relationship can be understood based on the underlying statistical mechanics of these devices. We present a model that includes the relevant interactions between the molecules. Our model for the first time accounts for partially zippered probe-target hybrids in a physically realistic manner, and also includes target-target binding in solution. Large segments of the target molecules are not bound to the probes, often in an asymmetric pattern, emphasizing the importance of modeling zippering properly. The resultant fit between the model and training data using optimized parameters is excellent, and it also does well at predicting test data.

q-bio.BM↗

arXiv2003

Return to return point memory

We describe a new class of systems exhibiting return point memory (RPM) that are different from those discussed before in the context of ferromagnets. We show numerically that one dimensional random Ising antiferromagnets have RPM, when configurations evolve from a large field. However, RPM is violated when started from some stable configurations at finite field unlike in the ferromagnetic case. This implies that the standard approach to understanding ferromagnetic RPM systems will fail for this case. We also demonstrate RPM with a set of variables that keep track of spin flips at each site. Conventional RPM for the spin configuration is a projection of this result, suggesting that spin flip variables might be a more fundamental representation of the dynamics. We also present a mapping that embeds the antiferromagnetic chain in a two dimensional ferromagnetic model, and prove RPM for spin exchange dynamics in the interior of the chain with this mapping.

cond-mat.stat-mech↗

arXiv2003

Correlations and scaling in one-dimensional heat conduction

We examine numerically the full spatio-temporal correlation functions for all hydrodynamic quantities for the random collision model introduced recently. The autocorrelation function of the heat current, through the Kubo formula, gives a thermal conductivity exponent of 1/3 in agreement with the analytical prediction and previous numerical work. Remarkably, this result depends crucially on the choice of boundary conditions: for periodic boundary conditions (as opposed to open boundary conditions with heat baths) the exponent is approximately 1/2. This is expected to be a generic feature of systems with singular transport coefficients. All primitive hydrodynamic quantities scale with the dynamic critical exponent predicted analytically.

cond-mat.stat-mech↗

arXiv2003

One dimensional heat conductivity exponent from random collision model

We study numerically the thermal conductivity coefficient $κ$ as a function of system length $L$ for several different quasi one dimensional models: classical gases of hard spheres with both longitudinal and transverse degrees of freedom. We introduce a model that is ergodic and highly chaotic but also conserves energy and momentum, and is very useful because it shows scaling even at small system sizes. We find that $κ\sim L^α$ over more than two decades, with $α$ very close to the analytical prediction of 1/3.

cond-mat.stat-mech↗