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Papers by Joe Pule

Research paper thumbnail of Models for equilibrium BEC superradiance

Journal of physics, Jul 1, 2004

We study the effect of electromagnetic radiation on the condensate of a Bose gas. In an earlier p... more We study the effect of electromagnetic radiation on the condensate of a Bose gas. In an earlier paper we considered the problem for two simple models showing the cooperative effect between Bose-Einstein condensation and superradiance. In this paper we formalise the model suggested by Ketterle et al in which the Bose condensate particles have a two level structure. We present a soluble microscopic Dicke type model describing a thermodynamically stable system. We find the equilibrium states of the system and compute the thermodynamic functions giving explicit formulae expressing the cooperative effect between Bose-Einstein condensation and superradiance.

Research paper thumbnail of Propagating Edge States for a Magnetic Hamiltonian

Mathematical Physics Electronic Journal, 2002

We study the quantum mechanical motion of a charged particle moving in a half plane (x > 0) subje... more We study the quantum mechanical motion of a charged particle moving in a half plane (x > 0) subject to a uniform constant magnetic field B directed along the z-axis and to an arbitrary impurity potential W B , assumed to be weak in the sense that ||W B || ∞ < δB, for some δ small enough. We show rigorously a phenomenon pointed out by Halperin in his work on the quantum Hall effect, namely the existence of current carrying and extended edge states in such a situation. More precisely, we show that there exist states propagating with a speed of size B 1/2 in the y-direction, no matter how fast W B fluctuates. As a result of this, we obtain that the spectrum of the Hamiltonian is purely absolutely continuous in a spectral interval of size γB (for some γ < 1) between the Landau levels of the unperturbed system (i.e. the system without edge or potential), so that the corresponding eigenstates are extended.

Research paper thumbnail of Long cycles in the infinite-range-hopping Bose–Hubbard model

Journal of Mathematical Physics, 2009

In this paper we study the relation between long cycles and Bose–Einstein condensation in the inf... more In this paper we study the relation between long cycles and Bose–Einstein condensation in the infinite-range Bose–Hubbard model. We obtain an expression for the cycle density involving the partition function for a Bose–Hubbard Hamiltonian with a single-site correction. Inspired by the approximating Hamiltonian method we conjecture a simplified expression for the short cycle density as a ratio of single-site partition functions. In the absence of condensation we prove that this simplification is exact and use it to show that in this case the long cycle density vanishes. In the presence of condensation we can justify this simplification when a gauge-symmetry breaking term is introduced in the Hamiltonian. Assuming our conjecture is correct, we compare numerically the long cycle density with the condensate and find that although they coexist, in general, they are not equal.

Research paper thumbnail of The spectrum of a magnetic Schrödinger operator with randomly located delta impurities

Journal of Mathematical Physics, 2000

We consider a single band approximation to the random Schrödinger operator in an external magneti... more We consider a single band approximation to the random Schrödinger operator in an external magnetic field. The spectrum of such an operator has been characterized in the case where delta impurities are located on the sites of a lattice. In this paper we generalize these results by letting the delta impurities have random positions as well as strengths; they are located in squares of a lattice with a general bounded distribution. We characterize the entire spectrum of this operator when the magnetic field is sufficiently high. We show that the whole spectrum is pure point, the energy coinciding with the first Landau level is infinitely degenerate, and that the eigenfunctions corresponding to other Landau band energies are exponentially localized.

Research paper thumbnail of The Invariant Measures at Weak Disorder for the Two-Line Anderson Model

Reviews in Mathematical Physics, 2004

We study the invariant measures in the weak disorder limit, for the Anderson model on two coupled... more We study the invariant measures in the weak disorder limit, for the Anderson model on two coupled chains. These measures live on a three-dimensional projective space, and we use a total set of functions on this space to characterize the measures. We find that at several points of the spectrum, there are anomalies similar to that first found by Kappus and Wegner for the single chain at zero energy.

Research paper thumbnail of Lifshits tails for random smooth magnetic vortices

Journal of Mathematical Physics, 2004

We study the density of states of the Pauli Hamiltonian with a Poisson random distribution of smo... more We study the density of states of the Pauli Hamiltonian with a Poisson random distribution of smooth finite-width vortices and we obtain classical bounds for the Lifshits tails for them. These Hamiltonians are smooth approximations to the self-adjoint extensions of the Aharonov–Bohm Hamiltonian. In this case because pairs of impurities are coupled by the magnetic field we cannot use the Laplace characteristic functional.

Research paper thumbnail of Pauli approximations to the self-adjoint extensions of the Aharonov–Bohm Hamiltonian

Journal of Mathematical Physics, 2003

It is well known that the formal Aharonov–Bohm Hamiltonian operator, describing the interaction o... more It is well known that the formal Aharonov–Bohm Hamiltonian operator, describing the interaction of a charged particle with a magnetic vortex, has a four-parameter family of self-adjoint extensions, which reduces to a two-parameter family if one requires that the Hamiltonian commutes with the angular momentum operator. The question we study here is which of these self-adjoint extensions can considered as limits of regularized Aharonov–Bohm Hamiltonians, that is Pauli Hamiltonians in which the magnetic field corresponds to a flux tube of nonzero diameter. We show that not all the self-adjoint extensions in this two-parameter family can be obtained by these approximations, but only two one-parameter subfamilies. In these two cases we can choose the gyromagnetic ratio in the approximating Pauli Hamiltonian in such a way that we get convergence in the norm resolvent sense to the corresponding self-adjoint extension.

Research paper thumbnail of Lowest Lyapunov Exponents for the Armchair Nanotube

We compute sum of the two the lowest Lyapunov exponents ∞2N¡1 + ∞2N of a tight- binding model for... more We compute sum of the two the lowest Lyapunov exponents ∞2N¡1 + ∞2N of a tight- binding model for an single-wall armchair carbon nanotube with point impurities to lowest (second) order in the disorder parameter ‚. The result is that ∞2N¡1 + ∞2N » ‚ 2 N ¡1 , where N is the number of hexagons around the perimeter. This is similar to the result of Schulz-Baldes (20) for the standard Anderson model on a strip, but because there are only two conducting channels near the Fermi level (centre of the spectral band), this implies that the scattering length is proportional to the diameter of the tube as predicted by Todorov and White (10).

Research paper thumbnail of Characterization of the Spectrum of the Landau Hamiltonian with Delta Impurities

Communications in Mathematical Physics, 1999

Research paper thumbnail of Long Cycles in a Perturbed Mean Field Model of a Boson Gas

Journal of Statistical Physics, 2005

In this paper we give a precise mathematical formulation of the relation between Bose condensatio... more In this paper we give a precise mathematical formulation of the relation between Bose condensation and long cycles and prove its validity for the perturbed mean field model of a Bose gas. We decompose the total density ρ = ρ short + ρ long into the number density of particles belonging to cycles of finite length (ρ short) and to infinitely long cycles (ρ long) in the thermodynamic limit. For this model we prove that when there is Bose condensation, ρ long is different from zero and identical to the condensate density. This is achieved through an application of the theory of large deviations. We discuss the possible equivalence of ρ long = 0 with off-diagonal long range order and winding paths that occur in the path integral representation of the Bose gas.

Research paper thumbnail of 4 Models for Equilibrium BEC

Motivated by recent experiments with superradiant Bose-Einstein Condensate (BEC) we consider simp... more Motivated by recent experiments with superradiant Bose-Einstein Condensate (BEC) we consider simple microscopic models describing rigorously the interference of the two cooperative phenomena, BEC and radiation, in thermodynamic equilibrium. Our resuts in equilibrium confirm the presence of the observed superradiant light scattering from BEC: (a) the equilibrium superradiance exists only below a certain transition temperature; (b) there is superradiance and matter-wave (BEC) enhancement due to the coherent coupling between light and matter.

Research paper thumbnail of The approximating Hamiltonian method for the imperfect boson gas

Journal of Physics A: Mathematical and General, 2006

The pressure for the Imperfect (Mean Field) Boson gas can be derived in several ways. The aim of ... more The pressure for the Imperfect (Mean Field) Boson gas can be derived in several ways. The aim of the present note is to provide a new method based on the Approximating Hamiltonian argument which is extremely simple and very general.

Research paper thumbnail of The canonical perfect Bose gas in Casimir boxes

Journal of Mathematical Physics, 2004

We study the problem of Bose–Einstein condensation in the perfect Bose gas in the canonical ensem... more We study the problem of Bose–Einstein condensation in the perfect Bose gas in the canonical ensemble, in anisotropically dilated rectangular parallelepipeds (Casimir boxes). We prove that in the canonical ensemble for these anisotropic boxes there is the same type of generalized Bose–Einstein condensation as in the grand-canonical ensemble for the equivalent geometry. However the amount of condensate in the individual states is different in some cases and so are the fluctuations.

Research paper thumbnail of On the nature of Bose–Einstein condensation enhanced by localization

Journal of Mathematical Physics, 2010

In a previous paper we established that for the perfect Bose gas and the mean-field Bose gas with... more In a previous paper we established that for the perfect Bose gas and the mean-field Bose gas with an external random or weak potential, whenever there is generalized Bose-Einstein condensation in the eigenstates of the single particle Hamiltonian, there is also generalized condensation in the kinetic energy states. In these cases Bose-Einstein condensation is produced or enhanced by the external potential. In the present paper we establish a criterion for the absence of condensation in single kinetic energy states and prove that this criterion is satisfied for a class of random potentials and weak potentials. This means that the condensate is spread over an infinite number of states with low kinetic energy without any of them being macroscopically occupied.

Research paper thumbnail of 6 Proof of the Variational Principle for a Pair Hamiltonian Boson Model

We give a two parameter variational formula for the grand-canonical pressure of the Pair Boson Ha... more We give a two parameter variational formula for the grand-canonical pressure of the Pair Boson Hamiltonian model. By using the Approximating Hamiltonian Method we provide a rigorous proof of this variational principle.

Research paper thumbnail of Models with recoil for Bose–Einstein condensation and superradiance

Journal of Physics A: Mathematical and General, 2005

In this paper we consider two models which exhibit equilibrium BEC superradiance. They are relate... more In this paper we consider two models which exhibit equilibrium BEC superradiance. They are related to two different types of superradiant scattering observed in recent experiments. The first one corresponds to the amplification of matter-waves due to Raman superradiant scattering from a cigar-shaped BE condensate, when the recoiled and the condensed atoms are in different internal states. The main mechanism is stimulated Raman scattering in two-level atoms, which occurs in a superradiant way. Our second model is related to the superradiant Rayleigh scattering from a cigar-shaped BE condensate. This again leads to a matter-waves amplification but now with the recoiled atoms in the same state as the atoms in the condensate. Here the recoiling atoms are able to interfere with the condensate at rest to form a matter-wave grating (interference fringes) which is observed experimentally.

Research paper thumbnail of Models with recoil for Bose–Einstein condensation and superradiance

Journal of Physics A: Mathematical and General, 2005

In this paper we consider two models which exhibit equilibrium BEC superradiance. They are relate... more In this paper we consider two models which exhibit equilibrium BEC superradiance. They are related to two different types of superradiant scattering observed in recent experiments. The first one corresponds to the amplification of matter-waves due to Raman superradiant scattering from a cigar-shaped BE condensate, when the recoiled and the condensed atoms are in different internal states. The main mechanism is stimulated Raman scattering in two-level atoms, which occurs in a superradiant way. Our second model is related to the superradiant Rayleigh scattering from a cigar-shaped BE condensate. This again leads to a matter-waves amplification but now with the recoiled atoms in the same state as the atoms in the condensate. Here the recoiling atoms are able to interfere with the condensate at rest to form a matter-wave grating (interference fringes) which is observed experimentally.

Research paper thumbnail of On solvable boson models

Journal of Mathematical Physics, 2008

The problem of equilibrium states and/or ground states of exactly solvable homogeneous boson mode... more The problem of equilibrium states and/or ground states of exactly solvable homogeneous boson models is stated and explicitly proved as a special case of the general variational problem of statistical mechanics in terms of quasi-free states. We apply the result to a model of superradiant Bose-Einstein condensation and to the Pairing Boson Model.

Research paper thumbnail of On nonhomogeneous Bose condensation

Journal of Mathematical Physics, 2005

We prove, in great generality, that in a system of bosons, whenever Bose condensation in a nonzer... more We prove, in great generality, that in a system of bosons, whenever Bose condensation in a nonzero mode occurs then there is also spontaneous breaking of translation symmetry. In particular the proof holds for realistic Bose systems with two-body superstable interaction. This generalizes an old result proving that the occurrence of Bose-Einstein condensation in the zero mode implies spontaneous breaking

Research paper thumbnail of The Thermodynamic Limit for Finite Dimensional Classical and Quantum Disordered Systems

Reviews in Mathematical Physics, 2004

We provide a very simple proof for the existence of the thermodynamic limit for the quenched spec... more We provide a very simple proof for the existence of the thermodynamic limit for the quenched specific pressure for classical and quantum disordered systems on a d-dimensional lattice, including spin glasses. We develop a method which relies simply on Jensen's inequality and which works for any disorder distribution with the only condition (stability) that the quenched specific pressure is bounded.

Research paper thumbnail of Models for equilibrium BEC superradiance

Journal of physics, Jul 1, 2004

We study the effect of electromagnetic radiation on the condensate of a Bose gas. In an earlier p... more We study the effect of electromagnetic radiation on the condensate of a Bose gas. In an earlier paper we considered the problem for two simple models showing the cooperative effect between Bose-Einstein condensation and superradiance. In this paper we formalise the model suggested by Ketterle et al in which the Bose condensate particles have a two level structure. We present a soluble microscopic Dicke type model describing a thermodynamically stable system. We find the equilibrium states of the system and compute the thermodynamic functions giving explicit formulae expressing the cooperative effect between Bose-Einstein condensation and superradiance.

Research paper thumbnail of Propagating Edge States for a Magnetic Hamiltonian

Mathematical Physics Electronic Journal, 2002

We study the quantum mechanical motion of a charged particle moving in a half plane (x > 0) subje... more We study the quantum mechanical motion of a charged particle moving in a half plane (x > 0) subject to a uniform constant magnetic field B directed along the z-axis and to an arbitrary impurity potential W B , assumed to be weak in the sense that ||W B || ∞ < δB, for some δ small enough. We show rigorously a phenomenon pointed out by Halperin in his work on the quantum Hall effect, namely the existence of current carrying and extended edge states in such a situation. More precisely, we show that there exist states propagating with a speed of size B 1/2 in the y-direction, no matter how fast W B fluctuates. As a result of this, we obtain that the spectrum of the Hamiltonian is purely absolutely continuous in a spectral interval of size γB (for some γ < 1) between the Landau levels of the unperturbed system (i.e. the system without edge or potential), so that the corresponding eigenstates are extended.

Research paper thumbnail of Long cycles in the infinite-range-hopping Bose–Hubbard model

Journal of Mathematical Physics, 2009

In this paper we study the relation between long cycles and Bose–Einstein condensation in the inf... more In this paper we study the relation between long cycles and Bose–Einstein condensation in the infinite-range Bose–Hubbard model. We obtain an expression for the cycle density involving the partition function for a Bose–Hubbard Hamiltonian with a single-site correction. Inspired by the approximating Hamiltonian method we conjecture a simplified expression for the short cycle density as a ratio of single-site partition functions. In the absence of condensation we prove that this simplification is exact and use it to show that in this case the long cycle density vanishes. In the presence of condensation we can justify this simplification when a gauge-symmetry breaking term is introduced in the Hamiltonian. Assuming our conjecture is correct, we compare numerically the long cycle density with the condensate and find that although they coexist, in general, they are not equal.

Research paper thumbnail of The spectrum of a magnetic Schrödinger operator with randomly located delta impurities

Journal of Mathematical Physics, 2000

We consider a single band approximation to the random Schrödinger operator in an external magneti... more We consider a single band approximation to the random Schrödinger operator in an external magnetic field. The spectrum of such an operator has been characterized in the case where delta impurities are located on the sites of a lattice. In this paper we generalize these results by letting the delta impurities have random positions as well as strengths; they are located in squares of a lattice with a general bounded distribution. We characterize the entire spectrum of this operator when the magnetic field is sufficiently high. We show that the whole spectrum is pure point, the energy coinciding with the first Landau level is infinitely degenerate, and that the eigenfunctions corresponding to other Landau band energies are exponentially localized.

Research paper thumbnail of The Invariant Measures at Weak Disorder for the Two-Line Anderson Model

Reviews in Mathematical Physics, 2004

We study the invariant measures in the weak disorder limit, for the Anderson model on two coupled... more We study the invariant measures in the weak disorder limit, for the Anderson model on two coupled chains. These measures live on a three-dimensional projective space, and we use a total set of functions on this space to characterize the measures. We find that at several points of the spectrum, there are anomalies similar to that first found by Kappus and Wegner for the single chain at zero energy.

Research paper thumbnail of Lifshits tails for random smooth magnetic vortices

Journal of Mathematical Physics, 2004

We study the density of states of the Pauli Hamiltonian with a Poisson random distribution of smo... more We study the density of states of the Pauli Hamiltonian with a Poisson random distribution of smooth finite-width vortices and we obtain classical bounds for the Lifshits tails for them. These Hamiltonians are smooth approximations to the self-adjoint extensions of the Aharonov–Bohm Hamiltonian. In this case because pairs of impurities are coupled by the magnetic field we cannot use the Laplace characteristic functional.

Research paper thumbnail of Pauli approximations to the self-adjoint extensions of the Aharonov–Bohm Hamiltonian

Journal of Mathematical Physics, 2003

It is well known that the formal Aharonov–Bohm Hamiltonian operator, describing the interaction o... more It is well known that the formal Aharonov–Bohm Hamiltonian operator, describing the interaction of a charged particle with a magnetic vortex, has a four-parameter family of self-adjoint extensions, which reduces to a two-parameter family if one requires that the Hamiltonian commutes with the angular momentum operator. The question we study here is which of these self-adjoint extensions can considered as limits of regularized Aharonov–Bohm Hamiltonians, that is Pauli Hamiltonians in which the magnetic field corresponds to a flux tube of nonzero diameter. We show that not all the self-adjoint extensions in this two-parameter family can be obtained by these approximations, but only two one-parameter subfamilies. In these two cases we can choose the gyromagnetic ratio in the approximating Pauli Hamiltonian in such a way that we get convergence in the norm resolvent sense to the corresponding self-adjoint extension.

Research paper thumbnail of Lowest Lyapunov Exponents for the Armchair Nanotube

We compute sum of the two the lowest Lyapunov exponents ∞2N¡1 + ∞2N of a tight- binding model for... more We compute sum of the two the lowest Lyapunov exponents ∞2N¡1 + ∞2N of a tight- binding model for an single-wall armchair carbon nanotube with point impurities to lowest (second) order in the disorder parameter ‚. The result is that ∞2N¡1 + ∞2N » ‚ 2 N ¡1 , where N is the number of hexagons around the perimeter. This is similar to the result of Schulz-Baldes (20) for the standard Anderson model on a strip, but because there are only two conducting channels near the Fermi level (centre of the spectral band), this implies that the scattering length is proportional to the diameter of the tube as predicted by Todorov and White (10).

Research paper thumbnail of Characterization of the Spectrum of the Landau Hamiltonian with Delta Impurities

Communications in Mathematical Physics, 1999

Research paper thumbnail of Long Cycles in a Perturbed Mean Field Model of a Boson Gas

Journal of Statistical Physics, 2005

In this paper we give a precise mathematical formulation of the relation between Bose condensatio... more In this paper we give a precise mathematical formulation of the relation between Bose condensation and long cycles and prove its validity for the perturbed mean field model of a Bose gas. We decompose the total density ρ = ρ short + ρ long into the number density of particles belonging to cycles of finite length (ρ short) and to infinitely long cycles (ρ long) in the thermodynamic limit. For this model we prove that when there is Bose condensation, ρ long is different from zero and identical to the condensate density. This is achieved through an application of the theory of large deviations. We discuss the possible equivalence of ρ long = 0 with off-diagonal long range order and winding paths that occur in the path integral representation of the Bose gas.

Research paper thumbnail of 4 Models for Equilibrium BEC

Motivated by recent experiments with superradiant Bose-Einstein Condensate (BEC) we consider simp... more Motivated by recent experiments with superradiant Bose-Einstein Condensate (BEC) we consider simple microscopic models describing rigorously the interference of the two cooperative phenomena, BEC and radiation, in thermodynamic equilibrium. Our resuts in equilibrium confirm the presence of the observed superradiant light scattering from BEC: (a) the equilibrium superradiance exists only below a certain transition temperature; (b) there is superradiance and matter-wave (BEC) enhancement due to the coherent coupling between light and matter.

Research paper thumbnail of The approximating Hamiltonian method for the imperfect boson gas

Journal of Physics A: Mathematical and General, 2006

The pressure for the Imperfect (Mean Field) Boson gas can be derived in several ways. The aim of ... more The pressure for the Imperfect (Mean Field) Boson gas can be derived in several ways. The aim of the present note is to provide a new method based on the Approximating Hamiltonian argument which is extremely simple and very general.

Research paper thumbnail of The canonical perfect Bose gas in Casimir boxes

Journal of Mathematical Physics, 2004

We study the problem of Bose–Einstein condensation in the perfect Bose gas in the canonical ensem... more We study the problem of Bose–Einstein condensation in the perfect Bose gas in the canonical ensemble, in anisotropically dilated rectangular parallelepipeds (Casimir boxes). We prove that in the canonical ensemble for these anisotropic boxes there is the same type of generalized Bose–Einstein condensation as in the grand-canonical ensemble for the equivalent geometry. However the amount of condensate in the individual states is different in some cases and so are the fluctuations.

Research paper thumbnail of On the nature of Bose–Einstein condensation enhanced by localization

Journal of Mathematical Physics, 2010

In a previous paper we established that for the perfect Bose gas and the mean-field Bose gas with... more In a previous paper we established that for the perfect Bose gas and the mean-field Bose gas with an external random or weak potential, whenever there is generalized Bose-Einstein condensation in the eigenstates of the single particle Hamiltonian, there is also generalized condensation in the kinetic energy states. In these cases Bose-Einstein condensation is produced or enhanced by the external potential. In the present paper we establish a criterion for the absence of condensation in single kinetic energy states and prove that this criterion is satisfied for a class of random potentials and weak potentials. This means that the condensate is spread over an infinite number of states with low kinetic energy without any of them being macroscopically occupied.

Research paper thumbnail of 6 Proof of the Variational Principle for a Pair Hamiltonian Boson Model

We give a two parameter variational formula for the grand-canonical pressure of the Pair Boson Ha... more We give a two parameter variational formula for the grand-canonical pressure of the Pair Boson Hamiltonian model. By using the Approximating Hamiltonian Method we provide a rigorous proof of this variational principle.

Research paper thumbnail of Models with recoil for Bose–Einstein condensation and superradiance

Journal of Physics A: Mathematical and General, 2005

In this paper we consider two models which exhibit equilibrium BEC superradiance. They are relate... more In this paper we consider two models which exhibit equilibrium BEC superradiance. They are related to two different types of superradiant scattering observed in recent experiments. The first one corresponds to the amplification of matter-waves due to Raman superradiant scattering from a cigar-shaped BE condensate, when the recoiled and the condensed atoms are in different internal states. The main mechanism is stimulated Raman scattering in two-level atoms, which occurs in a superradiant way. Our second model is related to the superradiant Rayleigh scattering from a cigar-shaped BE condensate. This again leads to a matter-waves amplification but now with the recoiled atoms in the same state as the atoms in the condensate. Here the recoiling atoms are able to interfere with the condensate at rest to form a matter-wave grating (interference fringes) which is observed experimentally.

Research paper thumbnail of Models with recoil for Bose–Einstein condensation and superradiance

Journal of Physics A: Mathematical and General, 2005

In this paper we consider two models which exhibit equilibrium BEC superradiance. They are relate... more In this paper we consider two models which exhibit equilibrium BEC superradiance. They are related to two different types of superradiant scattering observed in recent experiments. The first one corresponds to the amplification of matter-waves due to Raman superradiant scattering from a cigar-shaped BE condensate, when the recoiled and the condensed atoms are in different internal states. The main mechanism is stimulated Raman scattering in two-level atoms, which occurs in a superradiant way. Our second model is related to the superradiant Rayleigh scattering from a cigar-shaped BE condensate. This again leads to a matter-waves amplification but now with the recoiled atoms in the same state as the atoms in the condensate. Here the recoiling atoms are able to interfere with the condensate at rest to form a matter-wave grating (interference fringes) which is observed experimentally.

Research paper thumbnail of On solvable boson models

Journal of Mathematical Physics, 2008

The problem of equilibrium states and/or ground states of exactly solvable homogeneous boson mode... more The problem of equilibrium states and/or ground states of exactly solvable homogeneous boson models is stated and explicitly proved as a special case of the general variational problem of statistical mechanics in terms of quasi-free states. We apply the result to a model of superradiant Bose-Einstein condensation and to the Pairing Boson Model.

Research paper thumbnail of On nonhomogeneous Bose condensation

Journal of Mathematical Physics, 2005

We prove, in great generality, that in a system of bosons, whenever Bose condensation in a nonzer... more We prove, in great generality, that in a system of bosons, whenever Bose condensation in a nonzero mode occurs then there is also spontaneous breaking of translation symmetry. In particular the proof holds for realistic Bose systems with two-body superstable interaction. This generalizes an old result proving that the occurrence of Bose-Einstein condensation in the zero mode implies spontaneous breaking

Research paper thumbnail of The Thermodynamic Limit for Finite Dimensional Classical and Quantum Disordered Systems

Reviews in Mathematical Physics, 2004

We provide a very simple proof for the existence of the thermodynamic limit for the quenched spec... more We provide a very simple proof for the existence of the thermodynamic limit for the quenched specific pressure for classical and quantum disordered systems on a d-dimensional lattice, including spin glasses. We develop a method which relies simply on Jensen's inequality and which works for any disorder distribution with the only condition (stability) that the quenched specific pressure is bounded.