arXiv subjects

Eric Akkermans

Publications and source records attributed to Eric Akkermans.

At least 37 records · Page 2Linked to original sources

arXiv2018

Scale anomaly of a Lifshitz scalar: a universal quantum phase transition to discrete scale invariance

We demonstrate the existence of a universal transition from a continuous scale invariant phase to a discrete scale invariant phase for a class of one-dimensional quantum systems with anisotropic scaling symmetry between space and time. These systems describe a Lifshitz scalar interacting with a background potential. The transition occurs at a critical coupling $λ_{c}$ corresponding to a strongly attractive potential.

hep-th↗

arXiv2016

Numerical Study of Continuous and Discontinuous Dynamical Phase Transitions for Boundary Driven Systems

The existence and search for thermodynamic phase transitions is of unfading interest. In this paper, we present numerical evidence of dynamical phase transitions occurring in boundary driven systems with a constrained integrated current. It is shown that certain models exhibit a discontinuous transition between two different density profiles and a continuous transition between a time-independent and a time-dependent profile. We also checked that the KMP model does not exhibit phase transition in a range much larger than previously explored.

cond-mat.stat-mech↗

arXiv2016

Ramsey Interferometry of Particle-Hole Pairs in Tunnel Junctions

We present a method to probe real-time dynamics in quantum mesoscopic systems using Ramsey interferometry. This allows us to explore the effect of interactions on quasi-particles in the time domain. We investigate the dephasing effects of an ohmic environment on an electron-hole pair in a tunnel junction. We show that dynamical Coulomb blockade phenomena can be observed for resistances much smaller than the quantum of resistance. Moreover, the crossover between high and low impedance limits can be probed for a constant resistance by a proper control of the voltage modulation.

cond-mat.mes-hall↗

arXiv2016

Topological Boundary States in 1D: An Effective Fabry-Perot Model

We present a general and useful method to predict the existence, frequency, and spatial properties of gap states in photonic (and other) structures with a gapped spectrum. This method is established using the scattering approach. It offers a viewpoint based on a geometrical Fabry-Perot model. We demonstrate the capabilities of this model by predicting the behaviour of topological edge states in quasi-periodic structures. A proposition to use this model in Casimir physics is presented.

cond-mat.mes-hall↗

arXiv2015

Le Chatelier principle for out of equilibrium and boundary driven systems : application to dynamical phase transitions

A stability analysis of out of equilibrium and boundary driven systems is presented. It is performed in the framework of the hydrodynamic macroscopic fluctuation theory and assuming the additivity principle whose interpretation is discussed with the help of a Hamiltonian description. An extension of Le Chatelier principle for out of equilibrium situations is presented which allows to formulate the conditions of validity of the additivity principle. Examples of application of these results in the realm of classical and quantum systems are provided.

cond-mat.stat-mech↗

arXiv2014

Fractal energy spectrum of a polariton gas in a Fibonacci quasi-periodic potential

We report on the study of a polariton gas confined in a quasi-periodic one dimensional cavity, described by a Fibonacci sequence. Imaging the polariton modes both in real and reciprocal space, we observe features characteristic of their fractal energy spectrum such as the opening of mini-gaps obeying the gap labeling theorem and log-periodic oscillations of the integrated density of states. These observations are accurately reproduced solving an effective 1D Schrödinger equation, illustrating the potential of cavity polaritons as a quantum simulator in complex topological geometries.

cond-mat.quant-gas↗

arXiv2013

Universal current fluctuations in the symmetric exclusion process and other diffusive systems

We show, using the macroscopic fluctuation theory of Bertini, De Sole, Gabrielli, Jona-Lasinio, and Landim, that the statistics of the current of the symmetric simple exclusion process (SSEP) connected to two reservoirs are the same on an arbitrary large finite domain in dimension $d$ as in the one dimensional case. Numerical results on squares support this claim while results on cubes exhibit some discrepancy. We argue that the results of the macroscopic fluctuation theory should be recovered by increasing the size of the contacts. The generalization to other diffusive systems is straightforward.

cond-mat.stat-mech↗

arXiv2012

Wave propagation in one-dimension: Methods and applications to complex and fractal structures

This chapter is a pedagogical review of methods and results for studying wave propagation in one-dimensional complex structures. We describe and compare the tight-binding, scattering matrix, transfer matrix and Riccati formalisms. We present examples for transport through finite-sized layered dielectric systems with periodic, quasi-periodic, fractal, disordered, and random structure, illustrating how can spatial structure affect the spectrum of modes as well as the local mode intensity.

physics.optics↗

arXiv2012

Statistical Mechanics and Quantum Fields on Fractals

Fractals define a new and interesting realm for a discussion of basic phenomena in quantum field theory and statistical mechanics. This interest results from specific properties of fractals, e.g., their dilatation symmetry and the corresponding absence of Fourier mode decomposition. Moreover, the existence of a set of distinct dimensions characterizing the physical properties (spatial or spectral) of fractals make them a useful testing ground for dimensionality dependent physical problems. This paper addresses specific problems including the behavior of the heat kernel and spectral zeta functions on fractals and their importance in the expression of spectral properties in quantum physics. Finally, we apply these results to specific problems such as thermodynamics of quantum radiation by a fractal blackbody.

cond-mat.stat-mech↗

arXiv2012

Spontaneous Emission from a Fractal Vacuum

Spontaneous emission of a quantum emitter coupled to a QED vacuum with a deterministic fractal structure of its spectrum is considered. We show that the decay probability does not follow a Wigner-Weisskopf exponential decrease but rather an overall power law behavior with a rich oscillatory structure, both depending on the local fractal properties of the vacuum spectrum. These results are obtained by giving first a general perturbative derivation for short times. Then we propose a simplified model which retains the main features of a fractal spectrum to establish analytic expressions valid for all time scales. Finally, we discuss the case of a Fibonacci cavity and its experimental relevance to observe these results.

math-ph↗

arXiv2012

Spatial Log Periodic Oscillations of First-Passage Observables in Fractals

For transport processes in geometrically restricted domains, the mean first-passage time (MFPT) admits a general scaling dependence on space parameters for diffusion, anomalous diffusion, and diffusion in disordered or fractal media. For transport in self-similar fractal structures, we obtain a new expression for the source-target distance dependence of the MFPT that exhibits both the leading power law behavior, depending on the Hausdorff and spectral dimension of the fractal, as well as small log periodic oscillations that are a clear and definitive signal of the underlying fractal structure. We also present refined numerical results for the Sierpinski gasket that confirm this oscillatory behavior.

cond-mat.stat-mech↗

arXiv2011

Ramsey Fringes and Time-domain Multiple-Slit Interference from Vacuum

Sequences of alternating-sign time-dependent electric field pulses lead to coherent interference effects in Schwinger vacuum pair production, producing a Ramsey interferometer, an all-optical time-domain realization of the multiple-slit interference effect, directly from the quantum vacuum. The interference, obeying fermionic quantum statistics, is manifest in the momentum dependence of the number of produced electrons and positrons along the linearly polarized electric field. The central value grows like $N^2$ for $N$ pulses [i.e., $N$ "slits"], and the functional form is well-described by a coherent multiple-slit expression. This behavior is generic for many driven quantum systems.

hep-th↗

arXiv2010

Thermodynamics of photons on fractals

A thermodynamical treatment of a massless scalar field (a "photon") confined to a fractal spatial manifold leads to an equation of state relating pressure to internal energy, $P V_s=U/d_s$, where $d_s$ is the spectral dimension and $V_s$ defines the "spectral volume". For regular manifolds, $V_s$ coincides with the usual geometric spatial volume, but on a fractal this is not necessarily the case. This is further evidence that on a fractal, momentum space can have a different dimension than position space. Our analysis also provides a natural definition of the vacuum (Casimir) energy of a fractal. We suggest ways that these unusual properties might be probed experimentally.

cond-mat.stat-mech↗

arXiv2009

Physical Consequences of Complex Dimensions of Fractals

It has recently been realized that fractals may be characterized by complex dimensions, arising from complex poles of the corresponding zeta function, and we show here that these lead to oscillatory behavior in various physical quantities. We identify the physical origin of these complex poles as the exponentially large degeneracy of the iterated eigenvalues of the Laplacian, and discuss applications in quantum mesoscopic systems such as oscillations in the fluctuation $Σ^2 (E)$ of the number of levels, as a correction to results obtained in Random Matrix Theory. We present explicit expressions for these oscillations for families of diamond fractals, also studied as hierarchical lattices.

cond-mat.mes-hall↗

arXiv2006

Numerical study of one-dimensional and interacting Bose-Einstein condensates in a random potential

We present a detailed numerical study of the effect of a disordered potential on a confined one-dimensional Bose-Einstein condensate, in the framework of a mean-field description. For repulsive interactions, we consider the Thomas-Fermi and Gaussian limits and for attractive interactions the behavior of soliton solutions. We find that the disorder average spatial extension of the stationary density profile decreases with an increasing strength of the disordered potential both for repulsive and attractive interactions among bosons. In the Thomas Fermi limit, the suppression of transport is accompanied by a strong localization of the bosons around the state k=0 in momentum space. The time dependent density profiles differ considerably in the cases we have considered. For attractive Bose-Einstein condensates, a bright soliton exists with an overall unchanged shape, but a disorder dependent width. For weak disorder, the soliton moves on and for a stronger disorder, it bounces back and forth between high potential barriers.

cond-mat.other↗

arXiv2005

Non exponential quasiparticle decay and phase relaxation in low dimensional conductors

We show that in low dimensional disordered conductors, the quasiparticle decay and the relaxation of the phase are not exponential processes. In the quasi-one dimensional case, both behave at small time as $e^{- (t/τ_{in})^{3/2}}$ where the inelastic time $τ_{in}$, identical for both processes, is a power $T^{2/3}$ of the temperature. This result implies the existence of an unusual distribution of relaxation times that we obtain.

cond-mat.mes-hall↗

arXiv2004

Bogomol'nyi bound and screw dislocations in a mesoscopic smectic-A

The de Gennes free energy functional of an infinite smectic-A liquid crystal at the dual point is shown to be topological and to depend only on the number of screw dislocations and the anisotropy. This result generalizes the existence of a Bogomol'nyi bound to an anisotropic system. The role of the boundary of a finite mesoscopic smectic is to provide a mechanism for the existence of thermodynamically stable screw dislocations. We obtain a closed expression for the corresponding free energy and a relation between the applied twist and the number of screw dislocations.

cond-mat.mes-hall↗

arXiv2004

Non-exponential relaxations in disordered conductors

We show that, in low dimensional conductors, the quasiparticle decay and the relaxation of the phase are not exponential processes. In quasi-one dimension, they scale as $e^{- (t/τ_N)^{3/2}}$ where the characteristic time $τ_{in}$, identical for both processes, is a power $T^{2/3}$ of the temperature. This result implies a distribution of relaxation times.

cond-mat.mes-hall↗