A model of hybridized bosons and fermions is studied beyond the mean field approximation. The divergent boson self-energy at zero temperature makes the Cooper pairing of fermions impossible. The frequency and momentum dependence of the self- energy and the condensation temperature $T_{c}$ of initially localized bosons are calculated analytically. The value of the boson condensation temperature $T_{c}$ is below $1K$ which rules out the boson-fermion model with the initially localized bosons as a phenomenological explanation of high-temperature superconductivity. The intra-cell density-density fermion-boson interaction dominates in the fermion self-energy. The model represents a normal metal with strongly damped bosonic excitations. The latter play the role of normal impurities.A model of hybridized bosons and fermions is studied beyond the mean field approximation. The divergent boson self-energy at zero temperature makes the Cooper pairing of fermions impossible. The frequency and momentum dependence of the self- energy and the condensation temperature $T_{c}$ of initially localized bosons are calculated analytically. The value of the boson condensation temperature $T_{c}$ is below $1K$ which rules out the boson-fermion model with the initially localized bosons as a phenomenological explanation of high-temperature superconductivity. The intra-cell density-density fermion-boson interaction dominates in the fermion self-energy. The model represents a normal metal with strongly damped bosonic excitations. The latter play the role of normal impurities.

Jan 1, 199613 citations

Excitation spectrum for interacting bosons

Kapil M. Khanna, B.K. Das

PhysicaNov 1, 197314 citations

Experimental signatures of bosonic pairing in a two-component Bose gas

Omar Almonajed, M. Iskin, Mehmet Özgür Oktel

Two-component bosonic droplets are commonly described within Bogoliubov theory, where beyond-mean-field quantum fluctuations stabilize the system against mean-field collapse. In the interaction regime where droplets form, however, the Bogoliubov excitation spectrum contains an imaginary branch associated with the underlying instability, which is typically omitted when evaluating the beyond-mean-field energy. Bosonic pairing theory provides an alternative description with a fully real excitation spectrum. In this work, we reformulate bosonic pairing theory within an operator formalism, making its underlying approximations transparent, and compare its predictions with those of Bogoliubov theory for a homonuclear binary Bose mixture across the crossover from a weakly interacting gas to the droplet regime. Working at fixed particle density, we determine the variational parameters of bosonic pairing theory self-consistently and focus on the regime in which both theories possess real excitation spectra, allowing a direct comparison. We find that bosonic pairing theory yields a lower grand potential than Bogoliubov theory and predicts qualitatively distinct correlation signatures, including enhanced long-wavelength interspecies momentum-space correlations and a finite density static structure factor at experimentally accessible low momenta. These differences persist over a broad range of interaction strengths and suggest that correlation and structure-factor measurements can provide direct experimental tests of bosonic pairing across the gas-to-droplet crossover.Two-component bosonic droplets are commonly described within Bogoliubov theory, where beyond-mean-field quantum fluctuations stabilize the system against mean-field collapse. In the interaction regime where droplets form, however, the Bogoliubov excitation spectrum contains an imaginary branch associated with the underlying instability, which is typically omitted when evaluating the beyond-mean-field energy. Bosonic pairing theory provides an alternative description with a fully real excitation spectrum. In this work, we reformulate bosonic pairing theory within an operator formalism, making its underlying approximations transparent, and compare its predictions with those of Bogoliubov theory for a homonuclear binary Bose mixture across the crossover from a weakly interacting gas to the droplet regime. Working at fixed particle density, we determine the variational parameters of bosonic pairing theory self-consistently and focus on the regime in which both theories possess real excitation spectra, allowing a direct comparison. We find that bosonic pairing theory yields a lower grand potential than Bogoliubov theory and predicts qualitatively distinct correlation signatures, including enhanced long-wavelength interspecies momentum-space correlations and a finite density static structure factor at experimentally accessible low momenta. These differences persist over a broad range of interaction strengths and suggest that correlation and structure-factor measurements can provide direct experimental tests of bosonic pairing across the gas-to-droplet crossover.

arXiv:2607.03902Jul 4, 20260 citations

Exact Evolution versus mean field with second-order correction for Bosons interacting via short-range two-body potential

Elif Kuz

We consider the evolution of $N$ bosons, where $N$ is large, with two-body interactions of the form $N^{3\beta}v(N^{\beta}\mathbf{\cdot})$ , $0\leq\beta\leq 1$ . The parameter $\beta$ measures the strength of interactions. We compare the exact evolution with an approximation which considers the evolution of a mean field coupled with an appropriate description of pair excitations, see [25, 26]. For $0\leq \beta < 1/2$ , we derive an error bound of the form $p(t)/N^\alpha$ , where $\alpha>0$ and $p(t)$ is a polynomial, which implies a specific rate of convergence as $N\rightarrow\infty$ .We consider the evolution of $N$ bosons, where $N$ is large, with two-body interactions of the form $N^{3\beta}v(N^{\beta}\mathbf{\cdot})$, $0\leq\beta\leq 1$. The parameter $\beta$ measures the strength of interactions. We compare the exact evolution with an approximation which considers the evolution of a mean field coupled with an appropriate description of pair excitations, see [25, 26]. For $0\leq \beta < 1/2$, we derive an error bound of the form $p(t)/N^\alpha$, where $\alpha>0$ and $p(t)$ is a polynomial, which implies a specific rate of convergence as $N\rightarrow\infty$.

arXiv:1511.00487Differential and Integral EquationsJul 1, 201726 citations

Second-order corrections to mean field evolution of weakly interacting Bosons. II

Manoussos G. Grillakis, Matei Machedon, Dionisios Margetis

arXiv:1003.4713Advances in MathematicsJul 29, 201191 citations

T_{c}

of initially localized bosons are calculated analytically. The value of the boson condensation temperature

T_{c}

is below

1K

which rules out the boson-fermion model with the initially localized bosons as a phenomenological explanation of high-temperature superconductivity. The intra-cell density-density fermion-boson interaction dominates in the fermion self-energy. The model represents a normal metal with strongly damped bosonic excitations. The latter play the role of normal impurities.

We consider the evolution of

N

bosons, where

N

is large, with two-body interactions of the form

N^{3\beta}v(N^{\beta}\mathbf{\cdot})

0\leq\beta\leq 1

. The parameter

\beta

measures the strength of interactions. We compare the exact evolution with an approximation which considers the evolution of a mean field coupled with an appropriate description of pair excitations, see [25, 26]. For

0\leq \beta < 1/2

, we derive an error bound of the form

p(t)/N^\alpha

, where

\alpha>0

and

p(t)

is a polynomial, which implies a specific rate of convergence as

N\rightarrow\infty