arXiv subjects

Felix Thiel

Publications and source records attributed to Felix Thiel.

At least 19 recordsLinked to original sources

arXiv2024

Versatile Top-Down Patterning Technique for Perovskite On-Chip Integration

Metal-halide perovskites (MHPs) have exciting optoelectronic properties and are under investigation for various applications, such as photovoltaics, light-emitting diodes, and lasers. An essential step towards exploiting the full potential of this class of materials is their large-scale, on-chip integration with high-resolution, top-down patterning. The development of such patterning methods for perovskite films is challenging because of their intrinsic ionic nature and adverse reactions with the solvents used in standard lithography processes. Here, we introduce a versatile and precise method comprising photolithography and reactive ion etching (RIE) processes that can be tuned to accommodate different perovskite compositions and morphologies. Our method utilizes conventional photoresists at reduced temperatures to create micron-sized features down to 1 ${\mu}$m, providing high reproducibility from chip to chip. The patterning technique is validated through atomic force microscopy (AFM), X-ray diffraction (XRD), optical spectroscopy, and scanning electron microscopy (SEM). It enables the scalable and high-throughput on-chip monolithic integration of MHPs.

cond-mat.mtrl-sci↗

arXiv2023

First-detection-time statistics in many-body quantum transport

We study the transport of many partially distinguishable and possibly interacting particles under the action of repeated projective measurements on a target space and investigate how the particles' interference affects the mean first detection time. We contrast the detection of exactly $n$ versus at least $n$ particles, explain divergences in the mean first detection time through spectral properties of the generating evolution operator, and illustrate our findings by an example.

quant-ph↗

arXiv2021

Ubiq: A System to Build Flexible Social Virtual Reality Experiences

While they have long been a subject of academic study, social virtual reality (SVR) systems are now attracting increasingly large audiences on current consumer virtual reality systems. The design space of SVR systems is very large, and relatively little is known about how these systems should be constructed in order to be usable and efficient. In this paper we present Ubiq, a toolkit that focuses on facilitating the construction of SVR systems. We argue for the design strategy of Ubiq and its scope. Ubiq is built on the Unity platform. It provides core functionality of many SVR systems such as connection management, voice, avatars, etc. However, its design remains easy to extend. We demonstrate examples built on Ubiq and how it has been successfully used in classroom teaching. Ubiq is open source (Apache License) and thus enables several use cases that commercial systems cannot.

cs.HC↗

arXiv2021

Uncertainty relation between detection probability and energy fluctuations

A classical random walker starting on a node of a finite graph will always reach any other node since the search is ergodic, namely it is fully exploring space, hence the arrival probability is unity. For quantum walks, destructive interference may induce effectively non-ergodic features in such search processes. Under repeated projective local measurements, made on a target state, the final detection of the system is not guaranteed since the Hilbert space is split into a bright subspace and an orthogonal dark one. Using this we find an uncertainty relation for the deviations of the detection probability from its classical counterpart, in terms of the energy fluctuations.

quant-ph↗

arXiv2020

Dark states of quantum search cause imperfect detection

We consider a quantum walk where a detector repeatedly probes the system with fixed rate $1/τ$ until the walker is detected. This is a quantum version of the first-passage problem. We focus on the total probability, $P_{\mathrm{det}}$, that the particle is eventually detected in some target state, for example on a node $r_{\mathrm{d}}$ on a graph, after an arbitrary number of detection attempts. Analyzing the dark and bright states for finite graphs, and more generally for systems with a discrete spectrum, we provide an explicit formula for $P_{\mathrm{det}}$ in terms of the energy eigenstates which is generically $τ$ independent. We find that disorder in the underlying Hamiltonian renders perfect detection: $P_{\mathrm{det}}=1$, and then expose the role of symmetry with respect to sub-optimal detection. Specifically, we give a simple upper bound for $P_{\mathrm{det}}$ that is controlled by the number of equivalent (with respect to the detection) states in the system. We also extend our results to infinite systems, for example the detection probability of a quantum walk on a line, which is $τ$-dependent and less than half, well below Polya's optimal detection for a classical random walk.

quant-ph↗

arXiv2020

Quantization of the mean decay time for non-Hermitian quantum systems

We show that the mean time, which a quantum particle needs to escape from a system to the environment, is quantized and independent from most dynamical details of the system. In particular, we consider a quantum system with a general Hermitian Hamiltonian $\hat{H}$ and one decay channel, through which probability dissipates to the environment with rate $Γ$. When the system is initially prepared exactly in the decay state, the mean decay time $\langle T \rangle$ is quantized and equal to $w/(2Γ)$. $w$ is the number of distinct energy levels, i.e. eigenvalues of $\hat{H}$, that have overlap with the decay state, and is also the winding number of a transform of the resolvent in the complex plane. Apart from the integer $w$, $\langle T \rangle$ is completely independent of the system's dynamics. The complete decay time distribution can be obtained from an electrostatic analogy and features rare events of very large dissipation times for parameter choices close to critical points, where $w$ changes, e.g. when a degeneracy is lifted. Experiments of insufficient observation time may thus measure a too small value of $w$. We discuss our findings in a disordered tight-binding model and in the two-level atom in a continuous-wave field.

quant-ph↗

arXiv2020

Non-Hermitian and Zeno limit of quantum systems under rapid measurements

We investigate in depth the relation between the first detection time of an isolated quantum system that is repeatedly perturbed by strong local measurements with a large fixed frequency $1/τ$, determining whether it is in some given state $| ψ_\text{d} \rangle$, and the time of absorption to the same state of the same system with the added imaginary potential $2i\hbar | ψ_\text{d} \rangle \langle ψ_\text{d} | / τ$. As opposed to previous works, we compare directly the solutions of both problems in the small $τ$, i.e., Zeno, limit. We find a scaling collapse in $F(t)$ with respect to $τ$ and compute the total detection probability as well as the moments of the first detection time probability density $F(t)$ in the Zeno limit. We show that both solutions approach the same result in this small $τ$ limit, as long as the initial state $| ψ_\text{in} \rangle$ is not parallel to the detection state, i.e. as long as $| \langle ψ_\text{d} | ψ_\text{in} \rangle | < 1$. However, when this condition is violated, the small probability density to detect the state on time scales much larger than $τ$ is precisely a factor of four different for all such times. We express the solution of the Zeno limit of both problems formally in terms of an electrostatic analogy. Our results are corroborated with numerical simulations.

quant-ph↗

arXiv2019

Uncertainty and symmetry bounds for the quantum total detection probability

We investigate a generic discrete quantum system prepared in state $|ψ_\text{in}\rangle$, under repeated detection attempts aimed to find the particle in state $|d\rangle$, for example a quantum walker on a finite graph searching for a node. For the corresponding classical random walk, the total detection probability $P_\text{det}$ is unity. Due to destructive interference, one may find initial states $|ψ_\text{in}\rangle$ with $P_\text{det}<1$. We first obtain an uncertainty relation which yields insight on this deviation from classical behavior, showing the relation between $P_\text{det}$ and energy fluctuations: $ ΔP \,\mathrm{Var}[\hat{H}]_d \ge | \langle d| [\hat{H}, \hat{D}] | ψ_\text{in} \rangle |^2$ where $ΔP = P_\text{det} - |\langleψ_\text{in}|d\rangle |^2$, and $\hat{D} = |d\rangle\langle d|$ is the measurement projector. Secondly, exploiting symmetry we show that $P_\text{det}\le 1/ν$ where the integer $ν$ is the number of states equivalent to the initial state. These bounds are compared with the exact solution for small systems, obtained from an analysis of the dark and bright subspaces, showing the usefulness of the approach. The upper bounds works well even in large systems, and we show how to tighten the lower bound in this case.

quant-ph↗

arXiv2019

Large fluctuations of the first detected quantum return time

How long does it take a quantum particle to return to its origin? As shown previously under repeated projective measurements aimed to detect the return, the closed cycle yields a geometrical phase which shows that the average first detected return time is quantized. For critical sampling times or when parameters of the Hamiltonian are tuned this winding number is modified. These discontinuous transitions exhibit gigantic fluctuations of the return time. While the general formalism of this problem was studied at length, the magnitude of the fluctuations, which is quantitatively essential, remains poorly characterized. Here, we derive explicit expressions for the variance of the return time, for quantum walks in finite Hilbert space. A classification scheme of the diverging variance is presented, for four different physical effects: the Zeno regime, when the overlap of an energy eigenstate and the detected state is small and when two or three phases of the problem merge. These scenarios present distinct physical effects which can be analyzed with the fluctuations of return times investigated here, leading to a topology-dependent time-energy uncertainty principle.

cond-mat.stat-mech↗

arXiv2019

Quantum total detection probability from repeated measurements II. Exploiting symmetry

A quantum walker on a graph, prepared in the state $| ψ_{\rm in} \rangle$, e.g. initially localized at node $r_{\rm in}$, is repeatedly probed, with fixed frequency $1/τ$, to test its presence at some target node $r_{\rm d}$ until the first successful detection. This is a quantum version of the first-passage problem. We investigate the total detection probability $P_{\rm det}$, i.e. the probability to eventually detect the particle after an arbitrary number of detection attempts. It is demonstrated that this total detection probability is less than unity in symmetric systems, where it is possible to find initial states which are shielded from the detector by destructive interference, so-called dark states. The identification of physically equivalent initial states yields an upper bound for $P_{\rm det}$ in terms of the reciprocal of the number $ν$ of physically equivalent states. The relevant subgroup of the system's symmetry operations is found to be the stabilizer of the detection state. Using this, we prove that all bright, i.e. surely detectable, states are symmetric with respect to the stabilizer. This implies that $P_{\rm det}$ can be obtained from a diagonalization of the "symmetrized" Hamiltonian, instead of having to find all eigenstates of the Hamiltonian.

quant-ph↗

arXiv2018

Reaction-diffusion on random spatial networks with scale-free jumping rates via effective medium theory

We study epidemic processes using a metapopulation approach on the line featuring random transport rates between arbitrarily distant sites. An average transport network is found using a recently developed variant of the effective medium approximation (EMA) that is capable of dealing with these long-range connections. Using a Feynman-Kac argument in the effective medium, we derive an estimate on the size of the infected domain, and reproduce the known result of its exponential growth in time. We hereby demonstrate the applicability of long-range EMA to dynamical processes on networks more intricate than simple diffusion.

physics.soc-ph↗

arXiv2018

The spectral dimension controls the decay of the quantum first detection probability

We consider a quantum system that is initially localized at $x_{in}$ and that is repeatedly projectively probed with a fixed period $τ$ at position $x_d$. We ask for the probability that the system is detected in $x_d$ for the very first time, $F_n$, where $n$ is the number of detection attempts. We relate the asymptotic decay and oscillations of $F_n$ with the system's energy spectrum, which is assumed to be absolutely continuous. In particular $F_n$ is determined by the Hamiltonian's measurement spectral density of states (MSDOS) $f(E)$ that is closely related to the density of energy states (DOS). We find that $F_n$ decays like a power law whose exponent is determined by the power law exponent $d_S$ of $f(E)$ around its singularities $E^*$. Our findings are analogous to the classical first passage theory of random walks. In contrast to the classical case, the decay of $F_n$ is accompanied by oscillations with frequencies that are determined by the singularities $E^*$. This gives rise to critical detection periods $τ_c$ at which the oscillations disappear. In the ordinary case $d_S$ can be identified with the spectral dimension found in the DOS. Furthermore, the singularities $E^*$ are the van Hove singularities of the DOS in this case. We find that the asymptotic statistics of $F_n$ depend crucially on the initial and detection state and can be wildly different for out-of-the-ordinary states, which is in sharp contrast to the classical theory. The properties of the first detection probabilities can alternatively be derived from the transition amplitudes. All our results are confirmed by numerical simulations of the tight-binding model, and of a free particle in continuous space both with a normal and with an anomalous dispersion relation. We provide explicit asymptotic formulae for the first detection probability in these models.

cond-mat.stat-mech↗

arXiv2017

First detected arrival of a quantum walker on an infinite line

The first detection of a quantum particle on a graph has been shown to depend sensitively on the sampling time τ . Here we use the recently introduced quantum renewal equation to investigate the statistics of first detection on an infinite line, using a tight-binding lattice Hamiltonian with nearest- neighbor hops. Universal features of the first detection probability are uncovered and simple limiting cases are analyzed. These include the small τ limit and the power law decay with attempt number of the detection probability over which quantum oscillations are superimposed. When the sampling time is equal to the inverse of the energy band width, non-analytical behaviors arise, accompanied by a transition in the statistics. The maximum total detection probability is found to occur for τ close to this transition point. When the initial location of the particle is far from the detection node we find that the total detection probability attains a finite value which is distance independent.

cond-mat.stat-mech↗

arXiv2017

Using Hilbert transform and classical chains to simulate quantum walks

We propose a simulation strategy which uses a classical device of linearly coupled chain of springs to simulate quantum dynamics, in particular the quantum walks. Through this strategy, we obtain the quantum wave function from classical evolution. Specially, this goal is achieved with the classical momenta of the particles on the chain and their Hilbert transform, from which we construct the many-body momentum and Hilbert transformed momentum pair correlation functions yielding the real and imaginary parts of the wave function, respectively. With such wave function, we show that the classical chain's energy and heat spreading densities can be related to the wave function's modulus square. This relation indicates a concept of "phonon random walks", and thus it provides a new perspective to understand ballistic heat transport. The results here may give a definite answer to Feynman's idea of using a classical device to simulate quantum physics.

cond-mat.stat-mech↗

arXiv2017

Anomalous diffusion in run-and-tumble motion

A random walk scheme, consisting of alternating phases of regular Brownian motion and Lévy walks, is proposed as a model for run-and-tumble bacterial motion. Within the continuous-time random walk approach we obtain the long-time and short-time behavior of the mean squared displacement of the walker as depending on the properties of dwelling time distribution in each phase. Depending on these distributions, normal diffusion, superdiffusion and ballistic spreading may arise.

physics.bio-ph↗

arXiv2017

Time averages in continuous time random walks

We investigate the time averaged squared displacement (TASD) of continuous time random walks with respect to the number of steps $N$, which the random walker performed during the data acquisition time $T$. We prove that the TASD, and as well the apparent diffusion constant, grow linearly with $N$, provided the steps possess a fourth moment and can not accumulate in small intervals. Consequently, the fluctuations of the latter are dominated by the fluctuations of $N$, and fluctuations of the walker's thermal history are irrelevant. Furthermore, we show that the relative scatter decays as $1/\sqrt{N}$, which suppresses all non-linear features in a plot of the TASD against the lag time. Parts of our arguments also hold for continuous time random walks with correlated steps.

cond-mat.stat-mech↗

arXiv2016

Effective medium approximation for lattice random walks with long-range jumps

We consider the random walk on a lattice with random transition rates and arbitrarily long-range jumps. We employ Bruggeman's effective medium approximation (EMA) to find the disorder averaged (coarse-grained) dynamics. The EMA procedure replaces the disordered system with a cleverly guessed reference system in a self-consistent manner. We give necessary conditions on the reference system and discuss possible physical mechanisms of anomalous diffusion. In case of a power-law scaling between transition rates and distance, lattice variants of Levy-ights emerge as the effective medium, and the problem is solved analytically, bearing the effective anomalous diffusivity. Finally, we discuss several example distributions, and demonstrate very good agreement with numerical simulations.

cond-mat.dis-nn↗

arXiv2015

Quantifying the non-ergodicity of scaled Brownian motion

We examine the non-ergodic properties of scaled Brownian motion, a non-stationary stochastic process with a time dependent diffusivity of the form $D(t)\simeq t^{α-1}$. We compute the ergodicity breaking parameter EB in the entire range of scaling exponents $α$, both analytically and via extensive computer simulations of the stochastic Langevin equation. We demonstrate that in the limit of long trajectory lengths $T$ and short lag times $Δ$ the EB parameter as function of the scaling exponent $α$ has no divergence at $α=1/2$ and present the asymptotes for EB in different limits. We generalise the analytical and simulations results for the time averaged and ergodic properties of scaled Brownian motion in the presence of ageing, that is, when the observation of the system starts only a finite time span after its initiation. The approach developed here for the calculation of the higher time averaged moments of the particle displacement can be applied to derive the ergodic properties of other stochastic processes such as fractional Brownian motion.

cond-mat.stat-mech↗