Quantum Instantons Research Articles

Magnetic Monopoles and Superinsulation in Josephson Junction Arrays

Electric-magnetic duality or S-duality, extending the symmetry of Maxwell’s equations by including the symmetry between Noether electric charges and topological magnetic monopoles, is one of the most fundamental concepts of modern physics. In two-dimensional systems harboring Cooper pairs, S-duality manifests in the emergence of superinsulation, a state dual to superconductivity, which exhibits an infinite resistance at finite temperatures. The mechanism behind this infinite resistance is the linear charge confinement by a magnetic monopole plasma. This plasma constricts electric field lines connecting the charge–anti-charge pairs into electric strings, in analogy to quarks within hadrons. However, the origin of the monopole plasma remains an open question. Here, we consider a two-dimensional Josephson junction array (JJA) and reveal that the magnetic monopole plasma arises as quantum instantons, thus establishing the underlying mechanism of superinsulation as two-dimensional quantum tunneling events. We calculate the string tension and the dimension of an electric pion determining the minimal size of a system capable of hosting superinsulation. Our findings pave the way for study of fundamental S-duality in desktop experiments on JJA and superconducting films.

Effects of quantum instantons on the thermodynamics of theCPN−1model

Using the 1/N expansion, we study the influence of quantum instantons on the thermodynamics of the CPN-1 model in 1+1 dimensions. We do this by calculating the pressure to next-to-leading order in 1/N, without quantum instanton contributions. The fact that the CP1 model is equivalent to the O(3) nonlinear sigma model allows for a comparison to the full pressure up to 1/N-2 corrections for N=3. Assuming validity of the 1/N expansion for the CP1 model makes it possible to argue that the pressure for intermediate temperatures is dominated by the effects of quantum instantons. A similar conclusion can be drawn for general N values by using the fact that the entropy should always be positive.

Non-Fermi liquid puzzle of MnSi at high pressure

The variation of the electrical resistivity of MnSi at low temperatures changes abruptly from T 2 to T 3/2 when the weak spin polarization is discontinuously suppressed at a hydrostatic pressure p c =14.6 kbar . The T 3/2 dependence of the non-polarized state prevails for p⪢ p c with a prefactor that is weakly pressure dependent and insensitive to sample purity. This contradicts the predictions of a nearly ferromagnetic Fermi liquid for p> p c anticipated from the weakly ferromagnetic state for p< p c. It highlights a novel aspect of the metallic state for p> p c, which most likely is related to unconventional dynamical properties of the spin density. Here I speculate on mechanisms that may form the basis for a future theoretical framework, e.g. incipient antiferromagnetism of itinerant ferromagnets, quantum instantons, changes of charge screening and quantum interference effects similar to frozen in disorder or related to the chirality of the spin fluctuations.

Renormalisation in quantum mechanics

We study a recently proposed quantum action depending on temperature. We construct a renormalisation group equation describing the flow of action parameters with temperature. At zero temperature the quantum action is obtained analytically and is found free of higher time derivatives. It makes the quantum action an ideal tool to investigate quantum chaos and quantum instantons.

Renormalisation in quantum mechanics, quantum instantons and quantum chaos

We suggest how to construct non-perturbatively a renormalized action in quantum mechanics. We discuss similarties and differences with the standard effective action. We propose that the new quantum action is suitable to define and compute quantum instantons and quantum chaos.

Quantum instantons and quantum chaos

We suggest a closed form expression for the path integral of quantum transition amplitudes to construct a quantum action. Based on this we propose rigorous definitions of both, quantum instantons and quantum chaos. As an example we compute the quantum instanton of the double well potential.

Closed path integrals and the quantum action.

We suggest a closed form expression for the path integral of quantum transition amplitudes. We introduce a quantum action with parameters different from the classical action. We present numerical results for the harmonic oscillator with weak perturbation, the quartic potential, and the double well potential. The quantum action is relevant for quantum chaos and quantum instantons.

Black hole decay and quantum instantons

We study the analytic structure of the S-matrix which is obtained from the reduced Wheeler-DeWitt wave function describing spherically symmetric gravitational collapse of massless scalar fields. The complex simple poles in the S-matrix lead to the wave functions that satisfy the same boundary condition as quasi-normal modes of a black hole, and correspond to the bounded states of the Euclidean Wheeler-DeWitt equation. These wave function are interpreted as quantum instantons.

Quantum hair, instantons, and black hole thermodynamics: some new results

We present results obtained by a consideration of the non-classical energy-momentum tensor associated with Euclidean instantons outside the event horizon of black holes. We demonstrate here how this allows for an analytic estimate to be made of the effect of discrete quantum hair on the temperature of the black hole, in which the role of violations of the weak energy condition associated with instantons is made explicit, and in which the previous results of Coleman, Preskill, and Wilczek are extended. Last, we demonstrate how the existence of a non-classical electric field outside the event horizon of black holes, uncovered by these authors, can be identified with a well-known effect in the Abelian Higgs mode] in two dimensions. In this case, there is a one-to-one connection between the discrete charge of a black hole and a topological phase in two dimensions.