相关论文: Some properties of the potential-to-ground state m…

The spectral landscape and the transport property of a translationally invariant network with side-coupled quantum dots are demonstrated within the tight-binding framework. For periodic environment band structure is demonstrated…

The mapping, exact or approximate, of a many-body problem onto an effective single-body problem is one of the most widely used conceptual and computational tools of physics. Here, we propose and investigate the inverse map of effective…

We study the interaction of a ground state with a class of trapping potentials. We track the precise asymptotic behavior of the solution if the interaction is weak, either because the ground state moves away from the potential or is very…

Understanding the behavior of quantum systems subject to magnetic fields is of fundamental importance and underpins quantum technologies. However, modeling these systems is a complex task, because of many-body interactions and because…

We obtain the exact ground state for the Calogero-Sutherland problem in arbitrary dimensions. In the special case of two dimensions, we show that the problem is connected to the random matrix problem for complex matrices, provided the…

For a quantum mechanical system with broken supersymmetry, we present a simple method of determining the ground state when the corresponding energy eigenvalue is sufficiently small. A concise formula is derived for the approximate ground…

We develop the theory of torsional rigidity -- a quantity routinely considered for Dirichlet Laplacians on bounded planar domains -- for Laplacians on metric graphs with at least one Dirichlet vertex. Using a variational characterization…

We study the topology of the space of harmonic maps from $S^2$ to \CP 2$. We prove that the subspaces consisting of maps of a fixed degree and energy are path connected. By a result of Guest and Ohnita it follows that the same is true for…

A recently introduced effective quantum potential theory is studied in a low momentum region of phase space. This low momentum approximation is used to show that the new effective quantum potential induces a space-dependent mass and a…

Standard variational methods tend to obtain upper bounds on the ground state energy of quantum many-body systems. Here we study a complementary method that determines lower bounds on the ground state energy in a systematic fashion, scales…

We consider charge transport for interacting many-body systems with a gapped ground state subspace which is finitely degenerate and topologically ordered. To any locality-preserving, charge-conserving unitary that preserves the ground state…

We analyze the inverse problem of Density Functional Theory using a regularized variational method. First, we show that given $k$ and a target density $\rho$, there exist potentials having $k^{\text{th}}$ bound mixed states which densities…

It is shown that the quantum ground state energy of particle of mass m and electric charge e moving on a compact Riemann surface under the influence of a constant magnetic field of strength B is E_0=eB/2m. Remarkably, this formula is…

Much progress has been made in the last few decades in developing the necessary mathematics for understanding the full implications of the quantum-mechanical many-body problem and why the material world appears to be as stable as it is…

Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…

We summarize unusual bound or localized states in quantum mechanics. Our guide through these intriguing phenomena is the classical physics of the upside-down pendulum. Taking advantage of the analogy between the corresponding Newton's…

The equivalence postulate approach to quantum mechanics entails a derivation of quantum mechanics from a fundamental geometrical principle. Underlying the formalism there exists a basic cocycle condition, which is invariant under…

A model system is considered where two dimensional electrons are confined by a harmonic potential in one direction, and are free in the other direction. Ground state in strong magnetic fields is investigated through numerical…

We study infinite systems of mean field weakly coupled intermittent maps in the Pomeau-Manneville scenario. We prove that the coupled system admits a unique ``physical'' stationary state, to which all absolutely continuous states converge.…

The nature of the ground states for a system composed of two coupled cavities with each containing a pair of dipole-coupled two-level atoms are studied over a wide range of detunings and dipole coupling strengths. The cases for three limits…