# Sascha WaldCoventry University | CU

Sascha Wald

PhD

## About

38

Publications

7,994

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240

Citations

Introduction

I am interested in out of equilibrium quantum dynamics of many-body system. My focus lies on the exact description of non-equilibrium dynamics and collective behaviour of systems in the vicinity of quantum critical points.

Additional affiliations

November 2020 - present

November 2019 - October 2020

October 2019 - October 2019

Education

September 2013 - September 2014

October 2012 - September 2013

October 2009 - September 2012

## Publications

Publications (38)

We investigate several entanglement-related quantities at finite-
temperature criticality in the three-dimensional quantum spherical model,
both as a function of temperature T and of the quantum parameter g, which
measures the strength of quantum fluctuations. While the von Neumann and the
Rényi entropies exhibit a volume-law for any g and T, the m...

The study of entanglement spectra is a powerful tool to detect or elucidate universal behavior in quantum many-body systems. We investigate the scaling of the entanglement (or Schmidt) gap δξ , i.e., the lowest-laying gap of the entanglement spectrum, at a two-dimensional quantum critical point. We focus on the paradigmatic quantum spherical model,...

Random walks are fundamental models of stochastic processes with applications in various fields, including physics, biology, and computer science. We study classical and quantum random walks under the influence of stochastic resetting on arbitrary networks. Based on the mathematical formalism of quantum stochastic walks, we provide a framework of c...

Flocks of animals represent a fascinating archetype of collective behavior in the macroscopic classical world, where the constituents, such as birds, concertedly perform motions and actions as if being one single entity. Here, we address the outstanding question of whether flocks can also form in the microscopic world at the quantum level. For that...

We investigate the influence of disorder on the spreading and entanglement properties of coined quantum walks. Specifically, we consider quantum walks on the line and explore the effects of quenched disorder in the coin operations. We find that coin disorder alters the usual ballistic transport properties of coined quantum walks considerably and yi...

Diverse T and B cell repertoires play an important role in mounting effective immune responses against a wide range of pathogens and malignant cells. The number of unique T and B cell clones is characterized by T and B cell receptors (TCRs and BCRs), respectively. Although receptor sequences are generated probabilistically by recombination processe...

Complex systems are more than the sum of their parts. When an extensive number of constituents come together and interact, intriguing collective phenomena arise. The study of these phenomena impacts diverse research areas, reaching from socioeconomics to quantum technologies. It is beyond the scope of this or any issue to capture all the latest dev...

Disorder in coined quantum walks generally leads to localization. We investigate the influence of the localization on the entanglement properties of coined quantum walks. Specifically, we consider quantum walks on the line and explore the effects of quenched disorder in the coin operations. After confirming that our choice of disorder localizes the...

We review some recent results on entanglement in the Quantum Spherical Model (QSM). The focus lays on the physical results rather than the mathematical details. Specifically, we study several entanglement-related quantities, such as entanglement entropies, and logarithmic negativity, in the presence of quantum and classical critical points, and in...

We investigate the finite-size scaling of the entanglement gap in the one-dimensional
long-range quantum spherical model (QSM). We focus on the weak long-range
QSM, for which the thermodynamic limit is well-defined. This model exhibits a
continuous phase transition, separating a paramagnetic from a ferromagnet phase. The
universality class of the t...

We review some recent results on entanglement in the Quantum Spherical Model (QSM). The focus lays on the physical results rather than the mathematical details. Specifically, we study several entanglement-related quantities, such asentanglement entropies, and logarithmic negativity, in the presence of quantum and classical critical points, and in m...

We investigate the finite-size scaling of the entanglement gap in the one dimensional long-range quantum spherical model (QSM). We focus on the weak long-range QSM, for which the thermodynamic limit is well-defined. This model exhibits a continuous phase transition, separating a paramagnetic from a ferromagnet phase. The universality class of the t...

Recent experimental advances have inspired the development of theoretical tools to describe the non-equilibrium dynamics of quantum systems. Among them an exact representation of quantum spin systems in terms of classical stochastic processes has been proposed. Here we provide first steps towards the extension of this stochastic approach to bosonic...

We study the entanglement dynamics of a one-dimensional hard-core quantum gas initially conﬁned in a box of size L with saturated density ρ = 1. The gas is suddenly released into a region of size 2L by moving one of the box edges. We show that the analytic prediction for the entanglement entropy obtained from quantum ﬂuctuating hydrodynamics holds...

Diverse T and B cell repertoires play an important role in mounting effective immune responses against a wide range of pathogens and malignant cells. The number of unique T and B cell clones is characterized by T and B cell receptors (TCRs and BCRs), respectively. Although receptor sequences are generated probabilistically by recombination processe...

Diverse T and B cell repertoires play an important role in mounting effective immune responses against a wide range of pathogens and malignant cells. The number of unique T and B cell clones is characterized by T and B cell receptors (TCRs and BCRs), respectively. Although receptor sequences are generated probabilistically by recombination processe...

We study the entanglement dynamics of a one-dimensional hard-core quantum gas initially confined in a box of size $L$ with saturated density $\rho=1$. The gas is suddenly released into a region of size $2L$ by moving one of the box edges. We show that the analytic prediction for the entanglement entropy obtained from quantum fluctuating hydrodynami...

The collective and purely relaxational dynamics of quantum many-body systems after a quench at temperature $T=0$, from a disordered state to various phases is studied through the exact solution of the quantum Langevin equation of the spherical and the $O(n)$-model in the limit $n\to\infty$. The stationary state of the quantum dynamics is shown to b...

The study of entanglement spectra is a powerful tool to detect or elucidate universal behaviour in quantum many-body systems. We investigate the scaling of the entanglement (or Schmidt) gap $\delta\xi$, i.e., the lowest laying gap of the entanglement spectrum, at a two-dimensional quantum critical point. We focus on the paradigmatic quantum spheric...

Random walks are fundamental models of stochastic processes with applications in various fields including physics, biology, and computer science. We study classical and quantum random walks under the influence of stochastic resetting on arbitrary networks. Based on the mathematical formalism of quantum stochastic walks, we provide a unifying descri...

We study the influence that collective transition phenomena have on quantum metrological protocols. The single spherical quantum spin (SQS) serves as stereotypical toy model that allows analytical insights on a mean-field level. First, we focus on equilibrium quantum criticality in the SQS and obtain the quantum Fisher information analytically, whi...

We study the influence that collective transition phenomena have on quantum metrological protocols. The single spherical quantum spin (SQS) serves as stereotypical toy model that allows analytical insights on a mean-field level. First, we focus on equilibrium quantum criticality in the SQS and obtain the quantum Fisher information analytically, whi...

We investigate several entanglement-related quantities at finite-temperature criticality in the three-dimensional quantum spherical model, both as a function of temperature $T$ and of the quantum parameter $g$, which measures the strength of quantum fluctuations. While the von Neumann and the R\'enyi entropies exhibit the volume-law for any $g$ and...

In classical mechanics, external constraints on the dynamical variables can be easily implemented within the Lagrangian formulation. Conversely, the extension of this idea to the quantum realm, which dates back to Dirac, has proven notoriously difficult due to the noncommutativity of observables. Motivated by recent progress in the experimental con...

A phenomenological construction of quantum Langevin equations, based on the physical criteria of (i) the canonical equal-time commutators, (ii) the Kubo formula, (iii) the virial theorem and (iv) the quantum fluctuation–dissipation theorem is presented. The case of a single harmonic oscillator coupled to a large external bath is analysed in detail....

We investigate the off-equilibrium dynamics of a classical spin system with O(n) symmetry in 2 < D < 4 spatial dimensions and in the limit n → ∞. The system is set up in an ordered equilibrium state and is subsequently driven out of equilibrium by slowly varying the external magnetic field h across the transition line hc = 0 at fixed temperature T...

A phenomenological construction of quantum Langevin equations, based on the physical criteria of (i) the canonical equal-time commutators, (ii) the Kubo formula, (iii) the virial theorem and (iv) the quantum fluctuation-dissipation theorem is presented. The case of a single harmonic oscillator coupled to a large external bath is analysed in detail....

A phenomenological construction of quantum Langevin equations, based on the physical criteria of (i) the canonical equal-time commutators, (ii) the Kubo formula, (iii) the virial theorem and (iv) the quantum fluctuation-dissipation theorem is presented. The case of a single harmonic oscillator coupled to a large external bath is analysed in detail....

In classical mechanics, external constraints on the dynamical variables can be easily implemented within the Lagrangian formulation. Conversely, the extension of this idea to the quantum realm, which dates back to Dirac, has proven notoriously difficult due to the non-commutativity of observables. Motivated by recent progress in the experimental co...

In classical mechanics, external constraints on the dynamical variables can be easily implemented within the Lagrangian formulation and form the basis for several interesting mechanical phenomena and devices. Conversely, the extension of this idea to the quantum realm, which dates back to Dirac, has proven notoriously difficult due to the non-commu...

We investigate the off-equilibrium dynamics of a classical spin system with $O(n)$ symmetry in $2< D <4$ spatial dimensions and in the limit $n\to \infty$. The system is set up in an ordered equilibrium state is and subsequently driven out of equilibrium by slowly varying the external magnetic field $h$ across the transition line $h_c=0$ at fixed t...

A system of neutral atoms trapped in an optical lattice and dispersively coupled to the field of an optical cavity can realize a variation of the Bose-Hubbard model with infinite-range interactions. This model exhibits a first order quantum phase transition between a Mott insulator and a charge density wave, with spontaneous symmetry breaking betwe...

The purely relaxational non-equilibrium dynamics of the quantum spherical model as described through a Lindblad equation is analysed. It is shown that the phenomenological requirements of reproducing the exact quantum equilibrium state as stationary solution and the associated classical Langevin equation in the classical limit $g\to 0$ fix the form...

The leading asymptotic behaviour of the Humbert functions $\Phi_2$, $\Phi_3$, $\Xi_2$ of two variables is found, when the absolute values of the two independent variables become simultaneosly large. New integral representations of these functions are given. These are re-expressed as inverse Laplace transformations and the asymptotics is then found...

The coherent quantum dynamics of a single bosonic spin variable, subject to a
constraint derived from the quantum spherical model of a ferromagnet, and
coupled to an external heat bath, is studied through the Lindblad equation for
the reduced density matrix. Closed systems of equations of motion for several
quantum observables are derived and solve...

Motivated by an analogy with the spin anisotropies in the quantum XY chain
and its reformulation in terms of spin-less Majorana fermions, its bosonic
analogue, the spin-anisotropic quantum spherical model, is introduced. The
exact solution of the model permits to analyse the influence of the
spin-anisotropy on the phase diagram and the universality...