482 research outputs found
Interpolating between random walk and rotor walk
We introduce a family of stochastic processes on the integers, depending on a
parameter and interpolating between the deterministic rotor walk
(p=0) and the simple random walk (p=1/2). This p-rotor walk is not a Markov
chain but it has a local Markov property: for each the
sequence of successive exits from is a Markov chain. The main result of
this paper identifies the scaling limit of the p-rotor walk with two-sided
i.i.d. initial rotors. The limiting process takes the form
, where is a doubly perturbed Brownian motion,
that is, it satisfies the implicit equation \begin{equation} X(t) =
\mathcal{B}(t) + a \sup_{s\leq t} X(s) + b \inf_{s\leq t} X(s) \end{equation}
for all . Here is a standard Brownian motion
and are constants depending on the marginals of the initial rotors on
and respectively. Chaumont and Doney [CD99] have
shown that the above equation has a pathwise unique solution , and that
the solution is almost surely continuous and adapted to the natural filtration
of the Brownian motion. Moreover, and [CDH00]. This last result, together with the main result of this
paper, implies that the p-rotor walk is recurrent for any two-sided i.i.d.
initial rotors and any .Comment: 22 pages, 2 figures; Remark about the connection between our model
and excited random walks with Markovian cookie stacks added. References adde
Random rotor walks and i.i.d. sandpiles on Sierpinski graphs
We prove that, on the infinite Sierpinski gasket graph SG, rotor walk with
random initial configuration of rotors is recurrent. We also give a necessary
condition for an i.i.d. sandpile to stabilize. In particular, we prove that an
i.i.d. sandpile with expected number of chips per site greater or equal to
three does not stabilize almost surely. Furthermore, the proof also applies to
divisible sandpiles and shows that divisible sandpile at critical density one
does not stabilize almost surely on SG.Comment: 13 pages, 3 figures; referee's suggestions implemented; to appear in
Statistics and Probability Letters (2024
Monte Carlo evaluation of the equilibrium isotope effects using the Takahashi-Imada factorization of the Feynman path integral
The Feynman path integral approach for computing equilibrium isotope effects
and isotope fractionation corrects the approximations made in standard methods,
although at significantly increased computational cost. We describe an
accelerated path integral approach based on three ingredients: the fourth-
order Takahashi-Imada factorization of the path integral, thermodynamic
integration with respect to mass, and centroid virial estimators for relevant
free energy derivatives. While the frst ingredient speeds up convergence to the
quantum limit, the second and third improve statistical convergence. The
combined method is applied to compute the equilibrium constants for isotope
exchange reactions H2+D=H+HD and H2+D2=2HD
Spectral statistics across the many-body localization transition
The many-body localization transition (MBLT) between ergodic and many-body
localized phase in disordered interacting systems is a subject of much recent
interest. Statistics of eigenenergies is known to be a powerful probe of
crossovers between ergodic and integrable systems in simpler examples of
quantum chaos. We consider the evolution of the spectral statistics across the
MBLT, starting with mapping to a Brownian motion process that analytically
relates the spectral properties to the statistics of matrix elements. We
demonstrate that the flow from Wigner-Dyson to Poisson statistics is a
two-stage process. First, fractal enhancement of matrix elements upon
approaching the MBLT from the metallic side produces an effective power-law
interaction between energy levels, and leads to a plasma model for level
statistics. At the second stage, the gas of eigenvalues has local interaction
and level statistics belongs to a semi-Poisson universality class. We verify
our findings numerically on the XXZ spin chain. We provide a microscopic
understanding of the level statistics across the MBLT and discuss implications
for the transition that are strong constraints on possible theories.Comment: 5 pages, 3 figure
Modernisations and digitalizations of fast timing techniques for γ - γ and e− - γ timing and lifetime measurements in middle-heavy rare earths nuclei
This doctoral thesis presents the modernisation and digitalization of two different experimental
techniques and the results of different nuclear structure experiments in: The Orange conversion
electron spectrometer setup was revised, rebuild in many hardware units and the usability has
been restored by extensive software development of a control and acquisition software. Two
different measurement modi are supported: a scan modes, which allows for conversion electron
spectroscopy of an energy range during γ-source and in-beam measurements and an continuous
mode, where one conversion electron energy can be selected by the strenghts of the magnetic
field generated by the Orange spectrometer. Additionally, the implementation and validation of
the digital fast timing technique with the recently commissioned fast-sampling digitizers Caen
V1730 and additionally V1751 has been carried out. The digitizers have been installed and
thoroughly been investigated and characterized in terms of time resolution and time walk and
the settings of the integrated digital constant fraction discriminators have been optimized for
digital fast-timing experiments. Both developments have successfully been commissioned in e− –
γ and γ – γ fast-timing lifetime measurements in nuclei belonging to the neutron midshell N =
104, A ≈ 180 region.
The lifetime results of four tungsten and osmium isotopes are discussed within the context
of the deformation and transitional phenomena in the neutron midshell N = 104 region. All
investigated nuclei lie at the edge of the strongly deformed region whose center is represented by
the midshell-midshell nucleus 170 Dy.
For 176,178,180 W, fast-timing methods using the newly revised and commissioned Orange conversion
electron spectrometer and the Cologne HORUS spectrometer were employed. Different fusion
evaporation reactions were utilized to populate excited states in these tungsten isotopes, allowing
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for the measurement of lifetimes for the 2+
1 , 41 , 61 , and 81 yrast states, with an additional
176 W. The extracted quadrupole deformation parameters,
measurement of the 10+
1 state in
reduced transition probabilities, and B4/2 ratios were compared with Interacting Boson Model 1
calculations, confirming the deformed prolate rotor nature of the investigated tungsten isotopes.
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In the case of 182 Os the low-lying yrast states 2+
1 , 41 , and 61 were studied using the newly
implemented and commissioned digital fast-timing technique of the IKP. For the first time,
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lifetimes were determined for the 4+
1 and 61 states, while the lifetime of the 21 state was
re-evaluated to remove inconsistencies in the literature. The obtained lifetimes and extracted
B(E2) values were analyzed in terms of collective signatures and transitional phenomena. The
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calculated B(E2; 4+
1 → 21 )/B(E2;21 → 01 ) ratio of 1.39(7) supported the interpretation of
182 Os as a rigid rotor, and its significance was discussed alongside neighboring isotopes and
isotones within the framework of the interacting boson model 1. Furthermore, the structure
of 182 Os was investigated under consideration of the influences of competing factors such as
the nearby collective deformed region, γ-soft rotors, X(5) symmetry, and neighboring regions of
shape coexistence in low excitation states. The study of higher-lying excitation bands in osmium
isotopes and the associated isotones helped explain the structural transitions occurring at 182 Os,
shedding light on the interplay of the different structural influences
Disorder and interference: localization phenomena
The specific problem we address in these lectures is the problem of transport
and localization in disordered systems, when interference is present, as
characteristic for waves, with a focus on realizations with ultracold atoms.Comment: Notes of a lecture delivered at the Les Houches School of Physics on
"Ultracold gases and quantum information" 2009 in Singapore. v3: corrected
mistakes, improved script for numerics, Chapter 9 in "Les Houches 2009 -
Session XCI: Ultracold Gases and Quantum Information" edited by C. Miniatura
et al. (Oxford University Press, 2011
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