306 research outputs found
How does an interacting many-body system tunnel through a potential barrier to open space?
The tunneling process in a many-body system is a phenomenon which lies at the
very heart of quantum mechanics. It appears in nature in the form of
alpha-decay, fusion and fission in nuclear physics, photoassociation and
photodissociation in biology and chemistry. A detailed theoretical description
of the decay process in these systems is a very cumbersome problem, either
because of very complicated or even unknown interparticle interactions or due
to a large number of constitutent particles. In this work, we theoretically
study the phenomenon of quantum many-body tunneling in a more transparent and
controllable physical system, in an ultracold atomic gas. We analyze a full,
numerically exact many-body solution of the Schr\"odinger equation of a
one-dimensional system with repulsive interactions tunneling to open space. We
show how the emitted particles dissociate or fragment from the trapped and
coherent source of bosons: the overall many-particle decay process is a quantum
interference of single-particle tunneling processes emerging from sources with
different particle numbers taking place simultaneously. The close relation to
atom lasers and ionization processes allows us to unveil the great relevance of
many-body correlations between the emitted and trapped fractions of the
wavefunction in the respective processes.Comment: 18 pages, 4 figures (7 pages, 2 figures supplementary information
Atom interferometry with trapped Bose-Einstein condensates: Impact of atom-atom interactions
Interferometry with ultracold atoms promises the possibility of ultraprecise
and ultrasensitive measurements in many fields of physics, and is the basis of
our most precise atomic clocks. Key to a high sensitivity is the possibility to
achieve long measurement times and precise readout. Ultra cold atoms can be
precisely manipulated at the quantum level, held for very long times in traps,
and would therefore be an ideal setting for interferometry. In this paper we
discuss how the non-linearities from atom-atom interactions on one hand allow
to efficiently produce squeezed states for enhanced readout, but on the other
hand result in phase diffusion which limits the phase accumulation time. We
find that low dimensional geometries are favorable, with two-dimensional (2D)
settings giving the smallest contribution of phase diffusion caused by
atom-atom interactions. Even for time sequences generated by optimal control
the achievable minimal detectable interaction energy is on
the order of 0.001 times the chemical potential of the BEC in the trap. From
there we have to conclude that for more precise measurements with atom
interferometers more sophisticated strategies, or turning off the interaction
induced dephasing during the phase accumulation stage, will be necessary.Comment: 28 pages, 13 figures, extended and correcte
Mean first-passage times for an ac-driven magnetic moment of a nanoparticle
The two-dimensional backward Fokker-Planck equation is used to calculate the
mean first-passage times (MFPTs) of the magnetic moment of a nanoparticle
driven by a rotating magnetic field. It is shown that a magnetic field that is
rapidly rotating in the plane {\it perpendicular} to the easy axis of the
nanoparticle governs the MFPTs just in the same way as a static magnetic field
that is applied {\it along} the easy axis. Within this framework, the features
of the magnetic relaxation and net magnetization of systems composed of
ferromagnetic nanoparticles arising from the action of the rotating field are
revealed.Comment: 7 pages, 1 figur
Dynamics of cold bosons in optical lattices: Effects of higher Bloch bands
The extended effective multiorbital Bose-Hubbard-type Hamiltonian which takes
into account higher Bloch bands, is discussed for boson systems in optical
lattices, with emphasis on dynamical properties, in relation with current
experiments. It is shown that the renormalization of Hamiltonian parameters
depends on the dimension of the problem studied. Therefore, mean field phase
diagrams do not scale with the coordination number of the lattice. The effect
of Hamiltonian parameters renormalization on the dynamics in reduced
one-dimensional optical lattice potential is analyzed. We study both the
quasi-adiabatic quench through the superfluid-Mott insulator transition and the
absorption spectroscopy, that is energy absorption rate when the lattice depth
is periodically modulated.Comment: 23 corrected interesting pages, no Higgs boson insid
Rapidly driven nanoparticles: Mean first-passage times and relaxation of the magnetic moment
We present an analytical method of calculating the mean first-passage times
(MFPTs) for the magnetic moment of a uniaxial nanoparticle which is driven by a
rapidly rotating, circularly polarized magnetic field and interacts with a heat
bath. The method is based on the solution of the equation for the MFPT derived
from the two-dimensional backward Fokker-Planck equation in the rotating frame.
We solve these equations in the high-frequency limit and perform precise,
numerical simulations which verify the analytical findings. The results are
used for the description of the rates of escape from the metastable domains
which in turn determine the magnetic relaxation dynamics. A main finding is
that the presence of a rotating field can cause a drastic decrease of the
relaxation time and a strong magnetization of the nanoparticle system. The
resulting stationary magnetization along the direction of the easy axis is
compared with the mean magnetization following from the stationary solution of
the Fokker-Planck equation.Comment: 24 pages, 4 figure
Bose-Hubbard model with occupation dependent parameters
We study the ground-state properties of ultracold bosons in an optical
lattice in the regime of strong interactions. The system is described by a
non-standard Bose-Hubbard model with both occupation-dependent tunneling and
on-site interaction. We find that for sufficiently strong coupling the system
features a phase-transition from a Mott insulator with one particle per site to
a superfluid of spatially extended particle pairs living on top of the Mott
background -- instead of the usual transition to a superfluid of single
particles/holes. Increasing the interaction further, a superfluid of particle
pairs localized on a single site (rather than being extended) on top of the
Mott background appears. This happens at the same interaction strength where
the Mott-insulator phase with 2 particles per site is destroyed completely by
particle-hole fluctuations for arbitrarily small tunneling. In another regime,
characterized by weak interaction, but high occupation numbers, we observe a
dynamical instability in the superfluid excitation spectrum. The new ground
state is a superfluid, forming a 2D slab, localized along one spatial direction
that is spontaneously chosen.Comment: 16 pages, 4 figure
Macroscopic superposition states of ultracold bosons in a double-well potential
We present a thorough description of the physical regimes for ultracold
bosons in double wells, with special attention paid to macroscopic
superpositions (MSs). We use a generalization of the Lipkin-Meshkov-Glick
Hamiltonian of up to eight single particle modes to study these MSs, solving
the Hamiltonian with a combination of numerical exact diagonalization and
high-order perturbation theory. The MS is between left and right potential
wells; the extreme case with all atoms simultaneously located in both wells and
in only two modes is the famous NOON state, but our approach encompasses much
more general MSs. Use of more single particle modes brings dimensionality into
the problem, allows us to set hard limits on the use of the original two-mode
LMG model commonly treated in the literature, and also introduces a new mixed
Josephson-Fock regime. Higher modes introduce angular degrees of freedom and MS
states with different angular properties.Comment: 15 pages, 8 figures, 1 table. Mini-review prepared for the special
issue of Frontiers of Physics "Recent Progresses on Quantum Dynamics of
Ultracold Atoms and Future Quantum Technologies", edited by Profs. Lee, Ueda,
and Drummon
The what and where of adding channel noise to the Hodgkin-Huxley equations
One of the most celebrated successes in computational biology is the
Hodgkin-Huxley framework for modeling electrically active cells. This
framework, expressed through a set of differential equations, synthesizes the
impact of ionic currents on a cell's voltage -- and the highly nonlinear impact
of that voltage back on the currents themselves -- into the rapid push and pull
of the action potential. Latter studies confirmed that these cellular dynamics
are orchestrated by individual ion channels, whose conformational changes
regulate the conductance of each ionic current. Thus, kinetic equations
familiar from physical chemistry are the natural setting for describing
conductances; for small-to-moderate numbers of channels, these will predict
fluctuations in conductances and stochasticity in the resulting action
potentials. At first glance, the kinetic equations provide a far more complex
(and higher-dimensional) description than the original Hodgkin-Huxley
equations. This has prompted more than a decade of efforts to capture channel
fluctuations with noise terms added to the Hodgkin-Huxley equations. Many of
these approaches, while intuitively appealing, produce quantitative errors when
compared to kinetic equations; others, as only very recently demonstrated, are
both accurate and relatively simple. We review what works, what doesn't, and
why, seeking to build a bridge to well-established results for the
deterministic Hodgkin-Huxley equations. As such, we hope that this review will
speed emerging studies of how channel noise modulates electrophysiological
dynamics and function. We supply user-friendly Matlab simulation code of these
stochastic versions of the Hodgkin-Huxley equations on the ModelDB website
(accession number 138950) and
http://www.amath.washington.edu/~etsb/tutorials.html.Comment: 14 pages, 3 figures, review articl
Fast extraction of neuron morphologies from large-scale SBFSEM image stacks
Neuron morphology is frequently used to classify cell-types in the mammalian cortex. Apart from the shape of the soma and the axonal projections, morphological classification is largely defined by the dendrites of a neuron and their subcellular compartments, referred to as dendritic spines. The dimensions of a neuron’s dendritic compartment, including its spines, is also a major determinant of the passive and active electrical excitability of dendrites. Furthermore, the dimensions of dendritic branches and spines change during postnatal development and, possibly, following some types of neuronal activity patterns, changes depending on the activity of a neuron. Due to their small size, accurate quantitation of spine number and structure is difficult to achieve (Larkman, J Comp Neurol 306:332, 1991). Here we follow an analysis approach using high-resolution EM techniques. Serial block-face scanning electron microscopy (SBFSEM) enables automated imaging of large specimen volumes at high resolution. The large data sets generated by this technique make manual reconstruction of neuronal structure laborious. Here we present NeuroStruct, a reconstruction environment developed for fast and automated analysis of large SBFSEM data sets containing individual stained neurons using optimized algorithms for CPU and GPU hardware. NeuroStruct is based on 3D operators and integrates image information from image stacks of individual neurons filled with biocytin and stained with osmium tetroxide. The focus of the presented work is the reconstruction of dendritic branches with detailed representation of spines. NeuroStruct delivers both a 3D surface model of the reconstructed structures and a 1D geometrical model corresponding to the skeleton of the reconstructed structures. Both representations are a prerequisite for analysis of morphological characteristics and simulation signalling within a neuron that capture the influence of spines
- …