arXiv subjects

Gert-Ludwig Ingold

Publications and source records attributed to Gert-Ludwig Ingold.

At least 37 records · Page 2Linked to original sources

arXiv2016

Negative Entropies in Casimir and Casimir-Polder Interactions

It has been increasingly becoming clear that Casimir and Casimir-Polder entropies may be negative in certain regions of temperature and separation. In fact, the occurrence of negative entropy seems to be a nearly ubiquitous phenomenon. This is most highlighted in the quantum vacuum interaction of a nanoparticle with a conducting plate or between two nanoparticles. It has been argued that this phenomenon does not violate physical intuition, since the total entropy, including the self-entropies of the plate and the nanoparticle, should be positive. New calculations, in fact, seem to bear this out at least in certain cases.

quant-ph↗

arXiv2015

Disentangling geometric and dissipative origins of negative Casimir entropies

Dissipative electromagnetic response and scattering geometry are potential sources for the appearance of a negative Casimir entropy. We show that the dissipative contribution familiar from the plane-plane geometry appears also in the plane-sphere and the sphere-sphere geometries and adds to the negative Casimir entropy known to exist in these geometries even for perfectly reflecting objects. Taking the sphere-sphere geometry as an example, we carry out a scattering-channel analysis which allows to distinguish between the contributions of different polarizations. We demonstrate that dissipation and geometry share a common feature making possible negative values of the Casimir entropy. In both cases there exists a scattering channel whose contribution to the Casimir free energy vanishes in the high-temperature limit. While the mode-mixing channel is associated with the geometric origin, the transverse electric channel is associated with the dissipative origin of the negative Casimir entropy. By going beyond the Rayleigh limit, we find even for large distances that negative Casimir entropies can occur also for Drude-type metals provided the dissipation strength is sufficiently small.

quant-ph↗

arXiv2014

Geometric origin of negative Casimir entropies: A scattering-channel analysis

Negative values of the Casimir entropy occur quite frequently at low temperatures in arrangements of metallic objects. The physical reason lies either in the dissipative nature of the metals as is the case for the plane-plane geometry or in the geometric form of the objects involved. Examples for the latter are the sphere-plane and the sphere-sphere geometry, where negative Casimir entropies can occur already for perfect metal objects. After appropriately scaling out the size of the objects, negative Casimir entropies of geometric origin are particularly pronounced in the limit of large distances between the objects. We analyze this limit in terms of the different scattering channels and demonstrate how the negativity of the Casimir entropy is related to the polarization mixing arising in the scattering process. If all involved objects have a finite zero-frequency conductivity, the channels involving transverse electric modes are suppressed and the Casimir entropy within the large-distance limit is found to be positive.

quant-ph↗

arXiv2014

Negative Casimir Entropies in Nanoparticle Interactions

Negative entropy has been known in Casimir systems for some time. For example, it can occur between parallel metallic plates modeled by a realistic Drude permittivity. Less well known is that negative entropy can occur purely geometrically, say between a perfectly conducting sphere and a conducting plate. The latter effect is most pronounced in the dipole approximation, which is reliable when the size of the sphere is small compared to the separation between the sphere and the plate. Therefore, here we examine cases where negative entropy can occur between two electrically and magnetically polarizable nanoparticles or atoms, which need not be isotropic, and between such a small object and a conducting plate. Negative entropy can occur even between two perfectly conducting spheres, between two electrically polarizable nano-particles if there is sufficient anisotropy, between a perfectly conducting sphere and a Drude sphere,and between a sufficiently anisotropic electrically polarizable nano-particle and a transverse magnetic conducting plate.

quant-ph↗

arXiv2014

Unitary dynamics and finite-time measurements: a case study

The inhibition of the decay of a quantum system by frequent measurements is known as quantum Zeno effect. Beyond the limit of projective measurements, the interplay between the unitary dynamics of the system and the coupling to a measurement apparatus becomes relevant. We explore this interplay by considering a quantum particle moving on a one-dimensional chain. A local measurement by coupling to an apparatus with a two-dimensional Hilbert space detects the presence of the particle on a specific chain site. The decay of the population is studied analytically for a two-site chain and numerically for a larger system as a function of the measurement time and the time between subsequent measurements. Particular attention is given to the shift of the energy of the measured site due to the coupling to the apparatus. The decay of the initial population can be hindered or accelerated, depending on the chosen system and the coupling parameters.

quant-ph↗

arXiv2014

Casimir effect from a scattering approach

The Casimir force is a spectacular consequence of the existence of vacuum fluctuations and thus deserves a place in courses on quantum theory. We argue that the scattering approach within a one-dimensional field theory is well suited to discuss the Casimir effect. It avoids in a transparent way divergences appearing in the evaluation of the vacuum energy. Furthermore, the scattering approach connects in a natural manner to the standard discussion of one-dimensional scattering problems in a quantum theory course. Finally, it allows to introduce students to the methods employed in the current research literature to determine the Casimir force in real-world systems.

quant-ph↗

arXiv2014

Anomalies in the specific heat of a free damped particle: The role of the cutoff in the spectral density of the coupling

The properties of a dissipative system depend on the spectral density of the coupling to the environment. Mostly, the dependence on the low-frequency behavior is in the focus of interest. However, in order to avoid divergencies, it is also necessary to suppress the spectral density of the coupling at high frequencies. Interestingly, the very existence of this cutoff may lead to a mass renormalization which can have drastic consequences for the thermodynamic properties of the dissipative system. Here, we explore the role which the cutoff in the spectral density of the coupling plays for a free damped particle and we compare the effect of an algebraic cutoff with that of a sharp cutoff.

cond-mat.stat-mech↗

arXiv2014

Thermodynamic anomalies in the presence of dissipation: from the free particle to the harmonic oscillator

A free particle coupled to a heat bath can exhibit a number of thermodynamic anomalies like a negative specific heat or reentrant classicality. These low-temperature phenomena are expected to be modified at very low temperatures where finite-size effects associated with the discreteness of the energy spectrum become relevant. In this paper, we explore in which form the thermodynamic anomalies of the free damped particle appear for a damped harmonic oscillator. Since the discreteness of the oscillator's energy spectrum is fully accounted for, the results are valid for arbitrary temperatures. As expected, they are in agreement with the third law of thermodynamics and indicate how the thermodynamic anomalies of the free damped particle can be reconciled with the third law. Particular attention is paid to the transition from the harmonic oscillator to the free particle when the limit of the oscillator frequency to zero is taken.

cond-mat.stat-mech↗

arXiv2013

Metaplectic sheets and caustic traversals in the Weyl representation

The quantum Hamiltonian generates in time a family of evolution operators. Continuity of this family holds within any choice of representation and, in particular, for the Weyl propagator, even though its simplest semiclassical approximation may develop caustic singularities. The phase jumps of the Weyl propagator across caustics have not been previously determined. The semiclassical appproximation relies on individual classical trajectories together with their neighbouring tangent map. Based on the latter, one defines a continuous family of unitary tangent propagators, with an exact Weyl representation that is close to the full semiclassical approximation in an appropriate neighbourhood. The phase increment of the semiclassical Weyl propagator, as a caustic is crossed, is derived from the facts that the corresponding family of tangent operators belong to the metaplectic group and that the products of the tangent propagators are obtained from Gaussian integrals. The Weyl representation of the metaplectic group is here presented, with the correct phases determined within an intrinsic ambiguity for the overall sign. The elements that fully determine the phase increment across a particular caustic are then analysed.

math-ph↗

arXiv2013

Reentrant classicality of a damped system

For a free particle, the coupling to its environment can be the relevant mechanism to induce quantum behavior as the temperature is lowered. We study general linear environments with a spectral density proportional to ω^s at low frequencies and consider in particular the specific heat of the free damped particle. For super-Ohmic baths with s>=2, a reentrant classical behavior is found. As the temperature is lowered, the specific heat decreases from the classical value of k_B/2, thereby indicating the appearence of quantum effects. However, the classical value of the specific heat is restored as the temperature approaches zero. This surprising behavior is due to the suppressed density of bath degrees of freedom at low frequencies. For s<2, the specific heat at zero temperature increases linearly with s from -k_B/2 to k_B/2. An Ohmic bath, s=1, is thus very special in the sense that it represents the only case where the specific heat vanishes at zero temperature.

quant-ph↗

arXiv2012

Classical Casimir interaction in the plane-sphere geometry

We study the Casimir interaction in the plane-sphere geometry in the classical limit of high temperatures. In this limit, the finite conductivity of the metallic plates needs to be taken into account. For the Drude model, the classical Casimir interaction is nevertheless found to be independent of the conductivity so that it can be described by a single universal function depending only on the aspect ratio $x=L/R$ where $L$ is the interplate distance and $R$ the sphere radius. This universal function differs from the one found for perfect reflectors and is in principle amenable to experimental tests. The asymptotic approach of the exact result to the Proximity Force Approximation appears to be well fitted by polynomial expansions in $\ln x$.

quant-ph↗

arXiv2012

Transport of flexible chiral objects in a uniform shear flow

The transport of slightly deformable chiral objects in a uniform shear flow is investigated. Depending on the equilibrium configuration one finds up to four different asymptotic states that can be distinguished by a lateral drift velocity of their center of mass, a rotational motion about the center of mass and deformations of the object. These deformations influence the magnitudes of the principal axes of the second moment tensor of the considered object and also modify a scalar index characterizing its chirality. Moreover, the deformations induced by the shear flow are essential for the phenomenon of dynamical symmetry breaking: Objects that are achiral under equilibrium conditions may dynamically acquire chirality and consequently experience a drift in the lateral direction.

cond-mat.soft↗

arXiv2012

Beyond Zeno: Approaching Infinite Temperature upon Repeated Measurements

The influence of repeated projective measurements on the dynamics of the state of a quantum system is studied in dependence of the time lag $τ$ between successive measurements. In the limit of infinitely many measurements of the occupancy of a single state the total system approaches a uniform state. The asymptotic approach to this state is exponential in the case of finite Hilbert space dimension. The rate characterizing this approach undergoes a sharp transition from a monotonically increasing to an erratically varying function of the time between subsequent measurements.

quant-ph↗

arXiv2011

Thermodynamic anomaly of the free damped quantum particle: the bath perspective

A possible definition of the specific heat of open quantum systems is based on the reduced partition function of the system. For a free damped quantum particle, it has been found that under certain conditions, this specific heat can become negative at low temperatures. In contrast to the conventional approaches focusing on the system degree of freedom, here we concentrate on the changes induced in the environment when the system is coupled to it. Our analysis is carried out for an Ohmic environment consisting of harmonic oscillators and allows to identify the mechanism by which the specific heat becomes negative. Furthermore, the formal condition for the occurrence of a negative specific heat is given a physical interpretation in terms of the total mass of bath oscillators and the system mass.

quant-ph↗

arXiv2010

Nonclassical phase-space trajectories for the damped harmonic quantum oscillator

The phase-space path-integral approach to the damped harmonic oscillator is analyzed beyond the Markovian approximation. It is found that pairs of nonclassical trajectories contribute to the path-integral representation of the Wigner propagating function. Due to the linearity of the problem, the sum coordinate of a pair still satisfies the classical equation of motion. Furthermore, it is shown that the broadening of the Wigner propagating function of the damped oscillator arises due to the time-nonlocal interaction mediated by the heat bath.

quant-ph↗

arXiv2009

The embedding method beyond the single-channel case: Two-mode and Hubbard chains

We investigate the relationship between persistent currents in multi-channel rings containing an embedded scatterer and the conductance through the same scatterer attached to leads. The case of two uncoupled channels corresponds to a Hubbard chain, for which the one-dimensional embedding method is readily generalized. Various tests are carried out to validate this new procedure, and the conductance of short one-dimensional Hubbard chains attached to perfect leads is computed for different system sizes and interaction strengths. In the case of two coupled channels the conductance can be obtained from a statistical analysis of the persistent current or by reducing the multi-channel scattering problem to several single-channel setups.

cond-mat.mes-hall↗

arXiv2009

Quantum dissipative Brownian motion and the Casimir effect

We explore an analogy between the thermodynamics of a free dissipative quantum particle and that of an electromagnetic field between two mirrors of finite conductivity. While a free particle isolated from its environment will effectively be in the high-temperature limit for any nonvanishing temperature, a finite coupling to the environment leads to quantum effects ensuring the correct low-temperature behavior. Even then, it is found that under appropriate circumstances the entropy can be a nonmonotonic function of the temperature. Such a scenario with its specific dependence on the ratio of temperature and damping constant also appears for the transverse electric mode in the Casimir effect. The limits of vanishing dissipation for the quantum particle and of infinite conductivity of the mirrors in the Casimir effect both turn out to be noncontinuous.

quant-ph↗

arXiv2009

Specific heat anomalies of open quantum systems

The evaluation of the specific heat of an open, damped quantum system is a subtle issue. One possible route is based on the thermodynamic partition function which is the ratio of the partition functions of system plus bath and of the bath alone. For the free damped particle it has been shown, however, that the ensuing specific heat may become negative for appropriately chosen environments. Being an open system this quantity then naturally must be interpreted as the change of the specific heat obtained as the difference between the specific heat of the heat bath coupled to the system degrees of freedom and the specific heat of the bath alone. While this difference may become negative, the involved specific heats themselves are always positive; thus, the known thermodynamic stability criteria are perfectly guaranteed. For a damped quantum harmonic oscillator, instead of negative values, under appropriate conditions one can observe a dip in the difference of specific heats as a function of temperature. Stylized minimal models containing a single oscillator heat bath are employed to elucidate the occurrence of the anomalous temperature dependence of the corresponding specific heat values. Moreover, we comment on the consequences for the interpretation of the density of states based on the thermal partitionfunction.

quant-ph↗