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Horia D. Cornean

Publications and source records attributed to Horia D. Cornean.

At least 55 records · Page 3Linked to original sources
arXiv2014

Metastable states when the Fermi Golden Rule constant vanishes

Resonances appearing by perturbation of embedded non-degenerate eigenvalues are studied in the case when the Fermi Golden Rule constant vanishes. Under appropriate smoothness properties for the resolvent of the unperturbed Hamiltonian, it is proved that the first order Rayleigh-Schrödinger expansion exists. The corresponding metastable states are constructed using this truncated expansion. We show that their exponential decay law has both the decay rate and the error term of order $\varepsilon^4$, where $\varepsilon$ is the perturbation strength.

math-ph↗
arXiv2013

On the steady state correlation functions of open interacting systems

We address the existence of steady state Green-Keldysh correlation functions of interacting fermions in mesoscopic systems for both the partitioning and partition-free scenarios. Under some spectral assumptions on the non-interacting model and for sufficiently small interaction strength, we show that the system evolves to a NESS which does not depend on the profile of the time-dependent coupling strength/bias. For the partitioned setting we also show that the steady state is independent of the initial state of the inner sample. Closed formulae for the NESS two-point correlation functions (Green-Keldysh functions), in the form of a convergent expansion, are derived. In the partitioning approach, we show that the 0th order term in the interaction strength of the charge current leads to the Landauer-Buettiker formula, while the 1st order correction contains the mean-field (Hartree-Fock) results.

math-ph↗
arXiv2013

On the Verdet constant and Faraday rotation for graphene-like materials

We present a rigorous and rather self-contained analysis of the Verdet constant in graphene- like materials. We apply the gauge-invariant magnetic perturbation theory to a nearest- neighbour tight-binding model and obtain a relatively simple and exactly computable formula for the Verdet constant, at all temperatures and all frequencies of sufficiently large absolute value. Moreover, for the standard nearest neighbour tight-binding model of graphene we show that the transverse component of the conductivity tensor has an asymptotic Taylor expansion in the external magnetic field where all the coefficients of even powers are zero.

math-ph↗
arXiv2012

Cayley transform applied to non-interacting quantum transport

We extend the Landauer-Büttiker formalism in order to accommodate both unitary and self-adjoint operators which are not bounded from below. We also prove that the pure point and singular continuous subspaces of the decoupled Hamiltonian do not contribute to the steady current. One of the physical applications is a stationary charge current formula for a system with four pseudo-relativistic semi-infinite leads and with an inner sample which is described by a Schrödinger operator defined on a bounded interval with dissipative boundary conditions. Another application is a current formula for electrons described by a one dimensional Dirac operator; here the system consists of two semi-infinite leads coupled through a point interaction at zero.

math-ph↗
arXiv2012

Optical Hall conductivity in bulk and nanostructured graphene beyond the Dirac approximation

We present a perturbative method for calculating the optical Hall conductivity in a tight-binding framework based on the Kubo formalism. The method involves diagonalization only of the Hamiltonian in absence of the magnetic field, and thus avoids the computational problems usually arising due to the huge magnetic unit cells required to maintain translational invariance in presence of a Peierls phase. A recipe for applying the method to numerical calculations of the magneto-optical response is presented. We apply the formalism to the case of ordinary and gapped graphene in a next-nearest neighbour tight-binding model as well as graphene antidot lattices. In both case, we find unique signatures in the Hall response, that are not captured in continuum (Dirac) approximations. These include a non-zero optical Hall conductivity even when the chemical potential is at the Dirac point energy. Numerical results suggest that this effect should be measurable in experiments.

cond-mat.mes-hall↗
arXiv2012

Memory effects in non-interacting mesoscopic transport

Consider a quantum dot coupled to two semi-infinite one-dimensional leads at thermal equilibrium. We turn on adiabatically a bias between the leads such that there exists exactly one discrete eigenvalue both at the beginning and at the end of the switching procedure. It is shown that the expectation on the final bound state strongly depends on the history of the switching procedure. On the contrary, the contribution to the final steady-state corresponding to the continuous spectrum has no memory, and only depends on the initial and final values of the bias.

math-ph↗
arXiv2012

MIMO capacity for deterministic channel models: sublinear growth

This is the second paper of the authors in a series concerned with the development of a deterministic model for the transfer matrix of a MIMO system. Starting from the Maxwell equations, we have described in \cite{BCFM} the generic structure of such a deterministic transfer matrix. In the current paper we apply the results of \cite{BCFM} in order to study the (Shannon-Foschini) capacity behavior of a MIMO system as a function of the deterministic spread function of the environment, and the number of transmitting and receiving antennas. The antennas are assumed to fill in a given, fixed volume. Under some generic assumptions, we prove that the capacity grows much more slowly than linearly with the number of antennas. These results reinforce previous heuristic results obtained from statistical models of the transfer matrix, which also predict a sublinear behavior.

cs.IT↗
arXiv2011

Sharp trace asymptotics for a class of 2D-magnetic operators

In this paper we prove a two-term asymptotic formula for for the spectral counting function for a 2D magnetic Schrödinger operator on a domain (with Dirichlet boundary conditions) in a semiclassical limit and with strong magnetic field. By scaling, this is equivalent to a thermodynamic limit of a 2D Fermi gas submitted to a constant external magnetic field. The original motivation comes from a paper by H. Kunz in which he studied, among other things, the boundary correction for the grand-canonical pressure and density of such a Fermi gas. Our main theorem yields a rigorous proof of the formulas announced by Kunz. Moreover, the same theorem provides several other results on the integrated density of states for operators of the type $(-ih\nabla- μ{\bf A})^2$ in $L^2(Ω)$ with Dirichlet boundary conditions.

math-ph↗
arXiv2011

Non-equilibrium steady-states for interacting open systems: exact results

Under certain conditions we prove the existence of a steady-state transport regime for interacting mesoscopic systems coupled to reservoirs (leads). The partitioning and partition-free scenarios are treated on an equal footing. Our time-dependent scattering approach is {\it exact} and proves, among other things the independence of the steady-state quantities from the initial state of the sample. Closed formulas for the steady-state current amenable for perturbative calculations w.r.t. the interaction strength are also derived. In the partitioning case we calculate the first order correction and recover the mean-field (Hartree-Fock) results.

cond-mat.mes-hall↗
arXiv2011

On the cotunneling regime of interacting quantum dots

Consider a bunch of interacting electrons confined in a quantum dot. The later is suddenly coupled to semi-infinite biased leads at an initial instant $t=0$. We identify the dominant contribution to the ergodic current in the off-resonant transport regime, in which the discrete spectrum of the quantum dot is well separated from the absolutely continuous spectrum of the leads. Our approach allows for arbitrary strength of the electron-electron interaction while the current is expanded in even powers of the (weak) lead-dot hopping constant $τ$. We provide explicit calculations for sequential tunneling and cotunneling contributions to the current. In the interacting case it turns out that the cotunneling current depends on the initial many-body configuration of the sample, while in the non-interacting case it does not, and coincides with the first term in the expansion of the Landauer formula w.r.t $τ$.

cond-mat.mes-hall↗
arXiv2011

A rigorous proof of the Landau-Peierls formula and much more

We present a rigorous mathematical treatment of the zero-field orbital magnetic susceptibility of a non-interacting Bloch electron gas, at fixed temperature and density, for both metals and semiconductors/insulators. In particular, we obtain the Landau-Peierls formula in the low temperature and density limit as conjectured by T. Kjeldaas and W. Kohn in 1957.

math-ph↗
arXiv2010

On the transfer matrix of a MIMO system

We develop a deterministic ab-initio model for the input-output relationship of a multiple-input multiple-output (MIMO) wireless channel, starting from the Maxwell equations combined with Ohm's Law. The main technical tools are scattering and geometric perturbation theories. The derived relationship can lead us to a deep understanding of how the propagation conditions and the coupling effects between the elements of multiple-element arrays affect the properties of a MIMO channel, e.g. its capacity and its number of degrees of freedom.

cs.IT↗
arXiv2010

Diamagnetism of quantum gases with singular potentials

We consider a gas of quasi-free quantum particles confined to a finite box, subjected to singular magnetic and electric fields. We prove in great generality that the finite volume grand-canonical pressure is jointly analytic in the chemical potential ant the intensity of the external magnetic field. We also discuss the thermodynamic limit.

math-ph↗
arXiv2010

Adiabatic non-equilibrium steady states in the partition free approach

Consider a small sample coupled to a finite number of leads, and assume that the total (continuous) system is at thermal equilibrium in the remote past. We construct a non-equilibrium steady state (NESS) by adiabatically turning on an electrical bias between the leads. The main mathematical challenge is to show that certain adiabatic wave operators exist, and to identify their strong limit when the adiabatic parameter tends to zero. Our NESS is different from, though closely related with the NESS provided by the Jak{\v s}i{ć}-Pillet-Ruelle approach. Thus we partly settle a question asked by Caroli {\it et al} in 1971 regarding the (non)equivalence between the partitioned and partition-free approaches.

math-ph↗
arXiv2010

A partition-free approach to transient and steady-state charge currents

We construct a non-equilibrium steady state and calculate the corresponding current for a mesoscopic Fermi system in the partition-free setting. To this end we study a small sample coupled to a finite number of semi-infinite leads. Initially, the whole system of quasi-free fermions is in a grand canonical equilibrium state. At t = 0 we turn on a potential bias on the leads and let the system evolve. We study how the charge current behaves in time and how it stabilizes itself around a steady state value, which is given by a Landauer-type formula.

math-ph↗
arXiv2010

Correlation and dimensional effects of trions in carbon nanotubes

We study the binding energies of singlet trions, i.e. charged excitons, in carbon nanotubes. The problem is modeled, through the effective-mass model, as a three-particle complex on the surface of a cylinder, which we investigate using both one- and two-dimensional expansions of the wave function. The effects of dimensionality and correlation are studied in detail. We find that the Hartree-Fock approximation significantly underestimates the trion binding energy. Combined with band structures calculated using a non-orthogonal nearest neighbour tight binding model, the results from the cylinder model are used to compute physical binding energies for a wide selection of carbon nanotubes. In addition, the dependence on dielectric screening is examined. Our findings indicate that trions are detectable at room temperature in carbon nanotubes with radius below 8Å.

quant-ph↗