NVU dynamics. III. Simulating molecules at constant potential energy

This is the final paper in a series that introduces geodesic molecular dynamics at constant potential energy. This dynamics is entitled NVU dynamics in analogy to standard energy-conserving Newtonian NVE dynamics. In the first two papers [Ingebrigtsen et al., J. Chem. Phys. 135, 104101 (2011); ibid, 104102 (2011)], a numerical algorithm for simulating geodesic motion of atomic systems was developed and tested against standard algorithms. The conclusion was that the NVU algorithm has the same desirable properties as the Verlet algorithm for Newtonian NVE dynamics, i.e., it is time-reversible and symplectic. Additionally, it was concluded that NVU dynamics becomes equivalent to NVE dynamics in the thermodynamic limit. In this paper, the NVU algorithm for atomic systems is extended to be able to simulate geodesic motion of molecules at constant potential energy. We derive an algorithm for simulating rigid bonds and test this algorithm on three different systems: an asymmetric dumbbell model, Lewis-Wahnstrom OTP, and rigid SPC/E water. The rigid bonds introduce additional constraints beyond that of constant potential energy for atomic systems. The rigid-bond NVU algorithm conserves potential energy, bond lengths, and step length for indefinitely long runs. The quantities probed in simulations give results identical to those of Nose-Hoover NVT dynamics. Since Nose-Hoover NVT dynamics is known to give results equivalent to those of NVE dynamics, the latter results show that NVU dynamics becomes equivalent to NVE dynamics in the thermodynamic limit also for molecular systems.Comment: 14 pages, 12 figure

Second-harmonic generation in optically trapped nonlinear particles with pulsed lasers

Pulsed lasers are used for simultaneous single-beam three-dimensional optical trapping of and second-harmonic generation in 50--100-nm nonlinear particles. The emission power of the frequency-doubled light, the trapping stability, and the particle degradation are investigated for KTP and LiNbO3 particles trapped by 25-kHz-repetition-rate Q-switched Nd:YAG and 76-MHz mode-locked Ti:sapphire l a s e r s . Typically 1 pW-10 nW of frequency-doubled light is detected from stably trapped particles. The particles may be used as probes for nonintrusively scanned near-field optical microscopy

Noisy regression and classification with continuous multilayer networks

We investigate zero temperature Gibbs learning for two classes of unrealizable rules which play an important role in practical applications of multilayer neural networks with differentiable activation functions: classification problems and noisy regression problems. Considering one step of replica symmetry breaking, we surprisingly find that for sufficiently large training sets the stable state is replica symmetric even though the target rule is unrealizable. Further, the classification problem is shown to be formally equivalent to the noisy regression problem.Comment: 7 pages, including 2 figure

Soliton-dynamical approach to a noisy Ginzburg-Landau model

We present a dynamical description and analysis of non-equilibrium transitions in the noisy Ginzburg-Landau equation based on a canonical phase space formulation. The transition pathways are characterized by nucleation and subsequent propagation of domain walls or solitons. We also evaluate the Arrhenius factor in terms of an associated action and find good agreement with recent numerical optimization studies.Comment: 4 pages (revtex4), 3 figures (eps

Ionisation by quantised electromagnetic fields: The photoelectric effect

In this paper we explain the photoelectric effect in a variant of the standard model of non relativistic quantum electrodynamics, which is in some aspects more closely related to the physical picture, than the one studied in [BKZ]: Now we can apply our results to an electron with more than one bound state and to a larger class of electron-photon interactions. We will specify a situation, where ionisation probability in second order is a weighted sum of single photon terms. Furthermore we will see, that Einstein's equality $$E_{kin}=h\nu-\bigtriangleup E>0$$ for the maximal kinetic energy $E_{kin}$ of the electron, energy $h\nu$ of the photon and ionisation gap $\bigtriangleup E$ is the crucial condition for these single photon terms to be nonzero.Comment: 59 pages, LATEX2

Droplet-target laser-plasma source for proximity x-ray lithography

A compact, high-brightness and practically debris-free laser-plasma soft x-ray source for proximity x-ray lithography is described. The target of the source is small liquid fluorocarbon droplets injected into vacuum with a piezoelectrically vibrated nozzle. Emission from helium- and hydrogenlike fluorine in the 1.2-1.7 nm wavelength range was determined to similar to 2X10(12) photons/(sr-pulse). which corresponds to a conversion efficiency of similar to 5% of the 70 mJ laser pulse. Exposure of a copolymer of PMMA-MAA confirms the measured photon flux. Debris production was approximately 70 pg/sr pulse. The applicability of the source for dedicated lithography systems is discussed. (C) 1996 American Institute of Physics

Entropy and typical properties of Nash equilibria in two-player games

We use techniques from the statistical mechanics of disordered systems to analyse the properties of Nash equilibria of bimatrix games with large random payoff matrices. By means of an annealed bound, we calculate their number and analyse the properties of typical Nash equilibria, which are exponentially dominant in number. We find that a randomly chosen equilibrium realizes almost always equal payoffs to either player. This value and the fraction of strategies played at an equilibrium point are calculated as a function of the correlation between the two payoff matrices. The picture is complemented by the calculation of the properties of Nash equilibria in pure strategies.Comment: 6 pages, was "Self averaging of Nash equilibria in two player games", main section rewritten, some new results, for additional information see http://itp.nat.uni-magdeburg.de/~jberg/games.htm

Liquid-jet target for laser-plasma soft x-ray generation

We describe a new liquid-target system for low-debris laser-plasma soft x-ray sources. The system is based on a microscopic liquid jet and is experimentally evaluated for 0.7-1 keV proximity lithography and water-window x-ray microscopy applications. Compared to an existing liquid-droplet target, this target system has the same low debris emission, high x-ray photon flux, and narrow spectral bandwidth. The advantages of the liquid-jet target include improved x-ray flux stability, increased range of suitable target liquids, and elimination of the need for temporal synchronization, thereby allowing less complex laser systems to be used. (C) 1996 American Institute of Physics

Reconstructing the Hopfield network as an inverse Ising problem

We test four fast mean field type algorithms on Hopfield networks as an inverse Ising problem. The equilibrium behavior of Hopfield networks is simulated through Glauber dynamics. In the low temperature regime, the simulated annealing technique is adopted. Although performances of these network reconstruction algorithms on the simulated network of spiking neurons are extensively studied recently, the analysis of Hopfield networks is lacking so far. For the Hopfield network, we found that, in the retrieval phase favored when the network wants to memory one of stored patterns, all the reconstruction algorithms fail to extract interactions within a desired accuracy, and the same failure occurs in the spin glass phase where spurious minima show up, while in the paramagnetic phase, albeit unfavored during the retrieval dynamics, the algorithms work well to reconstruct the network itself. This implies that, as a inverse problem, the paramagnetic phase is conversely useful for reconstructing the network while the retrieval phase loses all the information about interactions in the network except for the case where only one pattern is stored. The performances of algorithms are studied with respect to the system size, memory load and temperature, sample-to-sample fluctuations are also considered.Comment: 8 pages, 3 figure

Non-analytic microscopic phase transitions and temperature oscillations in the microcanonical ensemble: An exactly solvable 1d-model for evaporation

We calculate exactly both the microcanonical and canonical thermodynamic functions (TDFs) for a one-dimensional model system with piecewise constant Lennard-Jones type pair interactions. In the case of an isolated $N$-particle system, the microcanonical TDFs exhibit (N-1) singular (non-analytic) microscopic phase transitions of the formal order N/2, separating N energetically different evaporation (dissociation) states. In a suitably designed evaporation experiment, these types of phase transitions should manifest themselves in the form of pressure and temperature oscillations, indicating cooling by evaporation. In the presence of a heat bath (thermostat), such oscillations are absent, but the canonical heat capacity shows a characteristic peak, indicating the temperature-induced dissociation of the one-dimensional chain. The distribution of complex zeros (DOZ) of the canonical partition may be used to identify different degrees of dissociation in the canonical ensemble.Comment: version accepted for publication in PRE, minor additions in the text, references adde