arXiv subjects

Benjamin Hinrichs

Publications and source records attributed to Benjamin Hinrichs.

25 records · Page 2Linked to original sources

arXiv2022

Absence of Ground States in the Renormalized Massless Translation-Invariant Nelson Model

We consider a model for a massive uncharged non-relativistic particle interacting with a massless bosonic field, widely referred to as the Nelson model. It is well known, that an ultraviolet renormalized Hamilton operator exists in this case. Further, due to translation-invariance, it decomposes into fiber operators. In this paper, we treat the renormalized fiber operators. We give a description of the operator and form domains and prove that the fiber operators do not have a ground state. Our results hold for any non-zero coupling constant and arbitrary total momentum. Our proof for the absence of ground states is a new generalization of methods recently applied to related models. A major enhancement we provide, is that the method can be applied to models with degenerate ground state eigenspaces.

math-ph↗

arXiv2022

FKN Formula and Ground State Energy for the Spin Boson Model with External Magnetic Field

We consider the spin boson model with external magnetic field. We prove a path integral formula for the heat kernel, known as Feynman-Kac-Nelson (FKN) formula. We use this path integral representation to express the ground state energy as a stochastic integral. Based on this connection, we determine the expansion coefficients of the ground state energy with respect to the magnetic field strength and express them in terms of correlation functions of a continuous Ising model. From a recently proven correlation inequality, we can then deduce that the second order derivative is finite. As an application, we show existence of ground states in infrared-singular situations.

math-ph↗

arXiv2022

Existence of Ground States in the Infrared-Critial Spin Boson Model

We review recent results on the existence of ground states for the infrared-critical spin boson model, which describes the interaction of a massless bosonic field with a two-state quantum system. Explicitly, we derive a critical coupling $λ_{\mathsf c}>0$ such that the spin boson model exhibits a ground state for coupling constants $λ$ with $|λ|<λ_{\mathsf c}$. The proof combines a Feynman-Kac-Nelson formula for the spin boson model with external magnetic field, a 1D-Ising model correlation bound and a compactness argument in Fock space. Elaborating on the connection to a long-range 1D-Ising model, we briefly discuss the conjecture that the spin boson model does not have a ground state at large coupling. This note is based on joint work with David Hasler and Oliver Siebert.

math-ph↗

arXiv2021

Correlation Bound for a One-Dimensional Continuous Long-Range Ising Model

We consider a measure given as the continuum limit of a one-dimensional Ising model with long-range translationally invariant interactions. Mathematically, the measure can be described by a self-interacting Poisson driven jump process. We prove a correlation inequality, estimating the magnetic susceptibility of this model, which holds for small $L^1$-norm of the interaction function. The bound on the magnetic susceptibility has applications in quantum field theory and can be used to prove existence of ground states for the spin boson model.

math-ph↗

arXiv2021

On Existence of Ground States in the Spin Boson Model

We show the existence of ground states in the massless spin boson model without any infrared regularization. Our proof is non-perturbative and relies on a compactness argument. It works for arbitrary values of the coupling constant under the hypothesis that the second derivative of the ground state energy as a function of a constant external magnetic field is bounded.

math-ph↗

arXiv2011

Photon propagation in a discrete fiber network: An interplay of coherence and losses

We study light propagation in a photonic system that shows stepwise evolution in a discretized environment. It resembles a discrete-time version of photonic waveguide arrays or quantum walks. By introducing controlled photon losses to our experimental setup, we observe unexpected effects like sub-exponential energy decay and formation of complex fractal patterns. This demonstrates that the interplay of linear losses, discreteness and energy gradients leads to genuinely new coherent phenomena in classical and quantum optical experiments. Moreover, the influence of decoherence is investigated.

physics.optics↗

arXiv2011

Zitterbewegung, Bloch Oscillations and Landau-Zener Tunneling in a Quantum Walk

We experimentally investigate a discrete time quantum walk in a system of coupled fiber loops and observe typical phenomena known from the wave propagation in periodic structures as ballistic spreading or an oscillation between two internal quantum states similar to Zitterbewegung (trembling motion). If a position-dependent phase gradient is applied we find localization and Bloch oscillations of the field for moderate as well as Landau-Zener tunneling for strong phase gradients.

quant-ph↗