**Advanced quantum and statistical methods,**

**with applications in the construction of ultra-sensitive devices**

**(proiect incheiat)**

Project PN-II-ID-PCE-2011-3-0960 (115/2011), financed by the National Authority of Scientific Research, UEFISCDI.

Research team: Dr. Dragos-Victor Anghel (P.I.), Dr. Sergiu Cojocaru, Dr. Alexandru-George Nemnes, Ms. Irina Mihaela Dumitru (MSc student)

**Objectives**

The project is focused on the theoretical description of the physical properties of mesoscopic systems. These mesoscopic systems are nanoscopic devices (like the detector on the right) or components of such devices. Therefore we develop theoretical tools for the description of thermal and transport phenomena that take place in mesoscopic membranes, films, layered structures, bridges, and quasi 1D constrictions.

Our research plan can be roughly divided into *three sub-projects*.

*The first* sub-project will focus on the electron system and their interactions with phonons, disorder, and photons. Heat and electrical transport by electrons, as well as the noise, will be studied. The electrons subsystem is maybe the most important, since it is the one which determines the response of the detector and its figures of merit (Appl. Phys. Lett. **78**, 556, 2001, J. Low Temp. Phys. **123**, 197, 2001, Appl. Phys. Lett. **82**, 293, 2003).

*The second* sub-project will deal mainly with the elastic properties, acoustic waves and phonon modes in the system. The heat transport properties and thermal properties due to phonons, of mesoscopic plates, bridges and quasi 1D wires, will also be investigated here, starting from our previous works (Phys. Rev. Lett. 81, 2958, 1998, Phys. Rev. B **59**, 9854, 1999, Phys. Rev. B **70**, 125425, 2004, J. Phys. A: Math. Theor. **40**, 10429, 2007, Phys. Rev. B **76**, 165425, 2007).

*The third* sub-project is related to the disorder of the system. The detector is built of amorphous materials (both the membrane and the metallic leads) and the disorder will be described as an ensemble of two-level systems (TLS). We shall employ the model introduced in Phys. Rev. B **75**, 064202 (2007) to describe the TLSs and their interaction with the phonons, photons and electrons (see also EPL **83**, 56004, 2008, Phys. Rev. B **78**, 094202, 2008, Rom. J. Phys. **54**, 65, 2009, Rom. J. Phys. **55**, 903, 2010). Beside this, we shall investigate in general the properties of two-level systems in the standard tunneling model (STM) by building more detailed microscopic models and we shall introduce more advanced models for the description of the glassy properties of mesoscopic systems.

**Method and approach**

For a detector of electromagnetic radiation, like the one presented in the figure, the electron gas is maybe the most important subsystem because it forms the *thermal sensing element* (TSE). Therefore special attention should be paid to its modeling. Novel statistical mechanics techniques will be applied for this. We have shown recently (* *Phys. Lett. A

**372**, 5745, 2008, Phys. Lett. A

**376**, 892, 2012, Phys. Scr. 2012, 014079, 2012) that interacting particles in mesoscopic system may not obey the typical Bose and Fermi statistics, but they may be described by a generalization of this, called the fractional exclusion statistics (FES) (Phys. Rev. Lett.

**67**, 937, 1991). The general description of interacting particle systems as ideal FES gases was enables by some amendments of the FES fromalism, introduced in EPL

**87**, 60009 (2009) and discussed further in EPL

**90**, 10006 (2010). We proposed a stochastic method for simulating the time evolution of such a system in J. Stat. Mech. P09011 (2010). We shall extend this method to describe the thermodynamics of more general FES systems as well as the heat and particle transport through quasi 1D wires (EPL

**94**, 60004, 2011, J. Phys.: Conf. Ser.

**338,**012002, 2012).

We describe the electron-phonon interaction in membranes and layered structures, using the specific form of the phonon modes calculated for these structures. Using these results, we shall be able to calculate the noise and dissipation in nanoscopic detectors. We will also model the electrons systems in the electrically conducting leads and their interaction with the phonons. The study of electron-phonon interaction for this kind of structures is expected to lead to interesting results.

At working temperature, the thicknesses of the components of the detectors are smaller than both the dominant phonon wavelength and the phonon’s mean free path. Therefore a 3D phonon gas model, consisting of simple longitudinally and transversely polarized phonon modes with linear dispersions does not apply here. The vibrations of such systems are linear superpositions of longitudinal and transversal waves, which have strong nonlinear dispersion relations. Moreover, the detector is a complicated layered structure, composed of different materials, with different electric, acoustic and electromagnetic properties (see the figure above). The structure may be cut, so there are constrictions or bridges. Finally, the whole system is connected to the bulk. The surfaces of the detectors are not perfectly specular and especially the edges may be quite rough, due to the cutting process. Therefore, during this project, we shall identify the key constituents of the device, find their phonon modes and dispersion relations – eventually by solving numerically the equations of elasticity – and then assemble these elements to describe the whole system. Heat propagation along membranes of non-constant thickness is an important problem for mesoscopic devices that will be addressed in this project. The calculations will be done for the concrete elements and materials used in the experiments.

**Previous reports:**

Report 2015 (part 1 and part 2)

**Publications related to the project**

**S. Cojocaru**, Temperature dependence of magnetization of a nanosize Heisenberg ferromagnet, Opt. and Adv. Mat. – Rap. Comm. 5, 1196 (2011).**D. V. Anghel**,*Universal features in the thermodynamics and heat transport by particles of any statistics*, J. Phys.: Conf. Ser.**338,**012002 (2012)**D. V. Anghel**,**A.S. Parvan**,**A.S. Khvorostukhin**,*Fractional exclusion statistics applied to relativistic nuclear matter*, Physica A 391, 2313 (2012).**D. V. Anghel**,*Fractional exclusion statistics -- the method to describe interacting particle systems as ideal gases*, Phys. Scr. 2012, 014079 (2012).**S. Cojocaru**,**L. A. Dohotaru**, and**V. A. Moskalenko**,*Shape anisotropy and magnetization of ferromagnetic nanostructures*, J. Nano- and Optoelectronics**7**, 719 (2012).**S. Cojocaru**,*Effect of boundary conditions on magnetization of a nano-size ferromagnet*, Rom. Rep. Phys. 64, 1207 (2012).**S. Cojocaru**,*Phenomenologic versus microscopic description of the nanoparticle magnetization*, Proc. of the MSCMP, Chisinau, R. Moldova, ISBN: 978-9975-66-290-6, p. 38 (2012).**G.A. Nemnes**and**S. Antohe**,*Spin filtering in graphene nanoribbons with Mn-doped boron nitride inclusions*, Mater. Sci. Eng. B**178**, 1347 (2013).**S. Cojocaru**,*Contrasting behavior of free-standing and embedded magnetic nanoparticles*, Rom. Rep. Phys.**65**, 832 (2013).- S. Cojocaru, L.A. Dohotaru, V.A. Moscalenco, Phenomenologic versus microscopic description of the nanoparticle magnetization, Rom. J. Phys.
**58**, 955 (2013). **G.A. Nemnes**,*Spin filtering effects in wurtzite and graphite-like AlN nanowires with Mn impurities*, Journal of Nanomaterials 408475 (2013).**G.A. Nemnes**and**D.V. Anghel**,*Fractional exclusion statistics in systems with localized states*, J. Phys.: Conf. Series 410, 012120 (2013).**Dragos-Victor Anghel**,**George Alexandru Nemnes**,**Francesca Gulminelli**,*Equivalence between fractional exclusion statistics and self-consistent mean-field theory in interacting-particle systems in any number of dimensions*, Phys. Rev. E 88, 042150 (2013).**D. V. Anghel**and**D. Churochkin**,*The anisotropic glassy properties of decagonal quasicrystals*, Adv. Cond. Matt. Phys. 2013, 419202 (2013).**Dragos-Victor Anghel**,*From Fractional Exclusion Statistics Back to Bose and Fermi Distributions*, Phys. Lett. A 377, 2922 (2013).**G.A. Nemnes**and**C. Visan**,*Ab initio investigation of spin-filter effects in GaN nanowires with transitional metal impurities*, Eur. Phys. J. Plus,**128**, 131 (2013).**S. Cojocaru**,**L. Dohotaru**, and**V. Moscalenco**,*The Effect of Size, Shape and Environment on Magnetic Properties of a Nanoparticle: Microscopic Model Analysis*, Proc. ICNBME-2013; International Conference on Nanotechnologies and Biomedical Engineering, ed. S. Raylean, (ASM, Chisinau) ISBN: 978-9975-62-343-8, pp. 322-325, (2013).**George Alexandru Nemnes**and**Dragos-Victor Anghel**,*Fractional exclusion statistics in non-homogeneous interacting particle systems*, Rom. Rep. Phys.**66**, 336 (2014).**S. Cojocaru**,**A. Naddeo**and**R. Citro**,*Modiffication of the Bloch Law in Ferromagnetic Nanostructures*, EPL**106**, 17001 (2014).**G. A. Nemnes**and**A. Nicolaev**,*Transport in ferrocene single molecules for terahertz applications*, Phys. Chem. Chem. Phys.**16**, 18478 (2014).**G. A. Nemnes**and**D. V. Anghel**,*GLASSY BEHAVIOR OF DISORDERED FRACTIONAL EXCLUSION STATISTICS SYSTEMS*, Rom. J. Phys.**60**, 691 (2015).**G. A. Nemnes**and**C. Visan**,*Electron transport properties of fulgide-based photochromic switches*, RSC Advances**5**, 26438 (2015).**G. A. Nemnes**and**C. Visan**,*Ab initio vibrational and thermal properties of carbon allotropes: polycyclic and rectangular networks*, Comp. Mat. Sci.**109**, 14 (2015).**A. E. Stanciu**,**G. A. Nemnes**, and**A. Manolescu**,*Thermoelectric effects in nanostructured quantum wires in the non-linear temperature regime*, Rom. J. Phys.**60**, 716 (2015).**A. A. Nila**,**G. A. Nemnes**, and**A. Manolescu**,*Ab initio investigation of optical properties in triangular graphene - boron nitride core-shell nanostructures*, Rom. J. Phys.**60**, 697 (2015).**S. Cojocaru**and**D. V. Anghel**,*Transfer of Heat Between Electrons and Phonons in Metallic Nanostructures*, International Federation for Medical and Biological Engineering Proceedings Series**55**, 21 (2015), ISBN: 978-981-287-735-2 (print) 978-981-287-736-9 (online)**D. V. Anghel**and**S. Cojocaru**,*Electron-phonon heat exchange in layered nano-systems*, Solid State Communications**227**56 (2016) (arXiv1508.05184).**S. Cojocaru**and**D. V. Anghel***Low-temperature electron-phonon heat transfer in metal films*, Phys. Rev. B**93**, 115405 (2016).**D. V. Anghel**,*The stumbling block of the Gibbs entropy: the reality of the negative absolute temperatures*, EPJ Web of Conferences**108**, 02007 (2016).**G. A. Nemnes**,**C. Visan**,**D. V. Anghel**,**A. Manolescu**,*Molecular dynamics of halogenated graphene - hexagonal boron nitride nanoribbons*, J. Phys: Conf. Ser.**738**, 012027 (2016); arXiv:1606.00725.**D. V. Anghel**and**G. A. Nemnes**,*The application of the fractional exclusion statistics to the BCS theory—A redefinition of the quasiparticle energies*, Physica A**458**, 276 (2016).**D. V. Anghel**and**G. A. Nemnes**,*The role of the chemical potential in the BCS theory*, Physica A**464**, 74 (2016); arXiv:1604.07812.**G. A. Nemnes**and**D. V. Anghel**,*A drift-diffusion model based on the fractional exclusion statistics*, J. Phys.: Conf. Ser. 738, 012006 (2016).**C. Visan**and**G. A. Nemnes**, Ab Initio Investigations of Thermoelectric Effects in Graphene - Boron Nitride Nanoribbons, EPJ Web of Conferences 108, 02045 (2016).

**Activities related to the project**

###### 2011

- 6.10-6.11.2011: Visit at the BLTP JINR-Dubna, Russia (D. V. Anghel and A. G. Nemnes)
- 1.11.2011: D. V. Anghel,
*A model for the dynamic defects in disordered materials*, seminar at the BLTP JINR-Dubna, Russia.

- 1.11.2011: D. V. Anghel,

###### 2012

- 23-25.02.2012: Visit at the University of Rhode Island (D. V. Anghel).
- 24.02.2012: D. V. Anghel,
*Fractional exclusion statistics vs. Fermi liquid theory -- a paradigm shift*, seminar at the University of Rhode Island

- 24.02.2012: D. V. Anghel,
- 26.02-4.03.2012: American Physical Society March Meeting, Boston, Massachusetts (D. V. Anghel)
- 27.02.2012: D. V. Anghel and D. Churochkin,
*Amended tunneling model to explain the anisotropy of the glassy properties of crystals and quasicrystals*, APS March Meeting 2012, Boston, Massachusetts (poster). - 2.03.2012: D. V. Anghel,
*Fractional exclusion statistics: the paradigm to describe interacting particle systems*, APS March Meeting 2012, Boston, Massachusetts (oral).

- 27.02.2012: D. V. Anghel and D. Churochkin,
- 23.04-22.05.2012: Visit at the BLTP JINR-Dubna, Russia (D. V. Anghel).
- 15.05.2012: D. V. Anghel,
*Fractional exclusion statistics vs. Fermi liquid theory - a paradigm shift*, seminar at the BLTP JINR-Dubna, Russia.

- 15.05.2012: D. V. Anghel,
- 13-16.06.2012: Visit at the Nanoscience Center, University of Jyväskylä, Finland.
- 2-5.07.2012: visit at the Laboratoire de Physique Corpusculaire de CAEN
- 3.07.2012: D. V. Anghel, Seminar
*Fractional Exclusion Statistics for Interacting Particle Systems*

- 3.07.2012: D. V. Anghel, Seminar
- 9-14.07.2012: Dubna - Nano2012 Conference (D. V. Anghel)
- 10.07.2012: D. V. Anghel,
*Fractional exclusion statistics -- the paradigm for the description of systems of interacting particles*(poster).

- 10.07.2012: D. V. Anghel,
- 16-19.07.2012: Dr.Vitalie Eremeev (Pontificia Universidad Católica de Chile) visits our group
- 19.07.2012/10:00: Dr. Vitalie Eremeev,
*Thermally generated long-lived correlations in cavity QED*(seminar in the Department of Theoretical Physics, IFIN-HH)

- 19.07.2012/10:00: Dr. Vitalie Eremeev,
- 23-27.07.2012: International Conference on Nanoscience + Technology (ICN+T2012)
- 24.07.2012: D. V. Anghel,
*The anisotropy of the glassy properties of crystals and quasicrystals explained in an amended tunneling model*(poster) - 24.07.2012: D. V. Anghel,
*Fractional exclusion statistics versus Fermi liquid theory – a paradigm shift*(poster)

- 24.07.2012: D. V. Anghel,
- 12-26.08.2012: I. Dumitru participates in The 22nd Jyväskylä Summer School
- 19.08-1.09.2012: Visit at the Nanoscience Center, University of Jyväskylä, Finland.
- 29.08.2012: D. V. Anghel, Seminar at the Nanoscience Center
*Fractional exclusion statistics -- concept and applications* - 30.08.2012: D. V. Anghel, Seminat at the Aalto University, O. V. Luonasmaa Lab,
*Fractional exclusion statistics -- concept and applications*

- 29.08.2012: D. V. Anghel, Seminar at the Nanoscience Center
*2.09-8.09.2012: D. V. Anghel and G. A. Nemnes*participate in the International Conference on Mathematical Modeling in Physical Science, Budapest, Hungary.- 6.09.2012: D. V. Anghel,
*Fractional exclusion statistics: the concept and some applications*(Invited lecture) - 6.09.2012: G. A. Nemnes,
*Fractional exclusion statistics in disordered interacting systems*(Invited lecture)

- 6.09.2012: D. V. Anghel,
- 10-15.09.2012: S. Cojocaru participates in the 6
^{th}Int. Conf. on Materials Science and Cond Matter Physics, Vadul-lui-Voda, R. Moldova- S. Cojocaru,
*Phenomenological versus microscopical description of the nanoparticle magnetization*, (oral presentation).

- S. Cojocaru,
- 21.10-11.11.2012: Visit at the BLTP JINR-Dubna, Russia (D. V. Anghel).

###### 2013

**D. V. Anghel**, I. M. Dumitru, A. G. Nemnes, D. V. Churuchkin,*Models of two-levels systems for anisotropic glassy materials*,APS March Meeting 2013, Baltimore, USA, 18-22.03.2013 (Oral).**G.A. Nemnes**and D.V Anghel,*Modeling of nanoscale transport using fractional exclusion statistics*, APS March Meeting 2013, Baltimore, USA, 18-22.03.2013 (poster).**D. V. Anghel**, visit at the Cal. State University Fullerton (25-30.03.2013).**D. V. Anghel**,*Systems of interacting particles described as ideal gases with fractional exclusion statistics*, 29.03.2013 (1 hour lecture).**D. V. Anghel**,*Amended tunneling model for mesoscopic systems and anisotropic solids*, MRS Spring Meeting, 1-5.04.2013 (Poster)**D. V. Anghel**,*Universal heat conductance in any number of dimensions*, MRS Spring Meeting, 1-5.04.2013 (Oral).**G. A. Nemnes**and D. V. Anghel,*Modeling of nanoscale transport using fractional exclusion statistics*, MRS Spring Meeting 2013, San Francisco, USA, 1-5.2013 (poster).**S. Cojocaru**and V. Moscalenco,*The Effect of Size, Shape and Environment on Magnetic Properties of a**Nanoparticle: microscopic model analysis*, 2nd International Conference on Nanotechnologies and Biomedical , Chisinau, Republic of Moldova, April 18-20, 2013 (Invited talk).**D. V. Anghel**,*Fractional exclusion statistics -- the method to describe interacting particle systems as ideal gases*, Frontiers of Quantum and Mesoscopic Thermodynamics, 29 July - 3 August 2013, Prague, Czech Republic (Invited talk)**D. V. Anghel**,*Fractional exclusion statistics--perfection is in the eye of the beholder*, New Trends in the Research of Carbon Based Nanomaterials, September 22-25, 2013, Magurele, Jud. Ilfov, Romania (oral).**D. V. Anghel**,*An introduction to fractional exclusion statistics: how to transform general interacting particle systems into ideal gases*, TIM-13, 21-24.11.2013, Timisoara, Romania (oral).**D. V. Anghel**, Visit at the BLTP JINR-Dubna, Russia (6.10-10.11.2013)

###### 2014

- D. V. Anghel, Meeting of the Network "Nano-science and Nano-technology in South Europe" (SERINA), Atena, Grecia, 11.04.2014.

D. V. Anghel si G. A. Nemnes reprezinta IFIN-HH si Facultatea de Fizica in SERINA. - G. A. Nemnes,
*Monte Carlo simulations for transport modeling using fractional exclusion statistics*, IBWAP 2014, 2-4.07.2014, (Oral). - D. V. Anghel,
*Thermal properties of nanoscopic detectors*, IBWAP 2014, 2-4.07.2014, (Poster). - Organizing the workshop Advanced many-body and statistical methods in mesoscopic systems II, September, 1 -- 5, Brasov, Romania (D. V. Anghel was one of the organizers).
- S. Cojocaru,
*A Micrscopic Description Of Surface, Size And Shape Effects On Magnetic Properties Of Nanoparticles And Nanoclusters*, Advanced many-body and statistical methods in mesoscopic systems II, September 1 - 5, 2014, Brasov, Romania (invited talk). - G. A. Nemnes,
*Monte Carlo approach to fractional exclusion statistics and applications*, Advanced many-body and statistical methods in mesoscopic systems II, September 1 - 5, 2014, Brasov, Romania (oral). - S. Cojocaru,
*Some Mechanisms Relevant For The Control Of Magnetization In Ferromagnetic Nanoparticles*, 7th International Conference on Materials Science and Condensed Matter Physics (MSCMP 2014), 16--19 September 2014, Chisinau, R.Moldova, (Invited talk). -
D. V. Anghel, five lectures on the physiscs of nanoscopic systems at the Summer School for MSc and PhD students Hydrogen, Renewable Energy, Nanotechnology Applilcations. Physics of Mesoscopic systems, Universitatea Ferdowsi, Mashhad, Iran 17-19.06.2014.

- D. V. Anghel,
*An introduction to fractional exclusion statistics: thermodynamics and transport*, Complex and Magnetic Soft Matter Systems: Physico-Mechanical Properties and Structure (CMSMS 14), 29.09-3.10.2014, Dubna, Russia, (Invited lecture). - D. V. Anghel, Visit at the BLTP JINR-Dubna, Russia (28.09-2.11.2014).

###### 2015

**S. Cojocaru**, The 3rd International Conference on Nanotechnologies and Biomedical Engineering (ICNBME-2015), September 23-26, 2015, Chisinau, Moldova (invited oral presentation).**S. Cojocaru**,*A generalization of the Bloch law for the temperature dependent magnetization of ferromagnetic nanoparticles*, Advances in Nanophysics and Nanophotonics, 31.08-2.09.2015, Magurele, Romania (invited oral presentation).**D. V. Anghel**and**G. A. Nemnes**,*The BCS theory in the fractional exclusion statistics formalism*, Frontiers of Quantum and Mesoscopic Thermodynamics, 27 July - 1 August 2015, Prague, Czech Republic (invited oral presentation).**D. V. Anghel**and**S. Cojocaru**,*Electron-phonon heat exchange in the layered structure of nanodetectors*, Advances in Nanophysics and Nanophotonics, 31.08-2.09.2015, Magurele, Romania (invited oral presentation).**G. A. Nemnes**and**C. Visan**,*Ab initio investigations of spin transport and thermo-electric effects in graphene - boron nitride nanoribbons*, Mathematical Modeling and Computational Physics 2015, 13-17.07.2015, Stara Lesna, Slovacia (oral presentation).**D. V. Anghel**,*Gibbs vs Boltzmann statistics and the controversy about negative temperatures*, Mathematical Modeling and Computational Physics 2015, 13-17.07.2015, Stara Lesna, Slovacia (oral presentation).- Eds.
**D. Delion**,**D. V. Anghel**,**I. Ghiu**, and**S. Paraoanu**, Proceedings of the second edition of "Advanced many-body and statistical methods in mesoscopic systems", September 1-5, 2014, Brasov, Romania.

###### 2016

**S. Cojocaru**, Electron-Phonon Coupling and Heat Transfer in Layered Nanostructures at Low Temperatures, 4th Annual International Conference on Physics, 18-21 July 2016, Athens, Greece, p.12 (2016) (Invited talk).**S. Cojocaru**, Electron-Phonon Coupling In Layered Nanostructures at Low Temperatures, 8th International Conference On Materials Science and Condensed Matter Physics, September 12-16, 2016, Chisinau, Moldova, 2016 (Invited talk).**G. A. Nemnes**and D. V. Anghel, A drift-diffusion model based on the fractional exclusion statistics, International Conference on Mathematical Modeling in Physical Sciences, IC-MSQUARE 2016, Athens, 23 - 27 May 2016 (oral).**G. A. Nemnes**, Camelia Visan, D. V. Anghel and A. Manolescu, Molecular dynamics of halogenated graphene - hexagonal boron nitride nanoribbons, International Conference on Mathematical Modeling in Physical Sciences, IC-MSQUARE 2016, Athens, 23 - 27 May 2016 (Poster).**D. V. Anghel**and G. A, Nemnes, The Application of the Fractional Exclusion Statistics to the BCS Theory--a Redefinition of the Quasiparticle Energies, 5th International Conference on Superconductivity and Magnetism, 24-30.04.2016, Fethiye, Turkey (Oral).**D. V. Anghel**and S. Cojocaru, Electron-phonon heat exchange in layered nanostructures, 18th International Conference MATERIALS, METHODS & TECHNOLOGIES, 2630 June 2016, Elenite, Bulgaria (Oral).**D. V. Anghel**and S. Cojocaru, ELECTRON-PHONON INTERACTION IN NANOSTRUCTURES AT SUB-KELVIN TEMPERATURES, 16th INTERNATIONAL BALKAN WORKSHOP on APPLIED PHYSICS, 7-9.07.2016, Constanta, Romania (Oral).