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L S Schulman

Publications and source records attributed to L S Schulman.

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Multiple phases in stochastic dynamics: geometry and probabilities.

Stochastic dynamics is generated by a matrix of transition probabilities. Certain eigenvectors of this matrix provide observables, and when these are plotted in the appropriate multidimensional space the phases (in the sense of phase transitions) of the underlying system become manifest as extremal points. This geometrical construction, which we call an observable representation of state space, can allow hierarchical structure to be observed. It also provides a method for the calculation of the probability that an initial points ends in one or another asymptotic state.

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Stability of quantum breathers.

Using two methods we show that a quantized discrete breather in a 1D lattice is stable. One method uses path integrals and compares correlations for a (linear) local mode with those of the quantum breather. The other takes a local mode as the zeroth order system relative to which numerical, cutoff-insensitive diagonalization of the Hamiltonian is performed.

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Role of breathers in anomalous decay.

We have previously presented evidence for the formation of breathers in doped alkali halides subjected to a flash of UV light. Properties of these breathers, their phase space structure, robustness, decay, and propensity for formation, are studied here. Under a wide range of parameters and interionic potentials they form two-dimensional Kolmogorov-Arnold-Moser tori (less than generic) in phase space. Strobed views of these tori, useful in quantization, are shown. All features support the thesis of breather formation as the explanation for the luminescence decay anomaly that first motivated our breather proposal.

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Slow relaxation, confinement, and solitons.

Millisecond crystal relaxation has been used to explain anomalous decay in doped alkali halides. We attribute this slowness to Fermi-Pasta-Ulam solitons. Our model exhibits confinement of mechanical energy released by excitation. Extending the model to long times is justified by its relation to solitons, excitations previously proposed to occur in alkali halides. Soliton damping and observation are also discussed.

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Models of synchronized hippocampal bursts in the presence of inhibition. II. Ongoing spontaneous population events.

1. We extended our computer model of the CA3 region of the hippocampal slice in order to study spontaneous activity occurring in the presence and absence of synaptic inhibition. This was done by providing a steady inward current to the excitatory neurons, whose value was randomly chosen for each cell. With the parameters used, many of the excitatory cells would, if synaptically isolated, remain quiescent, whereas others would burst periodically with periods as brief as 750 ms. Simulations were run for as long as 10 s of neural activity. 2. In the presence of synaptic inhibition, neural activity became organized into recurring, partially synchronized events: clusters of neurons (6% to 12% of the population) would discharge together, with a period averaging 340 ms, shorter than the burst period of any individual neuron. A consequence of periodic clusters of cellular bursts was the widespread occurrence of periodic synchronized synaptic potentials, as have been observed in hippocampal slices and human temporal neocortical slices. The periods between these synaptic potentials are similar in the model to those observed experimentally. 3. The period could be slowed by either increasing the time constant of the slow inhibitory postsynaptic potential (IPSP), or by making the excitatory synapses more powerful. The period seems to be generated in part as follows. Consider those cells with rapid spontaneous discharge rates. An upper bound for the period corresponds to the interval between 1) such a cell's becoming responsive enough to an excitatory synaptic input to burst, and 2) such a cell's bursting spontaneously (i.e., in response to its own intrinsic inward current). For cells with rapid spontaneous discharge rates, the interval defined in this way is approximately 350 ms. 4. Different cells participated in each cluster. A given cluster was initiated by one cell or by two cells bursting together, and spread via excitatory synapses. Excitatory synaptic paths could be traced from the initiating cell(s), directly or through other participants, to all cells participating in a cluster. Spread of activity was limited by two mechanisms, so that not all cells synaptically excited by a participating cell would themselves participate. First, cells might be refractory from having participated in a recent cluster (since the intercluster period was less than the refractory time from a cellular burst to its responsiveness to a synaptic stimulus). Second, some cells might be synaptically inhibited. Synaptic inhibition in this model did not act rapidly enough to suppress the cluster totally.(ABSTRACT TRUNCATED AT 400 WORDS)

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