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Fermionic Casimir Effect in Case of Andreev Reflection

Aurel Bulgac, Piotr Magierski, Wirzba, A.

Published Jan 1, 2005• 6 citations
OpenAlex

Abstract

We describe the fermionic Casimir effect in the case of two spherical superfluid scatterers immersed in a normal Fermi system. It is shown that due to the focusing property of Andreev reflection this new Casimir-like energy is significantly enhanced when compared to the case of normal scatterers with specular reflection.

Related papers

Fermionic Casimir effect in case of Andreev reflection

Aurel Bulgac, Piotr Magierski, A Wirzba

We describe the Fermionic Casimir effect in the case of two spherical superfluid scatterers immersed in a normal Fermi system. It is shown that due to the focusing property of Andreev reflection this new Casimir-like energy is significantly enhanced when compared to the case of normal scatterers with specular reflection.

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Andreev Reflection in Bosonic Condensates

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We study the bosonic analog of Andreev reflection at a normal-superfluid interface where the superfluid is a boson condensate. We model the normal region as a zone where nonlinear effects can be neglected. Against the background of a decaying condensate, we identify a novel contribution to the current of reflected atoms. The group velocity of this Andreev reflected component differs from that of the normally reflected one. For a three-dimensional planar or two-dimensional linear interface Andreev reflection is neither specular nor conjugate.

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Katsumasa Nakayama, Kei Suzuki

The Jordan-Wigner transformation connects spin operators in one-dimensional spin systems and fermionic operators. In this work, we elucidate the relationship between the finite-size corrections in the spin representation and the fermionic Casimir effect in the corresponding fermion representation. In particular, we focus on the ground-state energy of one-dimensional transverse-field Ising and XY models, and show that all finite-size corrections can be interpreted as lattice fermionic Casimir effects. We further find several types of Casimir phenomena, such as the conventional Casimir energy from massless fields, damping behavior from massive fields, vanishing behavior from flat or nonrelativistic bands, and oscillating behavior from the finite-density effect. Our findings establish a dictionary between finite-size corrections in spin chains and fermionic Casimir effects, and provide experimentally relevant platforms for the fermionic Casimir phenomena.

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Oscillating Casimir force between two slabs in a Fermi sea

Li-Wei Chen, Guozhen Su, Jincan Chen +1 more

The Casimir effect for two parallel slabs immersed in an ideal Fermi sea is investigated at both zero and nonzero temperatures. It is found that the Casimir effect in a Fermi gas is distinctly different from that in an electromagnetic field or a massive Bose gas. In contrast to the familiar result that the Casimir force decreases monotonically with the increase of the separation L between two slabs in an electromagnetic field and a massive Bose gas, the Casimir force in a Fermi gas oscillates as a function of L. The Casimir force can be either attractive or repulsive, depending sensitively on the magnitude of L. In addition, it is found that the amplitude of the Casimir force in a Fermi gas decreases with the increase of the temperature, which also is contrary to the case in a Bose gas, since the bosonic Casimir force increases linearly with the increase of the temperature in the region T < T c , where T c is the critical temperature of the Bose—Einstein condensation.

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Quasi-Andreev reflection in inhomogeneous Luttinger liquids

Dmitrii L. Maslov, Paul M. Goldbart

Reflection of charge excitations at the step in the interaction strength in a Luttinger liquid can be of the Andreev type, even the interactions are purely repulsive. The region with stronger repulsion plays the role of a normal metal in a normal-metal/superconductor junction, whereas the region with weaker repulsion plays the role of a superconductor. It is shown that this quasi-Andreev reflection leads to a number of proximitylike effects, including the local enhancement (suppression) of superconducting fluctuations on the quasinormal (quasisuperconducting) side of the step and significant modification of the local density of states, as well as others. The observable consequences of these proximity effects are analyzed for the case of single- and two-particle tunneling from a normal-metal or superconducting tip into an inhomogeneous Luttinger-liquid wire.

arXiv:cond-mat/9711070•Physical review. B, Condensed matter•Apr 15, 1998•4 citations
We study the bosonic analog of Andreev reflection at a normal-superfluid interface where the superfluid is a boson condensate. We model the normal region as a zone where nonlinear effects can be neglected. Against the background of a decaying condensate, we identify a novel contribution to the current of reflected atoms. The group velocity of this Andreev reflected component differs from that of the normally reflected one. For a three-dimensional planar or two-dimensional linear interface Andreev reflection is neither specular nor conjugate.
The Jordan-Wigner transformation connects spin operators in one-dimensional spin systems and fermionic operators. In this work, we elucidate the relationship between the finite-size corrections in the spin representation and the fermionic Casimir effect in the corresponding fermion representation. In particular, we focus on the ground-state energy of one-dimensional transverse-field Ising and XY models, and show that all finite-size corrections can be interpreted as lattice fermionic Casimir effects. We further find several types of Casimir phenomena, such as the conventional Casimir energy from massless fields, damping behavior from massive fields, vanishing behavior from flat or nonrelativistic bands, and oscillating behavior from the finite-density effect. Our findings establish a dictionary between finite-size corrections in spin chains and fermionic Casimir effects, and provide experimentally relevant platforms for the fermionic Casimir phenomena.
The Casimir effect for two parallel slabs immersed in an ideal Fermi sea is investigated at both zero and nonzero temperatures. It is found that the Casimir effect in a Fermi gas is distinctly different from that in an electromagnetic field or a massive Bose gas. In contrast to the familiar result that the Casimir force decreases monotonically with the increase of the separation L between two slabs in an electromagnetic field and a massive Bose gas, the Casimir force in a Fermi gas oscillates as a function of L. The Casimir force can be either attractive or repulsive, depending sensitively on the magnitude of L. In addition, it is found that the amplitude of the Casimir force in a Fermi gas decreases with the increase of the temperature, which also is contrary to the case in a Bose gas, since the bosonic Casimir force increases linearly with the increase of the temperature in the region T < T c , where T c is the critical temperature of the Bose—Einstein condensation.
Reflection of charge excitations at the step in the interaction strength in a Luttinger liquid can be of the Andreev type, even the interactions are purely repulsive. The region with stronger repulsion plays the role of a normal metal in a normal-metal/superconductor junction, whereas the region with weaker repulsion plays the role of a superconductor. It is shown that this quasi-Andreev reflection leads to a number of proximitylike effects, including the local enhancement (suppression) of superconducting fluctuations on the quasinormal (quasisuperconducting) side of the step and significant modification of the local density of states, as well as others. The observable consequences of these proximity effects are analyzed for the case of single- and two-particle tunneling from a normal-metal or superconducting tip into an inhomogeneous Luttinger-liquid wire.