Analog quantum simulation of gravitational waves in a Bose-Einstein condensate

We show how to vary the physical properties of a Bose-Einstein condensate (BEC) in order to mimic an effective gravitational-wave spacetime. In particular, we focus in the simulation of the recently discovered creation of particles by real spacetime distortion in box-type traps. We show that, by modulating the speed of sound in the BEC, the phonons experience the effects of a simulated spacetime ripple with experimentally amenable parameters. These results will inform the experimental programme of gravitational wave astronomy with cold atoms.Comment: 9 pages. I. F. previously published as I. Fuentes-Guridi and I.Fuentes-Schuller. v2: minor changes, references adde

Analogue simulation of gravitational waves in a 3+1 -dimensional Bose-Einstein condensate

The recent detections of gravitational waves (GWs) by the LIGO and Virgo collaborations have opened the field of GW astronomy, intensifying interest in GWs and other possible detectors sensitive in different frequency ranges. Although strong GW producing events are rare and currently unpredictable, GWs can in principle be simulated in analogue systems at will in the lab. Simulation of GWs in a manifestly quantum system would allow for the study of the interaction of quantum phenomena with GWs. Such predicted interaction is exploited in a recently proposed Bose-Einstein condensate (BEC) based GW detector. In this paper, we show how to manipulate a BEC to mimic the effect of a passing GW. By simultaneously varying the external potential applied to the BEC, and an external magnetic field near a Feshbach resonance, we show that the resulting change in speed of sound can directly reproduce a GW metric. We also show how to simulate a metric used in the recently proposed BEC based GW detector, to provide an environment for testing the proposed metrology scheme of the detector. Explicit expressions for simulations of various GW sources are given. This result is also useful to generally test the interaction of quantum phenomena with GWs in a curved spacetime analogue experiment

Implementación de un plan de marketing digital en la empresa DMB Gráfica E. I. R. L., en la ciudad de Lima en el año 2023

El presente Trabajo de Suficiencia Profesional tiene como objetivo general la implementación de un plan de marketing digital en la empresa DMB Gráfica E.I.R.L. en la ciudad de Lima, en el año 2023. Dentro de los objetivos específicos se consideraron realizar el diagnóstico del marketing digital, la implementación en sí del marketing digital y finalmente la gestión eficiente y eficaz del marketing digital implementado. Se empleó para el diagnóstico la matriz FODA, el Análisis PESTEL, el Análisis de las 5 Fuerzas de Porter, el Diagrama causa – efecto de Ishikawa y el Análisis AMOFHIT. El plan de marketing digital estuvo conformado por el análisis situacional interno y externo, el diagnóstico organizacional, los objetivos y estrategias referidas a la página web, redes sociales, WhatsApp, publicidad digital en el mercado meta. La gestión eficiente y eficaz del marketing digital fue expuesta con los resultados obtenidos según los objetivos del del trabajo de suficiencia profesional. Se concluye que se ha implementado el marketing digital en DMB Gráfica E.I.R.L. y se han establecido los objetivos y estrategias para gestionarlo efectivamente.The present Professional Sufficiency Work has as general objective the implementation of a digital marketing plan in the company DMB Gráfica E.I.R.L. in the city of Lima, in the year 2023. Within the specific objectives, it was considered to carry out the diagnosis of digital marketing, the implementation of digital marketing itself and finally the efficient and effective management of the implemented digital marketing. The SWOT matrix, the PESTEL Analysis, the Porter's 5 Forces Analysis, the Ishikawa Cause-Effect Diagram and the AMOFHIT Analysis were used for the diagnosis. The digital marketing plan was made up of the internal and external situational analysis, the organizational diagnosis, the objectives and strategies related to the website, social networks, WhatsApp, digital advertising in the target market. The efficient and effective management of digital marketing was exposed with the results obtained according to the objectives of the work of professional sufficiency. It is concluded that digital marketing has been implemented in DMB Gráfica E.I.R.L. and objectives and strategies have been established to manage it effectively

Planeamiento estratégico para sociedad minera El Brocal S.A.A.

Sociedad Minera El Brocal es una empresa minera dedicada a la extracción, concentración y comercialización de minerales polimetálicos como la plata, el plomo, el zinc y el cobre. La empresa realiza sus operaciones en las unidades mineras de Colquijirca y la Planta Concentradora de Huaraucaca, localizadas en el distrito de Tinyahuarco, provincia de Pasco, región de Pasco, Perú. Sus oficinas administrativas están localizadas en el distrito de San Isidro, en la ciudad de Lima, Perú. La competitividad en la industria minera se caracteriza por la habilidad de los operadores de producir concentrados o metal a bajo costo, debido a que las empresas no tienen capacidad de influir en los precios de venta. En ese sentido, El Brocal cuenta con ventajas competitivas significativas, como es el ser titular de importantes yacimientos mineros, tener acceso a infraestructura (energía, transporte, etc.), y contar con mano de obra calificada, entre otras. Gran parte de sus esfuerzos y recursos económicos priorizan la culminación de la Planta 2, con una capacidad de producción de 11 mil TMS, que se complementa con la producción de la Planta 1, que es de 7 mil TMS. Juntas producirán un total de 18 mil TMS. Se propone que la visión se plantee en un horizonte de 15 años, al 2030, por la naturaleza del sector minero, y contempla la explotación del mineral, según la demanda del mercado nacional e internacional aprovechando la mayor rentabilidad del mismo, lo que garantizará las operaciones de “El Brocal”, comprometidos con el cuidado el medio ambiente y la responsabilidad social. El crecimiento de El Brocal se evidenciará con el incremento de su producción de concentrados de mineral, incrementará sus exploraciones mineras para garantizar su sostenibilidad en el tiempo, asimismo con el uso de la tecnología y la capacitación permanente de sus colaboradores contribuirá a reducir los costos operativos.Sociedad Minera El Brocal (Mining Company El Brocal) is a mining company that performs the extraction, concentration and commercialization of polymetallic ores: silver, lead, zinc and copper. The company operates at Colquijirca Mining Units and Huaraucaca Concentrating Plant, located in Tinyahuarco district, province of Pasco, department and region of Pasco, Peru. The administrative offices are located in San Isidro district, in Lima, Peru. Competitiveness at the mining industry is characterized by operators being able to produce low price concentrates or ores, due to the fact that companies do not have the availability to influence on the selling price. In that sense, El Brocal has a lot of significant advantages as the following: it is entitled at important mine sites, it has access to infrastructure (energy, transportation, etc.) and it has a qualified labor, among others. A big part of its effort and economic resources prioritize the culmination of Plant 2, whose production capacity is of eleven thousand DMT, which complements Plant 1 production of seven thousand DMT. Together they will produce a total of eighteen thousand DMT. It is proposed that the vision is set in a future of 15 years because of the nature of the mining sector, to the year 2030, and it considers the ore exploitation according to the national and international market demand, taking advantage of its highest sustainability, which will guarantee that “El Brocal” committed to caring for the environment and social responsibility. El Brocal growth will be evidenced by the increase of its ore concentrate production; its mining explorations will increase in order to guarantee its sustainability among time, as well as operation costs will decrease with the use of technology and permanent training of collaborators.Tesi

Frequency spectrum of an optical resonator in a curved spacetime

The effect of gravity and proper acceleration on the frequency spectrum of an optical resonator—both rigid or deformable—is considered in the framework of general relativity. The optical resonator is modeled either as a rod of matter connecting two mirrors or as a dielectric rod whose ends function as mirrors. Explicit expressions for the frequency spectrum are derived for the case that it is only perturbed slightly and variations are slow enough to avoid any elastic resonances of the rod. For a deformable resonator, the perturbation of the frequency spectrum depends on the speed of sound in the rod supporting the mirrors. A connection is found to a relativistic concept of rigidity when the speed of sound approaches the speed of light. In contrast, the corresponding result for the assumption of Born rigidity is recovered when the speed of sound becomes infinite. The results presented in this article can be used as the basis for the description of optical and opto-mechanical systems in a curved spacetime. We apply our results to the examples of a uniformly accelerating resonator and an optical resonator in the gravitational field of a small moving sphere. To exemplify the applicability of our approach beyond the framework of linearized gravity, we consider the fictitious situation of an optical resonator falling into a black hole

Gravitational time dilation in extended quantum systems: The case of light clocks in Schwarzschild spacetime

The precision of optical atomic clocks is approaching a regime where they resolve gravitational time dilation on smaller scales than their own extensions. Hence, an accurate description of quantum clocks has to take their spatial extension into account. In this article, as a first step toward a fully relativistic description of extended quantum clocks, we investigate a quantized version of Einstein's light clock fixed at a constant distance from a large massive object like the Earth. The model consists of a quantum light field in a one-dimensional cavity in Schwarzschild spacetime, where the distance between the mirrors is fixed by a rigid rod. By comparing a vertical and a horizontal clock, we propose an operational way to define the clock time when the clock resolves gravitational time dilation on scales smaller than its extension. In particular, we show that the time measured by the vertical light clock is equivalent to the proper time defined at its center. We also derive fundamental bounds on the precision of these clocks for measurements of proper time and the Schwarzschild radius

Phononic gravity gradiometry with Bose-Einstein condensates

Gravity gradiometry with Bose-Einstein condensates (BECs) has reached unprecedented precisions. The basis of this technique is the measurement of differential forces by interference of single-atom wave functions. In this article, we propose a gradiometry scheme where phonons, the collective oscillations of a trapped BEC's atoms are used instead. We show that our scheme could, in principle, enable high-precision measurements of gravity gradients of bodies such as the Earth or small spheres with masses down to the milligram scale. The fundamental error bound of our gravity gradiometry scheme corresponds to a differential force sensitivity in the nano-gal range per experimental realization on the length scale of the BEC

Frequency spectrum of an optical resonator in a curved spacetime

The effect of gravity and proper acceleration on the frequency spectrum of an optical resonator—both rigid or deformable—is considered in the framework of general relativity. The optical resonator is modeled either as a rod of matter connecting two mirrors or as a dielectric rod whose ends function as mirrors. Explicit expressions for the frequency spectrum are derived for the case that it is only perturbed slightly and variations are slow enough to avoid any elastic resonances of the rod. For a deformable resonator, the perturbation of the frequency spectrum depends on the speed of sound in the rod supporting the mirrors. A connection is found to a relativistic concept of rigidity when the speed of sound approaches the speed of light. In contrast, the corresponding result for the assumption of Born rigidity is recovered when the speed of sound becomes infinite. The results presented in this article can be used as the basis for the description of optical and opto-mechanical systems in a curved spacetime. We apply our results to the examples of a uniformly accelerating resonator and an optical resonator in the gravitational field of a small moving sphere. To exemplify the applicability of our approach beyond the framework of linearized gravity, we consider the fictitious situation of an optical resonator falling into a black hole.© 2018 The Author(s