Searcharxiv⌕ Search

arXiv subjects

Yukimi Goto

Publications and source records attributed to Yukimi Goto.

12 recordsLinked to original sources
arXiv2026

Asymptotics of Ground States for Helium-Like and Bosonic Atoms in a Two-Cluster Region

We study the asymptotic behavior of positive ground states of $N$-particle atomic Coulomb Hamiltonians in a two-cluster region. For the $N$-particle ground state $\psi$, its one-particle density $\rho$, and $(N-1)$-particle ground state $\phi$, we show that for $0<\alpha<1$, as $|x_N|\to\infty$, $\psi(x_1,\dots,x_N)/\sqrt{\rho(x_N)}= \phi(x_1,\dots,x_{N-1})+O(|x_N|^{-2+\alpha} \ln |x_N|)$ uniformly in the region $|x_i|\le |x_N|^{\alpha}$. In the region $|x_i|\le R_0\ln |x_N|$, the convergence rate is $O(|x_N|^{-2} (\ln |x_N|)^2)$. We also establish an $O(|x_N|^{-2})$ bound on the squared $L^2$ error. These results hold both below the essential spectrum and at threshold.

math-ph↗
arXiv2025

Superconductivity and Low Energy Excitations in an Attractive Hubbard Model

We study an attractive Hubbard model on bipartite lattices. In the grand canonical formalism,we prove the existence of superconducting long-range order in the ground state on Lieb lattices with the chemical potential corresponding to half filling. We also study the low-energy excitations above several ground states for the translationally invariant Hamiltonian. We prove the following: (i) The pairing excitations are gapless above the ground states when the number of fermions deviates from that of the half filling by the order of the volume. (ii) A certain class of single-fermion excitations shows a non-vanishing spectral gap above the ground state with an even number of fermions in a strong coupling and low-density regime.

math-ph↗
arXiv2025

Antiferromagnetic Long-Range Order in a Lattice Fermion Model

We study a lattice fermion model with antiferromagnetic interactions on the three-dimensional cubic lattice. The hopping term of the Hamiltonian has a Weyl-type dispersion. We prove that the model has reflection positivity. Moreover, by relying on the property, we prove the existence of the antiferromagnetic long-range order at low temperatures in a strong coupling regime.

math-ph↗
arXiv2025

Violation of Parity and Flavor Symmetries in a Nambu-Jona-Lasinio Model

We study a lattice Nambu-Jona-Lasinio model with certain continuous chiral and two-flavor symmetries. For the Hamiltonian of the model, we construct a ground state which breaks the parity and flavor symmetries. In our argument, the chiral symmetry plays a crucial role for proving the violation of the parity and flavor symmetries, although the model does not contain the so-called Wilson term.

hep-ph↗
arXiv2024

Nambu-Goldstone modes in a lattice Nambu-Jona-Lasinio model with multi flavor symmetries

We study a lattice Nambu-Jona-Lasinio model with SU(2) and SU(3) flavor symmetries of staggered fermions in the Kogut-Susskind Hamiltonian formalism. This type of four-fermion interactions has been widely used for describing low-energy behaviors of strongly interacting quarks as an effective model. In particular, we focus on the Nambu-Goldstone modes associated with the spontaneous breakdown of the flavor symmetries. In the strong coupling regime for the interactions, we prove the following: (i) For the spatial dimension $ν\ge 5$, the SU(3) model shows a long-range order at sufficiently low temperatures. (ii) In the case of the SU(2) symmetry, there appears a long-range order in the spatial dimension $ν\ge 3$ at sufficiently low temperatures. (iii) These results hold in the ground states as well. (iv) In general, if a long-range order emerges in this type of models, then there appear gapless excitations above the sector of the infinite-volume ground states. These are nothing but the Nambu-Goldstone modes associated with the spontaneous breakdown of the global rotational symmetry of flavors. (v) In particular, we establish that the number of the lineraly independent Nambu-Goldstone modes is equal to the number of the broken symmetry generators on the Hilbert space constructed from a certain symmetry-breaking infinite-volume ground state.

math-ph↗
arXiv2024

Absence of ground states for anions

We show that the $N$-electron Hamiltonian $H(N, Z)$ with the total nuclear charge $Z$ has no normalizable ground state if the ground state energy $E(N, Z)$ satisfies $E(N, Z)= E(N-1, Z)$ for $Z=N-1$. For anions $\mathrm{He}^-, \mathrm{Be}^-, \mathrm{N}^-, \mathrm{Ne}^-$, etc., many numerical results give strong evidence of the condition $E(N, Z)= E(N-1, Z)$.

math-ph↗
arXiv2024

Spontaneous mass generation and chiral symmetry breaking in a lattice Nambu-Jona-Lasinio model

We study a lattice Nambu-Jona-Lasinio model with interacting staggered fermions in the Kogut-Susskind Hamiltonian formalism. The model has a discrete chiral symmetry but not the usual continuous chiral symmetry. In a strong coupling regime for the four-fermion interaction, we prove that the mass of the fermions is spontaneously generated at sufficiently low non-zero temperatures in the dimensions $ν\ge 3$ of the model and zero temperature in $ν\ge 2$. Due to the phase transition, the discrete chiral symmetry of the model is broken. Our analysis is based on the reflection positivity for fermions and the method of the infrared bound.

math-ph↗
arXiv2021

The maximal negative ion of molecules in Schrödinger, Hartree-Fock, and Müller theories

Bounds are studied for the maximum number, $N_c$, of electrons that can be bound to $K$ atoms of the total nuclear charge $Z$. It is proved that $N_c < \min\{2Z+1, 1.22Z + 3Z^{1/3}\}$ in Schrödinger theory. This improves Lieb's bound $N_c < 2Z+K$ and extends Nam's results for an atom to the molecule. Moreover, the ionization conjectures for the molecules in Hartree-Fock and Müller theories are proved, i.e., $N_c \le Z + CKR_\mathrm{min}^{-3}$, where $R_\mathrm{min}$ is the minimal distance between atoms and $C$ is a universal constant.

math-ph↗
arXiv2019

Binding of atoms in Müller theory

We give a necessary and sufficient condition for the existence of molecules in Müller theory. Furthermore, we show that if a system is stable in Born-Oppenheimer approximation, then the bound on the positive excess charge $ Z-N \le cZ^{1-ε}$ follows.

math-ph↗