110 citations · 425 across the 34 of their papers we have counts for
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A fresh look at the Peierls-Onsager substitution
Horia D. Cornean, Bernard Helffer, Radu Purice
We formulate a general version of the Peierls-Onsager substitution for a finite family of Bloch eigenvalues under a local spectral gap hypothesis, via strongly localized tight-fram…
A rigorous Peierls-Onsager effective dynamics for semimetals in long-range magnetic fields
Horia D. Cornean, Bernard Helffer, Radu Purice
We consider periodic (pseudo)differential {elliptic operators of Schrödinger type} perturbed by weak magnetic fields not vanishing at infinity, and extend our previous analysis in…
Sharp spectral stability for a class of singularly perturbed pseudo-differential operators
Horia D. Cornean, Radu Purice
Let be a real Hörmander symbol of the type , let be a smooth function with all its derivatives globally bounded, and let…
Spectral analysis near a Dirac type crossing in a weak non-constant magnetic field
Horia D. Cornean, Bernard Helffer, Radu Purice
This is the last paper in a series of three in which we have studied the Peierls substitution in the case of a weak magnetic field. Here we deal with two Bloch eigenvalues whi…
Quantum observables as magnetic pseudodifferential operators
Viorel Iftimie, Radu Purice, Marius Mantoiu
In a series of papers we have argued that the 'basic' physical procedure of minimal coupling giving the quantum description of a Hamiltonian system interacting with a magnetic fiel…
Peierls' substitution for low lying spectral energy windows
Horia D. Cornean, Bernard Helffer, Radu Purice
We consider a magnetic Schrödinger operator perturbed by a weak magnetic field which slowly varies around a positive mean. In a previous paper we proved the appearance of a `L…
A Schatten -von Neumann class criterion for the magnetic Weyl calculus
Nassim Athmouni, Radu Purice
We prove criteria for a {\it 'magnetic' Weyl operator} to be in a Schatten-von Neuman class by extending a method developed by H. Cordes, T. Kato and G. Arsu.
Peierls substitution and magnetic pseudo-differential calculus
Horia D. Cornean, Viorel Iftimie, Radu Purice
We revisit the celebrated Peierls-Onsager substitution employing the magnetic pseudo-differential calculus for weak magnetic fields with no spatial decay conditions, when the non-m…
The Peierls-Onsager Effective Hamiltonian in a complete gauge covariant setting: Description of the spectrum
Viorel Iftimie, Radu Purice
Using the procedures in \cite{Bu} and \cite{GMS} and the magnetic pseudodifferential calculus we have developped in \cite{MP1,MPR1,IMP1,IMP2} we construct an effective Hamitonian t…
Magnetic Fourier Integral Operators
Viorel Iftimie, Radu Purice
In some previous papers we have defined and studied a 'magnetic' pseudodifferential calculus as a gauge covariant generalization of the Weyl calculus when a magnetic field is prese…
Adiabatic non-equilibrium steady states in the partition free approach
Horia D. Cornean, Pierre Duclos, Radu Purice
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-equilibr…
Magnetic calculus and semiclassical trace formulas
Bernard Helffer, Radu Purice
The aim of these notes is to show how the magnetic calculus developed in \cite{MP, IMP1, IMP2, MPR, LMR} permits to give a new information on the nature of the coefficients of the…
Coherent states in the presence of a variable magnetic field
Marius Mantoiu, Radu Purice, Serge Richard
We introduce magnetic coherent states for a particle in a variable magnetic field. They provide a pure state quantization of the phase space R^{2N} endowed with a magnetic symplect…
Commutator Criteria for Magnetic Pseudodifferential Operators
Viorel Iftimie, Marius Mantoiu, Radu Purice
The gauge covariant magnetic Weyl calculus has been introduced and studied in previous works. We prove criteria in terms of commutators for operators to be magnetic pseudo-differen…
The magnetic formalism; new results
Viorel Iftimie, Marius Mantoiu, Radu Purice
We review recent results on the magnetic pseudo-differential calculus both in symbolic and in -algebraic form. We also indicate some applications to spectral analysis of pseud…
Estimating the number of negative eigenvalues of a relativistic Hamiltonian with regular magnetic field
Viorel Iftimie, Marius Mantoiu, Radu Purice
We prove the analog of the Cwickel-Lieb-Rosenblum estimation for the number of negative eigenvalues of a relativistic Hamiltonian with magnetic field $B\in C^\infty_{\rm{pol}}(\mat…
Twisted Crossed Products and Magnetic Pseudodifferential Operators
Marius Mantoiu, Radu Purice, Serge Richard
There is a connection between the Weyl pseudodifferential calculus and crossed product C*-algebras associated with certain dynamical systems. And in fact both topics are involved i…
The Magnetic Weyl Calculus
Marius Mantoiu, Radu Purice
In the presence of a variable magnetic field, the Weyl pseudodifferential calculus must be modified. The usual modification, based on ``the minimal coupling principle'' at the leve…