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Fujii, Daisuke; Nakayama, Katsumasa*; Suzuki, Kei
Physics Letters B, 868, p.139758_1 - 139758_6, 2025/09
The Lifshitz formula has long served as a foundational framework for analyzing the Casimir effect under finite-temperature conditions. In this work, we extend its applicability to situations involving finite chemical potential, thereby incorporating quantum field contributions beyond thermal effects. We illustrate the broad utility of the resulting generalized formula by exploring characteristic features of the Casimir effect across a variety of setups, including different boundary conditions, temperature regimes, spatial dimensionalities, and chemical potential imbalances. This extended framework is particularly relevant to systems such as dense quark matter and Dirac/Weyl semimetals, where the chemical potential functions as a tunable parameter that influences the Casimir force.
Fujii, Daisuke; Nakayama, Katsumasa*; Suzuki, Kei
Physical Review D, 112(3), p.034020_1 - 034020_17, 2025/08
Times Cited Count：0We conduct a theoretical analysis of the Casimir effect arising from Dirac fermions in magnetized, finite-density matter. Our primary focus is on quark fields in the magnetic dual chiral density wave (MDCDW) phase, a candidate for an inhomogeneous ground state in strongly interacting Dirac systems. In this phase, the Casimir energy exhibits intricate oscillatory behavior as a function of separation distance, stemming from the combined effects of the chemical potential, external magnetic field, and spatial modulation of the ground state. To gain a deeper understanding, we decompose the Casimir energy into individual Landau level contributions, revealing distinct types of Casimir effects depending on whether the contribution originates from the lowest or higher Landau levels. We also highlight unique features that emerge due to energy level splitting between quark flavors, such as up and down quarks.
Fujii, Daisuke; Nakayama, Katsumasa*; Suzuki, Kei
Physical Review D, 110(1), p.014039_1 - 014039_15, 2024/07
Times Cited Count：4 Percentile：61.97(Astronomy & Astrophysics)The Casimir effect is known to be induced from photon fields confined by a small volume, and also its fermionic counterpart has been predicted in a wide range of quantum systems. Here, we investigate what types of Casimir effects can occur from quark fields in dense and thin quark matter. In particular, in the dual chiral density wave, which is a possible ground state of dense quark matter, we find that the Casimir energy oscillates as a function of the thickness of matter. This oscillating Casimir effect is regarded as an analog of that in Weyl semimetals and is attributed to the Weyl points in the momentum space of quark fields. In addition, we show that an oscillation is also induced from the quark Fermi sea, and the total Casimir energy is composed of multiple oscillations.
Nakayama, Katsumasa*; Suzuki, Kei
Physics Letters B, 843, p.138017_1 - 138017_7, 2023/08
Times Cited Count：8 Percentile：77.17(Astronomy & Astrophysics)The Casimir effect is a quantum phenomenon induced by the zero-point energy of relativistic fields confined in a finite-size system. This effect for photon fields has been studied for a long time, while the realization of counterparts for fermion fields in Dirac/Weyl semimetals is an open question. We theoretically demonstrate the typical properties of the Casimir effect for relativistic electron fields in Dirac/Weyl semimetals and show the results from an effective Hamiltonian for realistic materials such as Cd
As
and NaBi. We find an oscillation of the Casimir energy as a function of the thickness of the thin film, which stems from the existence of Dirac/Weyl nodes in momentum space. Experimentally, such an effect can be observed in thin films of semimetals, where the thickness dependence of thermodynamic quantities is affected by the Casimir energy.
Nakayama, Katsumasa*; Suzuki, Kei
Physical Review Research (Internet), 5(2), p.L022054_1 - L022054_6, 2023/06
The Casimir effect is a fundamental quantum phenomenon induced by the zero-point energy for a quantum field. It is well-known for relativistic fields with a linear dispersion relation, while its existence or absence for nonrelativistic fields with a quadratic dispersion is an unsettled question. Here, we investigate the Casimir effects for various dispersion relations on the lattice. We find that Casimir effects for dispersions proportional to an even power of momentum are absent in a long distance under some types of boundary conditions, while a remnant of the Casimir effect survives in a short distance. The concepts of such absence and remnants of Casimir effect help us to understand observables in finite-size materials with quantum fields on the lattice, such as thin films, narrow nanoribbons, and short nanowires. In terms of this effect, we also give a reinterpretation of the Casimir effect for massive fields.
Nakayama, Katsumasa*; Suzuki, Kei
Proceedings of Science (Internet), 430, p.379_1 - 379_9, 2023/04
The conventional Casimir effect has been studied in the continuous spacetime, but to elucidate its counterpart in the lattice space is an important subject. Here, we discuss various types of Casimir effects for quantum fields on the lattice. By using a definition of the Casimir energy on the lattice, we show that the Casimir effect for the Wilson fermion is similar to that for the continuous Dirac fermion. We apply our definition to an effective Hamiltonian describing Dirac semimetals, such as CdAs and NaBi, and find an oscillatory behavior of the Casimir energy as a function of film thickness of semimetals. We also study contributions from Landau levels under magnetic fields and the Casimir effect for nonrelativistic particle fields on the lattice.
Ishikawa, Tsutomu*; Nakayama, Katsumasa*; Suzuki, Kei
Physical Review D, 104(9), p.094515_1 - 094515_11, 2021/11
Times Cited Count：7 Percentile：41.75(Astronomy & Astrophysics)We investigate the Kondo effect with Wilson fermions. This is based on a mean-field approach for the chiral Gross-Neveu model including four-point interactions between a light Wilson fermion and a heavy fermion. For massless Wilson fermions, we demonstrate the appearance of the Kondo effect. We point out that there is a coexistence phase with both the light-fermion scalar condensate and Kondo condensate, and the critical chemical potentials of the scalar condensate are shifted by the Kondo effect. For negative-mass Wilson fermions, we find that the Kondo effect is favored near the parameter region realizing the Aoki phase. Our findings will be useful for understanding the roles of heavy impurities in Dirac semimetals, topological insulators, and lattice simulations.
Ishikawa, Tsutomu*; Nakayama, Katsumasa*; Suzuki, Kei
Physical Review Research (Internet), 3(2), p.023201_1 - 023201_23, 2021/06
The Casimir effect arises from the zero-point energy of particles in momentum space deformed by the existence of two parallel plates. For degrees of freedom on the lattice, its energy-momentum dispersion is determined so as to keep a periodicity within the Brillouin zone, so that its Casimir effect is modified. We study the properties of Casimir effect for lattice fermions, such as the naive fermion, Wilson fermion, and overlap fermion based on the M
bius domain-wall fermion formulation, in the 
, 
, and 
dimensional spacetime with the periodic or antiperiodic boundary condition. An oscillatory behavior of Casimir energy between odd and even lattice size is induced by the contribution of ultraviolet-momentum (doubler) modes, which realizes in the naive fermion, Wilson fermion in a negative mass, and overlap fermions with a large domain-wall height. Our findings can be experimentally observed in condensed matter systems such as topological insulators and also numerically measured in lattice simulations.
Ishikawa, Tsutomu*; Nakayama, Katsumasa*; Suzuki, Kei
Physics Letters B, 809, p.135713_1 - 135713_7, 2020/10
Times Cited Count：17 Percentile：79.18(Astronomy & Astrophysics)We propose a definition of the Casimir energy for free lattice fermions. From this definition, we study the Casimir effects for the massless or massive naive fermion, Wilson fermion, and (Mbius) domain-wall fermion in 1+1 dimensional spacetime with the spatial periodic or antiperiodic boundary condition. For the naive fermion, we find an oscillatory behavior of the Casimir energy, which is caused by the difference between odd and even lattice sizes. For the Wilson fermion, in the small lattice size of 
, the Casimir energy agrees very well with that of the continuum theory, which suggests that we can control the discretization artifacts for the Casimir effect measured in lattice simulations. We also investigate the dependence on the parameters tunable in Mbius domain-wall fermions. Our findings will be observed both in condensed matter systems and in lattice simulations with a small size.
mesons as a probe of Casimir effect for chiral symmetry breakingIshikawa, Tsutomu*; Nakayama, Katsumasa*; Suenaga, Daiki*; Suzuki, Kei
Physical Review D, 100(3), p.034016_1 - 034016_14, 2019/08
Times Cited Count：7 Percentile：34.33(Astronomy & Astrophysics)We propose mesons as probes to investigate finite-volume effects for chiral symmetry breaking at zero and finite temperatures. By using the 2+1-flavor linear sigma model with constituent light quarks, we analyze the Casimir effects for the 
mean fields; the chiral symmetry is rapidly restored by the antiperiodic boundary for light quarks, and the chiral symmetry breaking is catalyzed by the periodic boundary. We also show the phase diagram of the mean fields on the volume and temperature plane. For mesons, we employ an effective model based on the chiral-partner structure, in which the volume dependence of mesons is induced by the mean fields. We find that 
mesons are less sensitive to finite volume than mesons, which is caused by the insensitivity of 
mean fields. An anomalous mass shift of mesons at high temperature with the periodic boundary will be useful in examinations with lattice QCD simulations. The dependence on the number of compactified spatial dimensions is also studied.
Fujii, Daisuke; Nakayama, Katsumasa*; Suzuki, Kei
no journal, ,
At finite temperature, the Casimir effect is commonly analyzed using the Lifshitz formula. In this talk, we extend this Lifshitz formula to quantum fields at nonzero chemical potential. The resulting expression accommodates a wide range of settings different boundary conditions, finite temperatures, arbitrary spatial dimensions, and chemical-potential mismatch and exhibits characteristic behaviors in each case. This formula applies directly to dense quark matter and to Dirac/Weyl semimetals, where the chemical potential can be treated as a tunable parameter controlling the Casimir effect.
Suzuki, Kei; Fujii, Daisuke; Nakayama, Katsumasa*
no journal, ,
The conventional Casimir effect is defined for photon fields in the QED vacuum, whereas various quasiparticle fields realized in condensed matter systems can lead to novel types of Casimir-effect-like phenomena. In QCD and nuclear physics, such a situation is rare, but there are some possibilities in dense-QCD/nuclear matter. For example, the dual chiral density wave (DCDW) phase has been studied as the ground state of finite-density QCD. In this talk, we discuss the typical features of the Casimir effect in a small-size medium in such a ground state. The Casimir effect from quark fields leads to oscillations of physical quantities as a function of system size. A counterpart of this phenomenon is expected to appear also in Weyl semimetals, and we discuss the comparison between quark matter and Weyl semimetals.
Fujii, Daisuke; Suzuki, Kei; Nakayama, Katsumasa*
no journal, ,
Recently, new types of Casimir effects realized in condensed matter systems have been discovered. For example, the photonic Casimir effect in Weyl semimetals was found to exhibit remarkable behavior. This new type of Casimir effect may also be realized in dense quark matter. In this presentation, we discuss typical features of the Casimir effect in finite density QCD using the Nambu-Jona-Lasinio model. In particular, an remarkable behavior of the Casimir effect in the dual chiral density wave phase is revealed.
Ishikawa, Tsutomu*; Nakayama, Katsumasa*; Suzuki, Kei
no journal, ,
We propose a definition of the Casimir energy for free lattice fermions. From this definition, we study the Casimir effects for the massless or massive naive fermion, Wilson fermion, and (Mbius) domain-wall fermion in dimensional spacetime with the spatial periodic or antiperiodic boundary condition. For the naive fermion, we find an oscillatory behavior of the Casimir energy, which is caused by the difference between odd and even lattice sizes. For the Wilson fermion, in the small lattice size of , the Casimir energy agrees very well with that of the continuum theory, which suggests that we can control the discretization artifacts for the Casimir effect measured in lattice simulations. We also investigate the dependence on the parameters tunable in Mbius domain-wall fermions. Our findings will be observed both in condensed matter systems and in lattice simulations with a small size.
Suzuki, Kei; Ishikawa, Tsutomu*; Nakayama, Katsumasa*; Suenaga, Daiki*
no journal, ,
D mesons are expected to be clear probes of the chiral condensate. For the Casimir effect in the QCD vacuum, non-perturbative properties of the QCD vacuum are modified by the volume size and boundary conditions. In this talk, we focus on the modification of the chiral symmetry breaking by the Casimir effect and the response of D mesons. By using an effective Lagrangian based on chiral partner structures for D mesons, we discuss the dependences on volume, boundary, and temperature, and the applications to lattice QCD simulations.
Fujii, Daisuke; Nakayama, Katsumasa*; Suzuki, Kei
no journal, ,
One of the central questions in modern nuclear physics is which phases of matter are realized in QCD at finite density. While many studies have focused on spatially uniform phases, in recent years inhomogeneous chiral condensates have attracted considerable attention. A representative example is the dual chiral density wave (DCDW) phase, in which both the scalar and pseudoscalar condensates are spatially modulated. Such inhomogeneous chiral phases may be realized in the interior of neutron stars. In this talk, I will discuss the Casimir effect in quark matter including these inhomogeneous chiral condensates. I will further examine, in the neutron-star context, how they behave in the presence of an external magnetic field.
Ishikawa, Tsutomu*; Nakayama, Katsumasa*; Suzuki, Kei
no journal, ,
no abstracts in English
