a Study of the Disordered Boson Systems

We consider classical normal modes and noninteracting bosonic excitations in disordered systems. We emphasize generic aspects of such problems and parallels with disordered, noninteracting systems of fermions, and discuss in particular the relevance for bosonic excitations of symmetry classes known in the fermionic context. We also stress important differences between bosonic and fermionic problems. One of these follows from the fact that ground-state stability of a system requires all bosonic excitation energy levels to be positive, while stability in systems of noninteracting fermions is ensured by the exclusion principle, whatever the single-particle energies. As a consequence, simple models of uncorrelated disorder are less useful for bosonic systems than for fermionic ones, and it is generally important to study the excitation spectrum in conjunction with the problem of constructing a disorder-dependent ground state: we show how a mapping to an operator with chiral symmetry provides a useful tool for doing this. A second difference involves the distinction for bosonic systems between excitations which are Goldstone modes and those which are not. In the case of Goldstone modes we review established results illustrating the fact that disorder decouples from excitations in the low-frequency limit, above a critical dimension ${d}_{c},$ which in different circumstances takes the values ${d}_{c}=2$ and ${d}_{c}=0.$ For bosonic excitations which are not Goldstone modes, we argue that an excitation density varying with frequency as $\ensuremath{\rho}(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\omega}}^{4}$ is a universal feature in systems with ground states that depend on the disorder realization. We illustrate our conclusions with extensive analytical and some numerical calculations for a variety of models in one dimension.We consider classical normal modes and noninteracting bosonic excitations in disordered systems. We emphasize generic aspects of such problems and parallels with disordered, noninteracting systems of fermions, and discuss in particular the relevance for bosonic excitations of symmetry classes known in the fermionic context. We also stress important differences between bosonic and fermionic problems. One of these follows from the fact that ground-state stability of a system requires all bosonic excitation energy levels to be positive, while stability in systems of noninteracting fermions is ensured by the exclusion principle, whatever the single-particle energies. As a consequence, simple models of uncorrelated disorder are less useful for bosonic systems than for fermionic ones, and it is generally important to study the excitation spectrum in conjunction with the problem of constructing a disorder-dependent ground state: we show how a mapping to an operator with chiral symmetry provides a useful tool for doing this. A second difference involves the distinction for bosonic systems between excitations which are Goldstone modes and those which are not. In the case of Goldstone modes we review established results illustrating the fact that disorder decouples from excitations in the low-frequency limit, above a critical dimension ${d}_{c},$ which in different circumstances takes the values ${d}_{c}=2$ and ${d}_{c}=0.$ For bosonic excitations which are not Goldstone modes, we argue that an excitation density varying with frequency as $\ensuremath{\rho}(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\omega}}^{4}$ is a universal feature in systems with ground states that depend on the disorder realization. We illustrate our conclusions with extensive analytical and some numerical calculations for a variety of models in one dimension.

arXiv:cond-mat/0305445Physical review. B, Condensed matterOct 15, 2003144 citations

Theory of many-boson systems

Richard David Etters

Jan 1, 19650 citations

Bosons in a double-well potential: Understanding the interplay between disorder and interaction in a simple model

Qi Zhou, S. Das Sarma

We propose an exactly solvable model to reveal the physics of the interplay between interaction and disorder in bosonic systems. Considering interacting bosons in a double-well potential, in which disorder is mimicked by taking the energy level mismatch between the two wells to be randomly distributed, we find a ``two negatives make a positive'' effect. While disorder or interaction by itself suppresses the phase coherence between the two wells, both together enhance the phase coherence. This model captures several striking features of the disordered Bose-Hubbard model found in recent numerical simulations. Results at finite temperatures may help explain why a recent experiment did not find any evidence for the enhancement of phase coherence in a disordered bosonic system.We propose an exactly solvable model to reveal the physics of the interplay between interaction and disorder in bosonic systems. Considering interacting bosons in a double-well potential, in which disorder is mimicked by taking the energy level mismatch between the two wells to be randomly distributed, we find a ``two negatives make a positive'' effect. While disorder or interaction by itself suppresses the phase coherence between the two wells, both together enhance the phase coherence. This model captures several striking features of the disordered Bose-Hubbard model found in recent numerical simulations. Results at finite temperatures may help explain why a recent experiment did not find any evidence for the enhancement of phase coherence in a disordered bosonic system.

arXiv:1003.4059Physical Review AOct 11, 201010 citations

One-Dimensional Disordered Systems with Interactions

Korbinian Paul

xi The transport properties of a one dimensional disordered system of interacting spinpolarized electrons is studied using a bosonized field theory. In contrast to other approaches in that field [3], [2], a fully bosonized action on the Keldysh contour is used to calculate disorder averaged observables. After a brief introduction to Fermi and Luttinger liquids, we review bosonization, the Keldysh technique and disorder effects in mesoscopic systems. We calculate the first order correction to the clean conductivity in the disorder strength in order to develop a diagrammatic technique for a bosonized system on the Keldysh contour. Furthermore, the dissipative part of the self energy of the retarded plasmonic Green’s function is calculated via equations of motion in the high temperature regime. Corrections to the Drude conductivity of order = 1−K (weak interactions) and ωβ (high temperature) are calculated representing the terms beyond the saddle point approximation.xi The transport properties of a one dimensional disordered system of interacting spinpolarized electrons is studied using a bosonized field theory. In contrast to other approaches in that field [3], [2], a fully bosonized action on the Keldysh contour is used to calculate disorder averaged observables. After a brief introduction to Fermi and Luttinger liquids, we review bosonization, the Keldysh technique and disorder effects in mesoscopic systems. We calculate the first order correction to the clean conductivity in the disorder strength in order to develop a diagrammatic technique for a bosonized system on the Keldysh contour. Furthermore, the dissipative part of the self energy of the retarded plasmonic Green’s function is calculated via equations of motion in the high temperature regime. Corrections to the Drude conductivity of order = 1−K (weak interactions) and ωβ (high temperature) are calculated representing the terms beyond the saddle point approximation.

Jan 1, 20090 citations

{d}_{c},

which in different circumstances takes the values

{d}_{c}=2

and

{d}_{c}=0.

For bosonic excitations which are not Goldstone modes, we argue that an excitation density varying with frequency as $\ensuremath{\rho}(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\omega}}^{4}$ is a universal feature in systems with ground states that depend on the disorder realization. We illustrate our conclusions with extensive analytical and some numerical calculations for a variety of models in one dimension.