Many-body position operator in lattice fermionic systems with periodic boundary conditions

A total position operator $X$ in the position representation is derived for lattice fermionic systems with periodic boundary conditions. The operator is shown to be Hermitian, the generator of translations in momentum space, and its time derivative is shown to correspond to the total current operator in a periodic system. The operator is such that its moments can be calculated up to any order. To demonstrate its utility finite size scaling is applied to the Brinkman-Rice transition as well as metallic and insulating Gutzwiller wavefunctions.Comment: to appear in Journal of Physics A: Mathematical and General (reference will be added later

A gravimetric assessment of the Gotthard Base Tunnel geological model: insights from a novel gravity terrain-adaptation correction and rock physics data.

The Gotthard Base Tunnel (GBT) is a 57 km long railway tunnel, constructed in the Central Alps in Switzerland and extending mainly North-South across numerous geological units. We acquired 80 new gravity data points at the surface along the GBT profile and used 77 gravity measurements in the tunnel to test and constrain the shallow crustal, km-scale geological model established during the tunnel construction. To this end, we developed a novel processing scheme, which computes a fully 3D, density-dependent gravity terrain-adaptation correction (TAC), to consistently compare the gravity observations with the 2D geological model structure; the latter converted into a density model. This approach allowed to explore and quantify candidate rock density distributions along the GBT modelled profile in a computationally-efficient manner, and to test whether a reasonable fit can be found without structural modification of the geological model. The tested density data for the various lithologies were compiled from the SAPHYR rock physical property database. The tested models were evaluated both in terms of misfit between observed and synthetic gravity data, and also in terms of correlation between misfit trend and topography of the target profile. The results indicate that the locally sampled densities provide a better fit to the data for the considered lithologies, rather than density data averaged over a wider set of Alpine rock samples for the same lithology. Furthermore, using one homogeneous and constant density value for all the topographic corrections does not provide an optimal fit to the data, which instead confirms density variations along the profile. Structurally, a satisfactory fit could be found without modifying the 2D geological model, which thus can be considered gravimetry-proof. From a more general perspective, the gravity data processing routines and the density-dependent corrections developed in this case study represent a remarkable potential for further high-resolution gravity investigations of geological structures. The online version contains supplementary material available at 10.1186/s00015-022-00422-z

Quantum Monte Carlo Algorithm Based on Two-Body Density Functional Theory for Fermionic Many-Body Systems: Application to 3He

We construct a quantum Monte Carlo algorithm for interacting fermions using the two-body density as the fundamental quantity. The central idea is mapping the interacting fermionic system onto an auxiliary system of interacting bosons. The correction term is approximated using correlated wave functions for the interacting system, resulting in an effective potential that represents the nodal surface. We calculate the properties of 3He and find good agreement with experiment and with other theoretical work. In particular, our results for the total energy agree well with other calculations where the same approximations were implemented but the standard quantum Monte Carlo algorithm was usedComment: 4 pages, 3 figures, 1 tabl

Reconstruction of the polarization distribution of the Rice-Mele model

We calculate the gauge-invariant cumulants (and moments) associated with the Zak phase in the Rice-Mele model. We reconstruct the underlying probability distribution by maximizing the information entropy and applying the moments as constraints. When the Wannier functions are localized within one unit cell, the probability distribution so obtained corresponds to that of the Wannier function. We show that in the fully dimerized limit the magnitudes of the moments are all equal. In this limit, if the on-site interaction is decreased towards zero, the distribution shifts towards the midpoint of the unit cell, but the overall shape of the distribution remains the same. Away from this limit, if alternate hoppings are finite and the on-site interaction is decreased, the distribution also shifts towards the midpoint of the unit cell, but it does this by changing shape, by becoming asymmetric around the maximum, and by shifting. We also follow the probability distribution of the polarization in cycles around the topologically nontrivial point of the model. The distribution moves across to the next unit cell, its shape distorting considerably in the process. If the radius of the cycle is large, the shift of the distribution is accompanied by large variations in the maximum. © 2017 American Physical Society

Joint inversion of teleseismic and GOCE gravity data: application to the Himalayas

Our knowledge and understanding of the 3-D lithospheric structure of the Himalayas and the Tibetan Plateau is still challenging although numerous geophysical studies have been performed in the region. The GOCE satellite mission has the ambitious goal of mapping Earth's gravity field with unprecedented precision (i.e. an accuracy of 1-2 mGal for a spatial resolution of 100 km) to observe the lithosphere and upper-mantle structure. Consequently, it gives new insights in the lithospheric structure beneath the Himalayas and the Tibetan Plateau. Indeed, the GOCE gravity data now allow us to develop a new strategy for joint gravimetry-seismology inversion. Combined with teleseismic data over a large region in a joint inversion scheme, they will lead to lithospheric velocity-density models constrained in two complementary ways. We apply this joint inversion scheme to the Hi-CLIMB (Himalayan-Tibetan Continental Lithosphere during Mountain Building) seismological network which was deployed in South Tibet and the Himalayas for a 3-yr period. The large size of the network, the high quality of the seismological data and the new GOCE gravity data set allow us to image the entire lithosphere of this active area in an innovative way. We image 3-D low velocity and density structures in the middle crust that fit the location of discontinuous low S-velocity zones revealed by receiver functions in previous geophysical studies. In the deeper parts of our velocity model we image a positive anomaly interpreted to be the heterogenous Indian lithosphere vertically descending beneath the centre of the Tibetan Platea

Quantum quench in two dimensions using the variational Baeriswyl wave function

By combining the Baeriswyl wave function with equilibrium and time-dependent variational principles, we develop a nonequilibrium formalism to study quantum quenches for two-dimensional spinless fermions with nearest-neighbor hopping and repulsion. The variational ground-state energy, the charge-density wave (CDW) order parameter, and the short-time dynamics agree convincingly with the results of numerically exact simulations. We find that, depending on the initial and final interaction strength, the quenched system either exhibits oscillatory behavior or relaxes to a time-independent steady state. The time-averaged expectation value of the CDW order parameter rises sharply when crossing from the steady-state regime to the oscillating regime, indicating that the system, being nonintegrable, shows signs of thermalization with an effective temperature above or below the equilibrium critical temperature, respectively. © 2016 American Physical Society

Quantum quench in two dimensions using the variational Baeriswyl wave function

By combining the Baeriswyl wave function with equilibrium and time-dependent variational principles, we develop a nonequilibrium formalism to study quantum quenches for two-dimensional spinless fermions with nearest-neighbor hopping and repulsion. The variational ground-state energy, the charge-density wave (CDW) order parameter, and the short-time dynamics agree convincingly with the results of numerically exact simulations. We find that, depending on the initial and final interaction strength, the quenched system either exhibits oscillatory behavior or relaxes to a time-independent steady state. The time-averaged expectation value of the CDW order parameter rises sharply when crossing from the steady-state regime to the oscillating regime, indicating that the system, being nonintegrable, shows signs of thermalization with an effective temperature above or below the equilibrium critical temperature, respectively