Boson fermion
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Boson-Fermion Interactions and Theoretical Models
Bosonization of One-Dimensional Fermions
Keywords: Bosonization, One-Dimensional Fermions, Non-Equilibrium
The bosonization technique is a powerful method for studying one-dimensional fermions, especially out of equilibrium. This approach, developed within the Keldysh action formalism, allows for the analysis of free fermions and non-equilibrium Fermi edge singularities. It is particularly useful for investigating interacting quantum wires connected to electrodes with varying energy distributions. The technique reveals that non-equilibrium electron Green functions, measurable via tunneling spectroscopy, provide insights into energy distribution, zero-bias anomalies, and dephasing. These functions are expressed through functional determinants of single-particle "counting" operators, with time-dependent scattering phases intrinsically linked to the fractionalization of electron-hole excitations during tunneling and at boundaries with leads .
Fermion-Boson Stars: Formation and Stability
Keywords: Fermion-Boson Stars, Gravitationally Bound Structures, Stability
Fermion-boson stars are intriguing astrophysical objects composed of fermions and scalar particles. These stars are solutions to the coupled Einstein-Klein-Gordon-Euler (EKGE) system. One formation scenario involves a neutron star surrounded by an accreting cloud of a massive scalar field. Numerical simulations show that after gravitational cooling expels part of the initial scalar field, the system oscillates around an equilibrium configuration. This equilibrium is consistent with static solutions of the EKGE system. The presence of a fermionic core can stabilize configurations with nodes in the bosonic sector, similar to purely boson stars where ground and excited states coexist Giovanni2020Valdez-Alvarado2012.
Fermion-Charged-Boson Stars
Keywords: Fermion-Charged-Boson Stars, Stability, Mass-Radius Diagrams
Extending the concept of fermion-boson stars, researchers have studied systems where the bosonic dark matter is a charged scalar field. These fermion-charged-boson stars are analyzed for stability by computing critical curves across parameter space. The studies reveal that the fermion and boson sectors contribute differently to the total mass of the star. Mass-radius diagrams indicate that increasing the charge can result in more massive and compact stars, highlighting the complex interplay between fermionic and bosonic components in these exotic objects .
Spin-Spin Fermion-Mediated Interactions in Ultracold Bosons
Keywords: Spin-Spin Interactions, Ultracold Bosons, Fermion-Mediated Interactions
In ultracold boson-fermion mixtures, fermions can mediate spin-spin interactions between bosons, leading to long-range magnetic interactions. This phenomenon was observed in a mixture of a condensed Bose gas and a spin-polarized degenerate Fermi gas. Using Ramsey spectroscopy, researchers measured the interaction mediated by fermions, isolating it from mean-field frequency shifts due to direct collisions. The presence of the degenerate Fermi gas increased the boson spin-spin interaction, providing clear evidence of fermion-mediated interactions. This interaction can be tuned using a boson-fermion Feshbach resonance, potentially leading to new magnetic phases and extensions of the Bose-Hubbard model .
Numerical Studies of Fermion and Boson Models with Infinite-Range Interactions
Keywords: SYK Models, Entropy Density, Spin Glass Order
Numerical studies of fermion and boson models with random all-to-all interactions, known as SYK models, have provided insights into their thermodynamic properties. High-temperature expansions and exact diagonalization of the fermion model show consistency with the numerical solutions of the $N=\infty$ saddle point equations, indicating a non-zero entropy density at vanishing temperatures. For hard-core boson models, exact diagonalization suggests the presence of spin glass order. These studies also explore entanglement entropy and out-of-time-order correlators, contributing to our understanding of complex quantum systems .
Conclusion
The interplay between bosons and fermions spans a wide range of physical phenomena, from theoretical models of one-dimensional systems to the formation and stability of exotic astrophysical objects. Advances in experimental techniques, such as Ramsey spectroscopy and numerical simulations, continue to deepen our understanding of these interactions, revealing new phases of matter and potential applications in quantum technologies.
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