BGU Physics Department

Two seemingly distinct systems are analyzed and, somewhat unexpectedly, shown to be related.

System I - Electron in the field of a magnetic monopole: The problem is to find the states of a (spinless) electron moving on a sphere and subject to a CENTRAL magnetic field B emanating from a magnetic charge g. As was shown by Dirac in 1931 [see also Wu and Yang, Phys. Rev. D 12, 3845 (1975)] the (so far elusive) magnetic charge g and the electric charge e are related by the quantization condition 2eg = nc (n = 1, 2 . . . is the monopole number). In the continuum version the problem was solved in 1931 by Igor Tamm. I approach this problem from a "condensed matter point of view" using a tight binding model. The energy spectrum is calculated analytically as function of n and displays a beautiful pattern, which is entirely distinct from that of the Hofstadter butterfly. The systematics of level degeneracy is unusual and its analysis requires the construction of a theory of magnetic point symmetry groups. The spectrum of an electron hopping on the sites of a Fullerene reveals a set of magic (monopole) numbers.

System II - Electron in the field of a central charge: Spin-Orbit effects: The problem is to find the states of a (spinfull) electron moving on a sphere subject to a central electric field E emanating from an electric charge q. In a continuum geometry, spin-orbit interaction results i the familiar L·S coupling that affects atomic spectra. In a tight binding formalism, on the other hand, it leads to peculiar Aharonov-Casher effect, and the spectrum (calculated analytically) displays rich and beautiful pattern with some unexpected symmetries in which physics and geometry interlace.

Connection between I and II: I expose a remarkable relation between the two seemingly distinct physical problems: The energy spectrum in system II at a certain symmetry point is identical with the energy spectrum in system I at n = 1. Thus, it is principally possible to test the physics of an experimentally inaccessible system (magnetic monopole) in terms of an experimentally accessible one (electron subject to spin-orbit force induced by central electric field).

There are two main comparable sources of the energy of the deep ocean--winds and tides. There are various mechanisms for the indirect transformation of surface winds into the deep ocean. Here we show, using oceanic GCM, that the wind directly supply energy down to the bottom of the ocean when it is stochastic or when it is periodic with a frequency that is equal to the Coriolis frequency. Basically, under such conditions one of the wind components resonates with the Coriolis frequency. Using the finite depth Ekman layer model we show that when the wind stress is purely periodic with a frequency that is equal to the Coriolis frequency, the surface current speed is proportional to the depth of the ocean, the current speed decreases linearly with depth, and the total kinetic energy is proportional to the cube of the depth of the ocean. When the wind stress is stochastic the second moment of the surface current speed increases logarithmically as a function of depth, the current speed decreases linearly with depth in the deep ocean, and the total kinetic energy is proportional to the depth of the ocean. Our results suggest that (i) the wind contribution to the energy of the deep ocean may be significantly larger than that of tides and that (ii) the seminal, infinitely deep, depth depended Ekman layer model is ill defined when forced by stochastic wind (or periodic wind with a frequency that is equal to the Coriolis frequency) unless a friction term is added.

At 1997, Steven Chu, Claude Cohen-Tannoudji and William D. Phillips received the Nobel prize for their developments of methods to cool and trap atoms with laser light.

Since then, laser cooling and trapping of atoms have played an important role in achieving exotic phases of matter (i.e. the Bose-Einstein condensation, a form of matter where all the atoms are in the lowest possible energy state.)

Today, cold atoms in an optical lattice are routinely used as a Feynman-type 'analog quantum computer' for simulating complex quantum systems.

In this lecture I will give a short, nontechnical introduction to the exciting field of laser cooling and trapping and shall review some of it's modern applications.

Desertification, or vegetation degradation, is a major environmental problem. While much effort is focused on unraveling desertification mechanisms and devising warning signals for imminent desertification, little is known about reversing desertification once it has occurred. In this talk I will discuss vegetation restoration as a spatial resonance problem, drawing analogies from periodically forced oscillators. Methods of vegetation restoration involve periodic ground modulations, such as embankments or biological-crust removal, that capture runoff and along which the vegetation is planted. Using mathematical modeling and model analysis I will show that the common restoration practice - continuous vegetation plantation along the ground modulations to form stripe patterns, suffers from poor resilience to droughts and may result in total vegetation mortality and ecosystem collapse. By contrast, a fragmented plantation to form rhombic patterns is far more resilient and less costly.

פיסיקה לא-ליניארית עוסקת בדינמיקה של מערכות מורכבות שרחוקות משיווי משקל תרמודינמי. חוקרים בתחום זה מנסים לפשט מערכות מורכבות ולנבא התפתחויות בזמן ובמרחב, לדוגמא תורת הכאוס. מכיוון שרבות מהבעיות ביולוגיות, כימיות ,פיזיקליות, ואקולוגיות מכילות דרגות חופש ואינטרקציות רבות, יש לפיזיקה לא-ליניארית תפקיד דומיננטי בפיתוח הבנה בסיסית למודלים שדרושה לעולם הניסויי. בהרצאה, אמחיש בקצרה את העקרונות של דינמיקה לא ליניארית ואעמוד על טיבם של חלק מהמחקרים שנעשים בקבוצה שלנו, בתחום אגירת אנרגיה (כפיצול מים ליצירת דלק מימני) והרפואה (מערכת השמיעה

Real time observation and control of motion of electrons in atoms, molecules and nanostructures has been the holy grail of experimental science for many decades.
Developing the ability to monitor and steer electrons at subatomic resolution at their natural (attosecond) time scale bears the promise of revolutionary advances not only in physics, but also in chemistry, life sciences and the technologies of the future.
In my talk, I will introduce the key concepts of attosecond science, present the state-of-the art in the field, and discuss possible future directions and implications.

In the Stern–Gerlach effect, a magnetic field gradient splits particles into spatially separated paths according to their spin projection. The idea of exploiting this effect for creating coherent momentum superpositions for matter-wave interferometry appeared shortly after its discovery, almost a century ago, but was judged to be far beyond practical reach. Here we demonstrate a viable version of this idea [1]. Our scheme uses pulsed magnetic field gradients, generated by currents in an atom chip wire, and radio-frequency Rabi transitions between Zeeman sublevels. We transform an atomic Bose–Einstein condensate into a superposition of spatially separated propagating wavepackets and observe spatial interference fringes with a measurable phase repeatability. The method is versatile in its range of momentum transfer and the different available splitting geometries. These features make our method a good candidate for supporting a variety of future applications and fundamental studies.

[1] S. Machluf, Y. Japha, and R. Folman, Nat. Commun. 4, 1 (2013).

Entrainment to periodic forcing is frequently used and observed in oscillatory systems and pertains to various physical, chemical and biological applications. The periodic forcing however can be of two types: parametric or additive, i.e., impact in an active or passive fashion on the oscillatory behavior of the system, respectively. Yet, solely from experimental observations, the type of forcing is not always clear. An intriguing example is demonstrated by the human auditory system: inside the cochlea, the incoming sound wave results in a spatially localized response but from the experimental observations, the mechanism of the resonance is unclear. To advance the subject, we use a prototypical FitzHugh-Nagumo model and employ both parametric and additive forcing terms. Through numerical simulations and asymptotic (multiple times scale) theory, we find that for 1:1 resonance there is indeed a unique and universal signature for each one of the two types in the form of allowed phase shifts. Consequently, the results suggest a test that can help in distinguishing between the forcing mechanisms in general and in the auditory system, specifically.

In recent years, the properties of negatively charged nitrogen-vacancy centers in diamonds (NV) have been studied extensively due to their versatility; they can be used as quantum bits, highly sensitive magnetometers, single-photon sources and more. In this work, we are investigating the adiabaticity properties of the NV system; the NV's degenerate ground states, $m_s=\pm1$, can be split using an external magnetic field. The system is then prepared in a certain eigenstate, say $m_s=+1$, and we modulate the external magnetic field. If the system stayed in the same eigenstate throughout the modulation, we can say that the process is adiabatic. Different values of the external magnetic field (amplitude and frequency) control the adiabaticity of the process and for certain values, the system might completely tunnel out to another eigenstate. Using simulation and experiment, we will try to find a regime for which the process is adiabatic.

Fairy Circles are circular gaps of bare soil, puncturing the otherwise uniform perennial grass in the Namibian drylands. Their origin has been a source of controversy for the last 40 years, with various explanations ranging from poisonous gas, to feeding habits of ants, to pattern formation induced by lack of water. We propose a simple physical model for dryland vegetation, that exhibits pattern formation, to explain the reported observations.
In this talk I will shortly describe previous findings and theories, present our model and its properties, and them compare its results to field observations, highlighting dynamics operating in different time-scales in this system.

Combining superconducting qubits with mesoscopic devices that carry topological states of matter may lead to compact and improved qubit devices with properties useful for quantum computation. We introduce a hybrid device which combines a Josephson junction and a nano-wire carrying Majorana fermions. This device stores quantum information in superpositions of fermion parity states originating from the Majorana fermions, generating a highly isolated qubit whose coherence time could be greatly enhanced. We study the effect of the Majorana fermions on the quantum electrodynamics of the device embedded within an optical cavity and develop protocols to initialise, control and measure the qubit states.

I will describe two main directions in my lab: 1) DNA structure and dynamics in vitro and in vivo with super-resolution optical techniques, and 2) Reaction-diffusion dynamics in immune system.

In the first project we address a wide range of questions starting from pure polymer physics of DNA in vitro to chromatin organization and activity in vivo. To that end, we developed some original fluorescence optical tool and also adapted modern super-resolution optical techniques.

In the second project, we look at the dynamics of exchange of small signalling molecules between immune cells. Diffusion of molecules and their consumption by the cells creates localized concentration fields that affect the dynamics of the immune response. Characterizing this dynamics allows to address the basic question of immunology: how is it that our immune system works as an almost perfect - high gain/low noise - amplifier?

הקרב של יהושע בן נון נגד חמשת מלכי האמורי בעמק איילון והעמדת השמש והירח הם מהמאורעות המופלאים ורבי הרושם במקרא. במרוצת השנים ניסו פרשנים וחוקרים למצוא הסברים מציאותיים לתיאור האירוע השמיימי שנתפס כנס. ביניהן- אירוע נדיר של ליקוי חמה מלא, שהוא אירוע מרשים ביותר וסביר להניח כי הוא הותיר רושם עז אצל הצופים בו. בממוצע הסיכוי לראות ליקוי חמה מלא במקום כלשהו על פני כדור הארץ הוא אחת ל-370 שנים. השחזור של מועדי הליקוי הקדומים בעייתי וככל שהליקוי קדום יותר כן גדלה אי הוודאות בתיארוכו. עם זאת, נוסחאות מתמטיות מתקדמות ורשימת ליקויי חמה בעבר שהוכנה ע”י נאס”א, מאפשרים לשחזר את העיתוי והמסלול של ליקויי החמה בעבר בכל נקודה על פני כדור הארץ. באמצעות ניתוח מדוקדק של טקסטים מקראיים וחוץ מקראיים ופירושים חדשניים לתיאור המקראי, אנו מראים שניתן לפרש את הנס בגבעון כליקוי חמה טבעתי

Images of the natural world modified by eye movements are the actual input to the retina. Even during fixation on a single point, small movements of the eye, head, and other parts of the body continually modulate visual signals. Theoretical works predict that microscopic eye movements during fixation contribute to the efficient encoding of the natural scene by decorrelating the retinal response. Here we present the first experimental evidence of the effect.

The response of the salamander retina to natural images, in the presence and absence of fixational eye movements, has been measured. It was found that the retinal ganglion cells exhibit strong and extensive spatial correlations in the absence of fixational eye movements. Fixational eye movements substantially reduce the level of the spatial correlations, thus resulting in reduction of redundancy in the information streamed to the brain and increasing the efficiency of the retinal code.

We have experimentally confirmed, for the first time, the prediction that fixational eye movements reduce the correlations in retinal response. Our observations provide firm evidence of the contribution of fixational eye movements to the visual information processing.

A nonlinear system is a system in which the output is not directly proportional to the input. Those systems are of great interest in different disciplines in the exact sciences, as most natural systems are inherently nonlinear. Nonlinearity implies multiplicity of system states and possible transitions between them. These transitions can result in the emergence of oscillations, chaos and hysteresis, and, in spatially extended systems, in the formation of spatial patterns. Pattern formation is the emergence of visible orderly structures as outcome of self-organization. Examples of pattern formation phenomena can be found in chemistry, developmental biology, ecological systems, and physics. Pattern formation theory refer to the study of how feedbacks operating on small spatial scales give rise to a global behaviors of the systems that are manifested as the appearance of patterns. The formation of pattern can be either desirable or not. Therefore, it is important to study the different processes of pattern formation and understanding how to control them. An important application of pattern formation theory is the study of vegetation patterns in water-limited ecosystems. Vegetation pattern formation is a community-level means by which dryland ecosystems cope with water stress. Depending on the degree of water stress a variety of different patterns can emerge. Mathematical modelling and pattern formation analysis of these models can help us understanding what are the different factors that influence the productivity and resilience of ecosystems, and can be useful in devising ways to enhance the recovery of damaged ecosystems.

Ehud Strobach* and Golan Bel

*udistr@gmail.com

Climate models are often used to simulate past and future climate dynamics. They are composed of four main components that interact with each other – atmosphere, ocean, land surface and ice. A few dozens of such models were developed by different modeling groups over the world. The differences between the models are mainly associated with the different parameterizations they use (these are the effective representations of physical processes taking place over spatial and temporal scales that are not resolved by the model or processes that we have insufficient knowledge about their exact details).

On a decadal time scale, uncertainties in climate predictions can be attributed to two main sources – internal and model variability. Internal variability is the variation in the climate predictions of the same climate model initialized with different initial conditions. Model variability is the variation between the climate predictions of different climate models. The relative importance of these sources varies spatially and temporally.

Using a simple analysis, we decomposed the climate uncertainties in an ensemble of climate model predictions from a decadal experiment of the CMIP5 (Coupled Model Intercomparison Project Phase 5) project between 2006 to 2036. The relative contribution of each uncertainty source is assessed for the surface temperature and the 10m wind components. It will be shown that the importance of these sources greatly varies between the different climate variables, the seasons and the different regions on earth.

The Si(111)7 × 7 surface exposed to 0.1 L of O_2 and the carbonized Si(111) surface are investigated by electron spin resonance scanning tunneling microscopy (ESR-STM) using frequency sweeps and magnetic field sweeps.
Only after oxidizing the clean Si(111)7 × 7 or by using the carbonized Si(111), spatially averaged ESR-STM spectra exhibit several peaks and dips around the frequencies corresponding to g = 2. The energy difference between these features is close to the known hyperfine splitting of A ≅ 9 MHz for vacancies in SiC interacting with next-nearest neighbor ^29 Si. Such spectra with peaks and dips can be qualitatively reproduced by introducing a primary encounter of the lead electrons with the localized spin correlating the two spins which afterwards evolve in different local hyperfine fields, thus, developing a relative spin angle prior to tunneling. Preliminary results of the observation of the nuclear Zeeman transition of a single nuclear spin that were observed by an ENDOR type experiment will be discussed.
Results on adsorbed molecules, that were observed much faster time domain detection, will be presented.

תהליך הווצרותם של המבנים הגדולים ביקום, כגון קבוצות וצבירי גלקסיות, מלווה בהתנגשויות חזקות בין גופי-ענק המכילים בעיקר חומר אפל ופלסמה דלילה. התנגשויות מעין אלה חושפות את החומר האפל, משרות זרמים חזקים, וממגנטות את הפלסמה. בהרצאה נראה כי מודלים פשוטים לתופעה ניתנים לפתרון אנליטי, מסבירים תצפיות אסטרונומיות מסתוריות, ומגלים תופעות מפתיעות בדינמיקת הנוזלים.