相关论文: The Riemannium
A scheme is presented that enables a description of a paramagnetic Mott insulator in terms of free fermions. The main idea is to view the physical fermions as a part of a multi-band system and to allow for a correlation between the physical…
We find examples of duality among quantum theories that are related to arithmetic functions by identifying distinct Hamiltonians that have identical partition functions at suitably related coupling constants or temperatures. We are led to…
In this paper we provide a proof of the Riemann Hypothesis by relating the non-trivial zeros of the zeta function to a certain Sturm-Liouville eigenvalue problem on a finite interval.
We review the intriguing many-body physics resulting out of the interplay of a single, local impurity and the two-particle interaction in a one-dimensional Fermi system. Even if the underlying homogeneous correlated system is taken to be…
We present a systematic theory of dissipation in finite Fermi systems like nuclei and metallic clusters. This theory is based on the application of semiclassical methods and random matrix theory to linear response of many-body systems. The…
We construct a vector field E from the real and imaginary parts of an entire function xi (z) which arises in the quantum statistical mechanics of relativistic gases when the spatial dimension d is analytically continued into the complex z…
The relativistic Klein-Gordon system is studied as an illustration of Quantum Mechanics using non-Hermitian operators as observables. A version of the model is considered containing a generic coordinate- and energy-dependent…
The Riemann hypothesis states that all nontrivial zeros of the zeta function lie in the critical line $\Re(s)=1/2$. Hilbert and P\'olya suggested that one possible way to prove the Riemann hypothesis is to interpret the nontrivial zeros in…
A new approach to analyze the properties of the energy-momentum tensor $T(z)$ of conformal field theories on generic Riemann surfaces (RS) is proposed. $T(z)$ is decomposed into $N$ components with different monodromy properties, where $N$…
In this paper, we employ a semiperturbative theory to study the statistical structural properties of energy eigenfunctions (EFs) in many-body quantum chaotic systems consisting of a central system coupled to an environment. Under certain…
A simple model of noninteracting electrons with a separable one-body potential is used to discuss the possible pole structure of single particle Green's functions for fermions on unphysical sheets in the complex frequency plane as a…
We present a new method for calculating the Yang-Lee partition function zeros of a translationally invariant model of lattice fermions, exemplified by the Hubbard model. The method rests on a theorem involving the single electron…
From sand piles to electrons in metals, one of the greatest challenges in modern physics is to understand the behavior of an ensemble of strongly interacting particles. A class of quantum many-body systems such as neutron matter and cold…
This report concerns the energy of a zero-temperature many-body system of spin 1/2 fermions interacting via a two-body potential with a free space infinite scattering length and zero effective range; the Unitary limit. Given the…
We obtain a positive probability distribution or Q-function for an arbitrary fermionic many-body system. This is different to previous Q-function proposals, which were either restricted to a subspace of the overall Hilbert space, or used…
We study representations of the Schr\"odinger algebra in terms of operators in nonrelativistic conformal field theories. We prove a correspondence between primary operators and eigenstates of few-body systems in a harmonic potential. Using…
Starting from a Lagrangian, the electromagnetic field is quantized in the presence of a body rotating along its axis of symmetry. Response functions and fluctuation-dissipation relations are obtained. A general formula for rotational…
Equal-time commutators of different components of the energy-momentum tensor at spatially separated points are calculated for a relativistic quantum Fermi gas at finite temperature and density. Different definitions of such components, also…
Effective Field Theory (EFT) provides a powerful framework that exploits a separation of scales in physical systems to perform systematically improvable, model-independent calculations. Particularly interesting are few-body systems with…
Langevin/Fokker-Planck processes can be immersed in a larger frame by adding fictitious fermion variables. The (super)symmetry of this larger structure has been used to derive Morse theory in an elegant way. The original physical diffusive…