Random walks with thermalizing collisions in bounded regions; physical applications valid from the ballistic to diffusive regimes

The behavior of a spin undergoing Larmor precession in the presence of fluctuating fields is of interest to workers in many fields. The fluctuating fields cause frequency shifts and relaxation which are related to their power spectrum, which can be determined by taking the Fourier transform of the auto-correlation functions of the field fluctuations. Recently we have shown how to calculate these correlation functions for all values of mean free path (ballistic to diffusive motion) in finite bounded regions, using the model of persistent continuous time random walks (CTRW) for particles subject to scattering by fixed (frozen) scattering centers so that the speed of the moving particles is not changed by the collisions. In this work we show how scattering with energy exchange from an ensemble of scatterers in thermal equilibrium can be incorporated into the CTRW. We present results for 1,2 and 3 dimensions. The results agree for all these cases contrary to the previously studied 'frozen' models. Our results for the velocity autocorrelation function show a long time tail $\left( \sim t^{-1/2}\right)$, which we also obtain from conventional diffusion theory, with the same power, independent of dimensionality. Our results are valid for any Markovian scattering kernel as well as any kernel based on a scattering cross section $\sim1/v.$Comment: 43 pages, 12 figure

Frequency shifts and relaxation rates for spin 1/2 particles moving in electromagnetic fields

We discuss the behaviour of the Larmor frequency shift and the longitudinal relaxation rate due to non-uniform electromagnetic fields on an assembly of spin 1/2 particles, in adiabatic and nonadiabatic regimes. We also show some general relations between the various frequency shifts and between the frequency shifts and relaxation rates. The remarkable feature of all our results is that they were obtained without any specific assumptions on the explicit form of the correlation functions of the fields. Hence, we expect that our results are valid both for diffusive and ballistic regime of motion and arbitrary cell shapes and surface scattering. These results can then be applied to a wide variety of realistic systems

Self-organized escape of oscillator chains in nonlinear potentials

We present the noise free escape of a chain of linearly interacting units from a metastable state over a cubic on-site potential barrier. The underlying dynamics is conservative and purely deterministic. The mutual interplay between nonlinearity and harmonic interactions causes an initially uniform lattice state to become unstable, leading to an energy redistribution with strong localization. As a result a spontaneously emerging localized mode grows into a critical nucleus. By surpassing this transition state, the nonlinear chain manages a self-organized, deterministic barrier crossing. Most strikingly, these noise-free, collective nonlinear escape events proceed generally by far faster than transitions assisted by thermal noise when the ratio between the average energy supplied per unit in the chain and the potential barrier energy assumes small values

Pump-Probe Experiments on the Single-Molecule Magnet Fe8 : Measurement of Excited Level Lifetimes

We present magnetization measurements on the single molecule magnet Fe8 in the presence of pulsed microwave radiation. A pump-probe technique is used with two microwave pulses with frequencies of 107 GHz and 118 GHz and pulse lengths of several nanoseconds to study the spin dynamics via time-resolved magnetization measurements using a Hall probe magnetometer. We find evidence for short spin-phonon relaxation times of the order of one microsecond. The temperature dependence of the spin-phonon relaxation time in our experiments is in good agreement with previously published theoretical results. We also established the presence of very short energy diffusion times, that act on a timescale of about 70 ns.Comment: submitted to Phys. Rev. Lett. (01 March 2007

Constraining short-range spin-dependent forces with polarized helium 3 at the Laue-Langevin Institute

We have searched for a short-range spin-dependent interaction mediated by a hypothetical light scalar boson with CP-violating couplings to the neutron using the spin relaxation of hyperpolarized $^3$He. The walls of the $^3$He cell would generate a depolarizing pseudomagnetic field.Comment: Twelfth Conference on the Intersections of Particle and Nuclear Physics (CIPANP2015), Vail Marriott Mountain Resort, Vail, Colorado, US

The orbit method for locally nilpotent infinite-dimensional Lie algebras

Let $\mathfrak{n}$ be a locally nilpotent infinite-dimensional Lie algebra over $\mathbb{C}$. Let $\mathrm{U}(\mathfrak{n})$ and $\mathrm{S}(\mathfrak{n})$ be its universal enveloping algebra and its symmetric algebra respectively. Consider the Jacobson topology on the primitive spectrum of $\mathrm{U}(\mathfrak{n})$ and the Poisson topology on the primitive Poisson spectrum of $\mathrm{S}(\mathfrak{n})$. We provide a homeomorphism between the corresponding topological spaces (on the level of points, it gives a bijection between the primitive ideals of $\mathrm{U}(\mathfrak{n})$ and $\mathrm{S}(\mathfrak{n})$). We also show that all primitive ideals of $\mathrm{S}(\mathfrak{n})$ from an open set in a properly chosen topology are generated by their intersections with the Poisson center. Under the assumption that $\mathfrak{n}$ is a nil-Dynkin Lie algebra, we give two criteria for primitive ideals $I(\lambda)\subset\mathrm{S}(\mathfrak{n})$ and $J(\lambda)\subset\mathrm{U}(\mathfrak{n})$, $\lambda\in\mathfrak{n}^*$, to be nonzero. Most of these results generalize the known facts about primitive and Poisson spectrum for finite-dimensional nilpotent Lie algebras (but note that for a finite-dimensional nilpotent Lie algebra all primitive ideals $I(\lambda)$, $J(\lambda)$ are nonzero)

Non-equilibrium Magnetization Dynamics in the Fe_8 Single-Molecule Magnet Induced by High-Intensity Microwave Radiation

Resonant microwave radiation applied to a single crystal of the molecular magnet Fe_8 induces dramatic changes in the sample's magnetization. Transitions between excited states are found even though at the nominal system temperature these levels have negligible population. We find evidence that the sample heats significantly when the resonance condition is met. In addition, heating is observed after a short pulse of intense radiation has been turned off, indicating that the spin system is out of equilibrium with the lattice.Comment: Version to appear in Europhysics Letters. Minor changes and updated reference