**WELCOME TO THE UNIPD FORUM ON**

**CONDENSED MATTER FIELD THEORY**

**STAFF SCIENTISTS**

Prof. Dr. Alberto Amborsetti,
Prof. Dr. Luca Dell'Anna,
Prof. Dr. Pieralberto Marchetti,
Prof. Dr. Luca Salasnich

**RESEARCH FELLOWS**

Dr. Gianluca Francica, Prof. Dr. Alexander Yakimenko

**PHD STUDENTS**

Koichiro Furutani, Francesco Lorenzi, Marco Uguccioni, Andrea Bardin

The main goal of our forum is to promote and strengthen the investigation of quantum many-body systems by using the methods of statistical quantum field theory with Feynman path integrals and functional integration.

**Bose-Einstein Condensation, Superfluidity and BCS-BEC Crossover**

We study the thermodynamics of weakly-interacting
Bose and Fermi
superfluids (alkali-metal atoms like rubidium,
sodium and lithium, but also atomic hydrogen)
trapped in magnetic or magneto-optical traps.
We analyze single-particle and collective elementary
excitations by numerically solving both Bologliubov-de Gennes and
Popov equations. Moreover, we investigate
dynamical properties of Bose-Einstein
condensates (BECs) by using
the time-dependent 3D Gross-Pitaevskii equation,
which describes the macroscopic wave-function (order parameter)
of the Bose condensate. We are also investigating the dynamics
(collective excitations and free expansion) of a
two-component Fermi gas in the BCS-BEC crossover and the
formation of solitons in atomic mixtures of bosons
and fermions. In particular, we are developing a
reliable density functional for the unitary
Fermi gas (infinite scattering length) at zero and finite temperature.
Moreover, we are working on the many-body quantum tunneling
dynamics of bosond and spin-polarized fermions in a double-well potential.

**Low Dimensional and Disordered systems**

This research activity is focused on the study of low dimensional
and disordered systems. An interesting example is given by
graphene whose physical properties can be captured by an effective two
dimensional relativistic model. By applying inhomogeneous magnetic fields,
we examine the conditions
under which one can filter and collimate relativistic
Dirac-Weyl fermions.
We study also the interplay between disorder and intraction
in fermionic and bosonic lattice systems.
Our investigation is devoted to characterize the
glassy phase,
to study the effects on the critical
temperature, the behavior of charge fluctuations,
and the stability of the ground state, when the system
is coupled to a source of noise and dissipation.

**High Tc superconductors**

The cuprates high Tc superconductors are materials exhibiting amazing
experimental features from the point of view of Landau Fermi-liquid/BCS
theory, such as: an apparently incomplete Fermi surface, the so-called
Fermi arcs and a metal-insulator crossover in resistivity coexisting with
them, a superfluid density with non-BCS critical exponent.
After more than 40 years since their discovery there is still no agreement
on the nature of their normal and superconducting state. Following an
original idea of Anderson we are developing a gauge approach to them by
considering their low-energy holes, experimentally responsible for the
superconductivity, as resonances composed of a charged spinless and a
neutral spin 1/2 excitations glued together by a gauge interaction.
The non-BCS mechanism of superconductivity relies on the attraction
generated by antiferromagnetic
vortices attached to the holes.
We are computing physical quantities within this theoretical framework,
comparing their behaviour with experimental data.

**Quantum Origin of Van Der Waals Interactions**

Van der Waals forces are present in the totality of materials and
molecules in nature and, acting even over long distances, determine
the aggregation, dynamics and functionality of a wide variety of systems.
Protein-drug interactions, the stability of the dna double helix structure,
and cohesion between graphene sheets are just a few examples of phenomena
in which
van der Waals forces play a key role.
By using quantum techniques (the recently developed many-body dispersion
approach), our research activity shows how in a variety of nanostructures
the electronic charge fluctuations that give rise to van der Waals forces,
can easily extend over the entire system.

**Quantum Frontiers**

We are investigating the
quantum decoherence and the
entanglement
entropy in the Josephson effect for both superconductors and superfluids,
in cold trapped ions, in Rydberg atoms arrays trapped in optical
lattices, and in Kitaev chains. We are also studying
the
cosmic web formation by using large-scale
numerical simulations based on the nonlinear Schrodinger equation for the
cold dark matter. Finally, we are also working on the quantum statistical
mechanics of black
holes by using the Feynman path integral
with the Euclidean Einstein-Hilbert action functional.

**B.Sc. Thesis, M.Sc. Thesis and Ph.D. Thesis**

The members of our informal group offer theoretical theses to students of
the University of Padova. Theses for: Laurea Triennale
(6 weeks of full-time work), Laurea Magistrale (6 months of full-time work)
e Dottorato di Ricerca (3 years of full-time work).

For MSc and PhD theses the students must
be able to understand professionally the following books:

[1]
A. Altland and B.D. Simons, Condensed Matter Field Theory
(Cambridge Univ. Press, 2010).

[2]
N. Nagaosa, Quantum Field Theory in Condensed Matter Physics
(Springer, 1999).

[3]
L. Salasnich, Quantum Physics of Light and Matter (Springer, 2017).

**Scientific Publications of the Group**

The scientific publications of Prof. Dr. Alberto Ambrosetti can be found
here

The scientific publications of Prof. Dr. Luca Dell'Anna can be found
here

The scientific publications of Prof. Dr. Pieralberto Marchetti can be found
here

The scientific publications of Prof. Dr. Luca Salasnich can be found
here

**To Contact the Staff Scientsts**:

**E-mail**:
alberto.ambrosetti@unipd.it

**E-mail**:
luca.dellanna@unipd.it

**E-mail**:
pieralberto.marchetti@unipd.it

**E-mail**:
luca.salasnich@unipd.it

**Research Grants Obtained**

240 kEuro: Project "Quantum Atomic Mixtures: Droplets, Topological Structures, and Vortices" (2023-2024). National Coordinator: L. Salasnich. Research Groups: UNIPD (L. Salasnich and F. Ancilotto), CNR-INO (A. Burchianti, C. Fort, and F. Minardi), and UNIPR (S. Wimberger). From MUR (progetti PRIN 2022).

60 kEuro: Project "Ultracold atoms in curved geometries" (2022-2023). Research group: L. Salasnich (principal investigator) and K. Furutani, from University of Padova (progetti BIRD).

20 kEuro: Project "Time-dependent density functional theory of quantum atomic mixtures" (2019-2020). Research group: F. Ancilotto (principal investigator), L. Salasnich, and L. Dell'Anna, from University of Padova (progetti BIRD).

48 kEuro: Project "Static and dynamical properties of quantum gases in reduced dimensions" (2018-2019), to hire a junior postdoc. Research group: L. Salasnich (principal investigator), from Department of Physics and Astronomy "Galileo Galilei" (progetti per assegni dipartimentali).

3 kEuro: Individual grant "Fondo per il finanziamento delle attivita base di ricerca" (FFABR, 2017) to Luca Salasnich, from Italian Ministry of Education, University and Research (MIUR).

70 kEuro: Project "Superfluid properties of Fermi gases in optical potentials" (2016-2017). Research group: L. Dell'Anna (principal investigator), L. Salasnich, F. Ancilotto, and P. Silvestrelli, from University of Padova (progetti BIRD).

45 kEuro: Project "TF Model: teacher, peer and service tutoring for university students empowerment" (2015-2016). Research group: C. Biasin (principal investigator), L. Salasnich, A. Carnera, O. Pantano, and others, from University of Padova (progetti BIRD).

47 kEuro: Project "Spin-orbit coupling in two-dimensional ultracold fermionic gases" (2015-2016), to hire a junior postdoc. Research group: L. Salasnich (principal investigator) and G. Mazzarella, from University of Padova (progetti assegni junior).

87 kEuro: PRIN Project 2010LLKJBX "Collective Quantum Phenomena: from Strongly-Correlated Systems to Quantum Simulators" (2013-2015), National coordinator: G. Casati [total grant: 968.1 kEuro]. Padova research group of the PRIN Project: F. Toigo (local coordinator, until 30-09-2015), L. Salasnich (local coordinator, from 01-10-2015 to 31-01-2016), P.A. Marchetti, L. Dell'Anna, and G. Mazzarella. Financed by Ministero Istruzione Universita e Ricerca.

75 kEuro: Project "Macroscopic Quantum Properties of Ultracold Atoms under Optical Confinement" (2012-2014). Research group of the project: L. Salasnich (principal investigator), F. Toigo and L. Dell'Anna from Fondazione CARIPARO.

61.2 kEuro: Project "Quantum Information with Ultracold Atoms in Optical Lattices" (2012-2014). Research group: L. Salasnich (principal investigator), P.A. Marchetti, L. Dell'Anna, G. Mazzarella, from University of Padova.

2 kEuro: Research Grant "Top CNR Researchers of year 2005" to Luca Salasnich from Consiglio Nazionale delle Ricerche (CNR), October 2009.

76 kEuro: Project "Guided solitons in matter waves and optical waves with normal and anomalous dispersion" (2007-2009). Research group: F. Toigo (principal investigator), L. Salasnich, and F. Ancilotto, from Fondazione CARIPARO.

1 kEuro: Project "Matter-wave solitons in optical lattices" (2007-2008), from GNFM-INdAM. Research group: L. Salasnich (principal investigator).

**Organized workshops and events**

Minicolloquium Quantum gases as analogues of condensed matter systems at the CMD30-FisMat2023 Joint Conference, September 4-8, 2023, Milano (Italy).

International Conference Superstripes 2023: Quantum Complex Matter and Quantum Technology, Ischia, June 26 - July 1, 2023.

SuperFluctuations 2022 - International Conference, July 6-8, 2022, Padova (Italy).

SuperFluctuations 2021 - International Online Conference, June 14-16, 2020, Camerino-Padova (Italy).

SuperFluctuations 2020 - International Online Conference, June 22-23, 2020, Camerino-Padova (Italy).

Spring Online Workshop "Ultracold Quantum Matter", June 4, 2020, University of Padova (Italy).

SuperFluctuations 2019 - International Conference, September 2-4, 2019, Padova (Italy).

SuperFluctuations 2018 - International Conference on "Fluctuations and Highly Non Linear Phenomena in Superfluids and Superconductors", September 5-7, 2018, San Benedetto del Tronto (Italy).

SuperFluctuations 2017 - International Conference on "Fluctuations and Highly Non Linear Phenomena in Superfluids and Superconductors", September 6-8, 2017, San Benedetto del Tronto (Italy).

Focus Workshop on Long Range Interactions with Ultracold Atoms, September 21-22, 2016, International Institute of Physics, Natal (Brazil).

Winter Workshop on Ultracold Quantum Matter, January 11, 2016, Department of Physics and Astronomy "Galileo Galilei", University of Padova.

Novel Developments in Classical and Quantum Systems, June 4-5 2015, at the Botanical Garden, University of Padova. Padua Journal Club of Condensed Matter Theory, October-December 2013, at the Department of Physics and Astronomy "Galileo Galilei", University of Padova.

Third Padua Symposium on Correlations in Ultracold Atomic Systems, September 26-27 2013, at the Department of Physics and Astronomy "Galileo Galilei", University of Padova.

Second Padua Symposium on Nonlinear Phenomena and Correlations in Ultracold Atomic Gases, 18 September 2009, at the Department of Physics "Galileo Galilei", University of Padova.

Padua Symposium on Nonlinear Phenomena and Correlations in Ultracold Atomic Gases, 19 September 2008, at the Department of Physics "Galileo Galilei", University of Padua.

**FURTHER DETAILS ABOUT OUR THEORETICAL RESEARCH TECHNIQUES**

In our research activity we study the quantum statistical mechanics of identical bosons by using the formalism of functional integration for the bosonic field. We derive the equation of state of non-interacting and weakly-interacting bosons taking into account beyond-mean-field regularized Gaussian fluctuations. We analyze various properties of the mean-field time-dependent Gross-Pitaevskii equation. In particular this equation is equivalent to the zero-temperature equations of superfluid hydrodynamics proposed in 1949 by Landau. We investigate topological and solitonic solutions of the Gross-Pitaevskii equation.

We study the quantum statistical mechanics of identical fermions by using the formalism of functional integration for the fermionic field. We derive the equation of state of non-interacting and weakly-interacting repulsive fermions. We discuss the paring of electrons within the mean-field Bardeen-Cooper-Schrieffer (BCS) theory of low-temperature superconductivity and the Ginzburg-Landau theory, which is quite successful near the critical temperature. The BCS theory is extended to investigate the BCS-BEC crossover of ultracold atoms from the weak-coupling BCS regime of Cooper pairs to the strong-coupling regime where composite bosons form giving rise to Bose-Einstein condensation (BEC) of molecules.

We adopt on the quantization of electromagnetic waves, i.e. the light (visible or invisible to human eyes), within the so-called second quantization of the light field. In this framework the electromagnetic field can be expressed as a infinite sum of harmonic oscillators. These oscillators, which describe the possible frequencies of the radiation field, are quantized by introducing creation and annihilation operators acting on the Fock space of number representation. We study the Fock states of the radiation field and compare them with the coherent states. We consider two enlightening applications: the Casimir effect and the radiation field at finite temperature.

We use the formalism of the second quantization of the non-relativistic matter field, that is the Schrodinger field. Also the Schrodinger field can be expressed as a infinite sum of harmonic oscillators. These oscillators, which describe the possible eigenfrequencies of the matter field, are quantized by introducing creation and annihilation operators acting on the Fock space of number representation. Depending on the commutation rule, these ladder operators can model accurately bosonic and fermionic particles which interact among themselves or with the quantum electromagnetic field. The second quantization (also called quantum field theory) is the powerful tool to describe phenomena, both at zero and finite temperature, where the number of particles is not conserved or it is conserved only on the average.